Merge pull request #1 from QuantumPackage/dev-tc

Dev tc

.drone.yml

@@ -7,46 +7,46 @@ clone:
   depth: 10
 
 steps:
-
+  - name: configure debug
-- name: configure
     image: scemama666/qp2_env
     commands:
     - ./configure -i all -c ./config/gfortran_debug.cfg
     - bash -c "source quantum_package.rc ; exec qp_plugins download https://gitlab.com/scemama/qp_plugins_scemama"
     - bash -c "source quantum_package.rc ; exec qp_plugins install champ"
 
-- name: compile
+  - name: compile debug
     image: scemama666/qp2_env
     commands:
     - bash -c "source quantum_package.rc ; exec ninja"
 
-- name: testing
+  - name: testing debug
     image: scemama666/qp2_env
     commands:
     - bash -c "source quantum_package.rc ; TRAVIS=1 exec qp_test -a"
 
----
+  - name: configure fast
-kind: pipeline
-type: docker
-name: gfortran-avx
-
-clone:
-  depth: 10
-
-steps:
-
-- name: configure
     image: scemama666/qp2_env
     commands:
-  - ./configure -i all -c ./config/gfortran_avx.cfg
+    - ./configure -c ./config/gfortran_avx.cfg
 
-- name: compile
+  - name: compile fast
     image: scemama666/qp2_env
     commands:
     - bash -c "source quantum_package.rc ; exec ninja"
 
-- name: testing
+  - name: testing fast
     image: scemama666/qp2_env
     commands:
     - bash -c "source quantum_package.rc ; exec qp_test -a"
 
+  - name: notify
+    image: drillster/drone-email
+    settings:
+      host:
+        from_secret: hostname # irsamc.ups-tlse.fr
+      from:
+        from_secret: from # drone@irssv7.ups-tlse.fr
+      recipients:
+        from_secret: recipients # scemama@irsamc.ups-tlse.fr
+      when:
+        status: [changed, failure]

README.md

@@ -35,6 +35,12 @@ https://arxiv.org/abs/1902.08154
 * [Download the latest release](http://github.com/QuantumPackage/qp2/releases)
 * [Read the documentation](https://quantum-package.readthedocs.io) 
 
+# Discussion list
+
+For any questions or announcements regarding QuantumPackage, you can join our discussion list by registering [here](https://groupes.renater.fr/sympa/subscribe/quantum_package) or by sending an email to `quantum_package-request@groupes.renater.fr` .
+You can also look over its [archives](https://groupes.renater.fr/sympa/arc/quantum_package).
+
+
 # Build status
 
 * Master [![master build status](https://travis-ci.com/QuantumPackage/qp2.svg?branch=master)](https://travis-ci.org/QuantumPackage/qp2)

bin/qp_convert_output_to_ezfio

@@ -146,6 +146,17 @@ def write_ezfio(res, filename):
     ezfio.set_ao_basis_ao_nucl(at)
     ezfio.set_ao_basis_ao_prim_num(num_prim)
     ezfio.set_ao_basis_ao_power(power_x + power_y + power_z)
+    try:
+      normf = res.normf
+      if normf == 0:
+        ezfio.set_ao_basis_ao_normalized(True)
+      elif normf == 1:
+        ezfio.set_ao_basis_ao_normalized(False)
+      else:
+        print("BUG in NORMF")
+        sys.exit(0)
+    except AttributeError:
+      ezfio.set_ao_basis_ao_normalized(True)
 
     # ~#~#~#~#~#~#~ #
     # P a r s i n g #
@@ -224,7 +235,7 @@ def write_ezfio(res, filename):
           exponent += [p.expo for p in b.prim]
           ang_mom.append(str.count(s, "z"))
           shell_prim_num.append(len(b.prim))
-          shell_index += [nshell_tot+1] * len(b.prim)
+          shell_index += [nshell_tot] * len(b.prim)
 
     # ~#~#~#~#~ #
     # W r i t e #

bin/qp_set_frozen_core

@@ -11,8 +11,8 @@ Usage:
 
 Options:
     -q --query   Prints in the standard output the number of frozen MOs
-    -l --large   Use a small core
+    -l --large   Use a large core
-    -s --small   Use a large core
+    -s --small   Use a small core
     -u --unset   Unset frozen core
 
 

bin/qp_test

@@ -60,19 +60,14 @@ def main(arguments):
         print("Running tests for %s"%(bats_file))
         print("")
         if arguments["-v"]:
-            p = None
             if arguments["TEST"]:
                 test = "export TEST=%s ; "%arguments["TEST"]
             else:
                 test = ""
-            try:
             os.system(test+" python3 bats_to_sh.py "+bats_file+
                                     "| bash")
-            except:
-                if p:
-                    p.terminate()
         else:
-            subprocess.check_call(["bats", bats_file], env=os.environ)
+            subprocess.check_call(["bats", "--verbose-run", "--trace", bats_file], env=os.environ)
 
 
 

config/ifort_2019_avx.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : ifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel 
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DINTEL -DSET_NESTED
 

config/ifort_2019_avx_mpi.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : mpiifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DMPI -DINTEL -DSET_NESTED
 

config/ifort_2019_mpi_rome.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : mpiifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DINTEL -DSET_NESTED
 

config/ifort_2019_rome.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : ifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DINTEL -DSET_NESTED
 

config/ifort_2019_sse4.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : ifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DINTEL -DSET_NESTED
 

config/ifort_2019_sse4_mpi.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : mpiifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DMPI -DINTEL -DSET_NESTED
 

config/ifort_2019_xHost.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : ifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=64 -DINTEL -DSET_NESTED
 

config/ifort_2021_avx.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : ifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DINTEL 
 

config/ifort_2021_avx_mpi.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : mpiifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DMPI -DINTEL 
 

config/ifort_2021_mpi_rome.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : mpiifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DINTEL 
 

config/ifort_2021_rome.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : ifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DINTEL 
 

config/ifort_2021_sse4.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : ifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DINTEL 
 

config/ifort_2021_sse4_mpi.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : mpiifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=32 -DMPI -DINTEL 
 

config/ifort_2021_xHost.cfg

@@ -7,7 +7,7 @@
 #
 [COMMON]
 FC           : ifort -fpic
-LAPACK_LIB   : -mkl=parallel -lirc -lsvml -limf -lipps
+LAPACK_LIB   : -mkl=parallel
 IRPF90       : irpf90
 IRPF90_FLAGS : --ninja --align=64 -DINTEL 
 

configure

@@ -180,7 +180,7 @@ if [[ "${PACKAGES}.x" != ".x" ]] ; then
 fi
 
 if [[ ${PACKAGES} = all ]] ; then
-        PACKAGES="zlib ninja zeromq f77zmq gmp ocaml docopt resultsFile bats"
+        PACKAGES="zlib ninja zeromq f77zmq gmp ocaml docopt resultsFile bats bse"
 fi
 
 
@@ -281,8 +281,8 @@ EOF
 
             execute << EOF
               cd "\${QP_ROOT}"/external
-              tar -zxf qp2-dependencies/bats-v1.1.0.tar.gz
+              tar -zxf qp2-dependencies/bats-v1.7.0.tar.gz
-              ( cd bats-core-1.1.0/ ; ./install.sh \${QP_ROOT})
+              ( cd bats-core-1.7.0/ ; ./install.sh \${QP_ROOT})
 EOF
 
     else
@@ -354,12 +354,6 @@ echo "                 ||----w |     "
 echo "                 ||     ||     "
 echo "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~"
 echo ""
-echo "If you have PIP, you can install the Basis Set Exchange command-line tool:"
-echo ""
-echo "  ./configure -i bse"
-echo ""
-echo "This will enable the usage of qp_basis to install extra basis sets."
-echo ""
 echo ""
 printf "\e[m\n"
 

drone/Docker/README.md

@@ -1,8 +0,0 @@
-Docker files to build the containers used with DroneCI.
-
-Example:
-```
-docker build -t ubuntu/qp2_env .
-
-```
-

drone/Docker/Ubuntu/Dockerfile

@@ -1,27 +0,0 @@
-ARG UBUNTU_VERSION=20.04
-FROM ubuntu:${UBUNTU_VERSION} AS builder
-
-# Timezone for tzdata
-ARG tz=Etc/UTC
-RUN echo $tz > /etc/timezone && rm -rf /etc/localtime
-
-# Install
-RUN apt-get update && DEBIAN_FRONTEND=noninteractive apt-get install -y \
- git \
- curl \
- wget \
- python3 \
- gfortran \
- gcc \
- g++ \
- make \
- build-essential \
- rsync \
- unzip \
- libopenblas-dev \
- pkg-config \
- m4
-
-RUN ln -s /usr/bin/python3 /usr/bin/python
-
-

drone/compilation.sh

@@ -1,16 +0,0 @@
-#!/bin/bash
-# Stage 2
-
-# Extract cache from config stage
-cd ../
-tar -zxf $HOME/cache/config.tgz
-
-# Configure QP2
-cd qp2
-source ./quantum_package.rc
-ninja -j 1 -v || exit -1
-
-# Create cache
-cd ..
-tar -zcf $HOME/cache/compil.tgz qp2 && rm $HOME/cache/config.tgz
-

drone/configuration.sh

@@ -1,10 +0,0 @@
-#!/bin/bash
-# Stage 1
-
-# Configure QP2
-./configure --download all --install all --config ./config/travis.cfg || exit -1
-
-# Create cache
-cd ../
-tar -zcf $HOME/cache/config.tgz qp2
-

drone/drone_docker.yml

@@ -1,30 +0,0 @@
----
-kind: pipeline
-type: docker
-name: default
-
-clone:
-  depth: 10
-
-steps:
-- name: configure
-  pull: never
-  image: ubuntu/qp2_env
-  commands:
-  - ./configure -i all -c ./config/gfortran_debug.cfg
-  - source quantum_package.rc ; qp plugins download https://gitlab.com/scemama/qp_plugins_scemama
-  - source quantum_package.rc ; qp plugins install champ
-
-- name: compile
-  pull: never
-  image: ubuntu/qp2_env
-  commands:
-  - ninja
-
-- name: testing
-  pull: never
-  image: ubuntu/qp2_env
-  commands:
-  - qp test
-
-

drone/drone_ssh.yml

@@ -1,29 +0,0 @@
-kind: pipeline
-type: ssh
-name: default
-
-clone:
-  depth: 10
-
-server:
-  host: 130.120.229.139
-  user: test
-  password:
-        from_secret: ssh_pass
-
-steps:
-- name: configure
-  commands:
-  - ./configure -i all -c ./config/gfortran_debug.cfg
-  - source quantum_package.rc ; qp plugins download https://gitlab.com/scemama/qp_plugins_scemama
-  - source quantum_package.rc ; qp plugins install champ
-
-- name: compile
-  commands:
-  - ninja
-
-- name: testing
-  commands:
-  - qp test
-
-

drone/testing.sh

@@ -1,16 +0,0 @@
-#!/bin/bash
-# Stage 3
-
-# Extract cache from compile stage
-cd ../
-tar -zxf $HOME/cache/compil.tgz
-
-# Configure QP2
-cd qp2
-source ./quantum_package.rc
-exec qp_test -a && rm $HOME/cache/compil.tgz
-
-
-
-
-

etc/qp.rc

@@ -80,8 +80,6 @@ function qp()
       if [[ -d $NAME ]] ; then
         [[ -d $EZFIO_FILE ]] && ezfio unset_file
         ezfio set_file $NAME
-      else
-        qp_create_ezfio -h | more
       fi
       unset _ARGS
       ;;

external/Python/docopt.py

@@ -0,0 +1,579 @@
+"""Pythonic command-line interface parser that will make you smile.
+
+ * http://docopt.org
+ * Repository and issue-tracker: https://github.com/docopt/docopt
+ * Licensed under terms of MIT license (see LICENSE-MIT)
+ * Copyright (c) 2013 Vladimir Keleshev, vladimir@keleshev.com
+
+"""
+import sys
+import re
+
+
+__all__ = ['docopt']
+__version__ = '0.6.2'
+
+
+class DocoptLanguageError(Exception):
+
+    """Error in construction of usage-message by developer."""
+
+
+class DocoptExit(SystemExit):
+
+    """Exit in case user invoked program with incorrect arguments."""
+
+    usage = ''
+
+    def __init__(self, message=''):
+        SystemExit.__init__(self, (message + '\n' + self.usage).strip())
+
+
+class Pattern(object):
+
+    def __eq__(self, other):
+        return repr(self) == repr(other)
+
+    def __hash__(self):
+        return hash(repr(self))
+
+    def fix(self):
+        self.fix_identities()
+        self.fix_repeating_arguments()
+        return self
+
+    def fix_identities(self, uniq=None):
+        """Make pattern-tree tips point to same object if they are equal."""
+        if not hasattr(self, 'children'):
+            return self
+        uniq = list(set(self.flat())) if uniq is None else uniq
+        for i, c in enumerate(self.children):
+            if not hasattr(c, 'children'):
+                assert c in uniq
+                self.children[i] = uniq[uniq.index(c)]
+            else:
+                c.fix_identities(uniq)
+
+    def fix_repeating_arguments(self):
+        """Fix elements that should accumulate/increment values."""
+        either = [list(c.children) for c in self.either.children]
+        for case in either:
+            for e in [c for c in case if case.count(c) > 1]:
+                if type(e) is Argument or type(e) is Option and e.argcount:
+                    if e.value is None:
+                        e.value = []
+                    elif type(e.value) is not list:
+                        e.value = e.value.split()
+                if type(e) is Command or type(e) is Option and e.argcount == 0:
+                    e.value = 0
+        return self
+
+    @property
+    def either(self):
+        """Transform pattern into an equivalent, with only top-level Either."""
+        # Currently the pattern will not be equivalent, but more "narrow",
+        # although good enough to reason about list arguments.
+        ret = []
+        groups = [[self]]
+        while groups:
+            children = groups.pop(0)
+            types = [type(c) for c in children]
+            if Either in types:
+                either = [c for c in children if type(c) is Either][0]
+                children.pop(children.index(either))
+                for c in either.children:
+                    groups.append([c] + children)
+            elif Required in types:
+                required = [c for c in children if type(c) is Required][0]
+                children.pop(children.index(required))
+                groups.append(list(required.children) + children)
+            elif Optional in types:
+                optional = [c for c in children if type(c) is Optional][0]
+                children.pop(children.index(optional))
+                groups.append(list(optional.children) + children)
+            elif AnyOptions in types:
+                optional = [c for c in children if type(c) is AnyOptions][0]
+                children.pop(children.index(optional))
+                groups.append(list(optional.children) + children)
+            elif OneOrMore in types:
+                oneormore = [c for c in children if type(c) is OneOrMore][0]
+                children.pop(children.index(oneormore))
+                groups.append(list(oneormore.children) * 2 + children)
+            else:
+                ret.append(children)
+        return Either(*[Required(*e) for e in ret])
+
+
+class ChildPattern(Pattern):
+
+    def __init__(self, name, value=None):
+        self.name = name
+        self.value = value
+
+    def __repr__(self):
+        return '%s(%r, %r)' % (self.__class__.__name__, self.name, self.value)
+
+    def flat(self, *types):
+        return [self] if not types or type(self) in types else []
+
+    def match(self, left, collected=None):
+        collected = [] if collected is None else collected
+        pos, match = self.single_match(left)
+        if match is None:
+            return False, left, collected
+        left_ = left[:pos] + left[pos + 1:]
+        same_name = [a for a in collected if a.name == self.name]
+        if type(self.value) in (int, list):
+            if type(self.value) is int:
+                increment = 1
+            else:
+                increment = ([match.value] if type(match.value) is str
+                             else match.value)
+            if not same_name:
+                match.value = increment
+                return True, left_, collected + [match]
+            same_name[0].value += increment
+            return True, left_, collected
+        return True, left_, collected + [match]
+
+
+class ParentPattern(Pattern):
+
+    def __init__(self, *children):
+        self.children = list(children)
+
+    def __repr__(self):
+        return '%s(%s)' % (self.__class__.__name__,
+                           ', '.join(repr(a) for a in self.children))
+
+    def flat(self, *types):
+        if type(self) in types:
+            return [self]
+        return sum([c.flat(*types) for c in self.children], [])
+
+
+class Argument(ChildPattern):
+
+    def single_match(self, left):
+        for n, p in enumerate(left):
+            if type(p) is Argument:
+                return n, Argument(self.name, p.value)
+        return None, None
+
+    @classmethod
+    def parse(class_, source):
+        name = re.findall('(<\S*?>)', source)[0]
+        value = re.findall('\[default: (.*)\]', source, flags=re.I)
+        return class_(name, value[0] if value else None)
+
+
+class Command(Argument):
+
+    def __init__(self, name, value=False):
+        self.name = name
+        self.value = value
+
+    def single_match(self, left):
+        for n, p in enumerate(left):
+            if type(p) is Argument:
+                if p.value == self.name:
+                    return n, Command(self.name, True)
+                else:
+                    break
+        return None, None
+
+
+class Option(ChildPattern):
+
+    def __init__(self, short=None, long=None, argcount=0, value=False):
+        assert argcount in (0, 1)
+        self.short, self.long = short, long
+        self.argcount, self.value = argcount, value
+        self.value = None if value is False and argcount else value
+
+    @classmethod
+    def parse(class_, option_description):
+        short, long, argcount, value = None, None, 0, False
+        options, _, description = option_description.strip().partition('  ')
+        options = options.replace(',', ' ').replace('=', ' ')
+        for s in options.split():
+            if s.startswith('--'):
+                long = s
+            elif s.startswith('-'):
+                short = s
+            else:
+                argcount = 1
+        if argcount:
+            matched = re.findall('\[default: (.*)\]', description, flags=re.I)
+            value = matched[0] if matched else None
+        return class_(short, long, argcount, value)
+
+    def single_match(self, left):
+        for n, p in enumerate(left):
+            if self.name == p.name:
+                return n, p
+        return None, None
+
+    @property
+    def name(self):
+        return self.long or self.short
+
+    def __repr__(self):
+        return 'Option(%r, %r, %r, %r)' % (self.short, self.long,
+                                           self.argcount, self.value)
+
+
+class Required(ParentPattern):
+
+    def match(self, left, collected=None):
+        collected = [] if collected is None else collected
+        l = left
+        c = collected
+        for p in self.children:
+            matched, l, c = p.match(l, c)
+            if not matched:
+                return False, left, collected
+        return True, l, c
+
+
+class Optional(ParentPattern):
+
+    def match(self, left, collected=None):
+        collected = [] if collected is None else collected
+        for p in self.children:
+            m, left, collected = p.match(left, collected)
+        return True, left, collected
+
+
+class AnyOptions(Optional):
+
+    """Marker/placeholder for [options] shortcut."""
+
+
+class OneOrMore(ParentPattern):
+
+    def match(self, left, collected=None):
+        assert len(self.children) == 1
+        collected = [] if collected is None else collected
+        l = left
+        c = collected
+        l_ = None
+        matched = True
+        times = 0
+        while matched:
+            # could it be that something didn't match but changed l or c?
+            matched, l, c = self.children[0].match(l, c)
+            times += 1 if matched else 0
+            if l_ == l:
+                break
+            l_ = l
+        if times >= 1:
+            return True, l, c
+        return False, left, collected
+
+
+class Either(ParentPattern):
+
+    def match(self, left, collected=None):
+        collected = [] if collected is None else collected
+        outcomes = []
+        for p in self.children:
+            matched, _, _ = outcome = p.match(left, collected)
+            if matched:
+                outcomes.append(outcome)
+        if outcomes:
+            return min(outcomes, key=lambda outcome: len(outcome[1]))
+        return False, left, collected
+
+
+class TokenStream(list):
+
+    def __init__(self, source, error):
+        self += source.split() if hasattr(source, 'split') else source
+        self.error = error
+
+    def move(self):
+        return self.pop(0) if len(self) else None
+
+    def current(self):
+        return self[0] if len(self) else None
+
+
+def parse_long(tokens, options):
+    """long ::= '--' chars [ ( ' ' | '=' ) chars ] ;"""
+    long, eq, value = tokens.move().partition('=')
+    assert long.startswith('--')
+    value = None if eq == value == '' else value
+    similar = [o for o in options if o.long == long]
+    if tokens.error is DocoptExit and similar == []:  # if no exact match
+        similar = [o for o in options if o.long and o.long.startswith(long)]
+    if len(similar) > 1:  # might be simply specified ambiguously 2+ times?
+        raise tokens.error('%s is not a unique prefix: %s?' %
+                           (long, ', '.join(o.long for o in similar)))
+    elif len(similar) < 1:
+        argcount = 1 if eq == '=' else 0
+        o = Option(None, long, argcount)
+        options.append(o)
+        if tokens.error is DocoptExit:
+            o = Option(None, long, argcount, value if argcount else True)
+    else:
+        o = Option(similar[0].short, similar[0].long,
+                   similar[0].argcount, similar[0].value)
+        if o.argcount == 0:
+            if value is not None:
+                raise tokens.error('%s must not have an argument' % o.long)
+        else:
+            if value is None:
+                if tokens.current() is None:
+                    raise tokens.error('%s requires argument' % o.long)
+                value = tokens.move()
+        if tokens.error is DocoptExit:
+            o.value = value if value is not None else True
+    return [o]
+
+
+def parse_shorts(tokens, options):
+    """shorts ::= '-' ( chars )* [ [ ' ' ] chars ] ;"""
+    token = tokens.move()
+    assert token.startswith('-') and not token.startswith('--')
+    left = token.lstrip('-')
+    parsed = []
+    while left != '':
+        short, left = '-' + left[0], left[1:]
+        similar = [o for o in options if o.short == short]
+        if len(similar) > 1:
+            raise tokens.error('%s is specified ambiguously %d times' %
+                               (short, len(similar)))
+        elif len(similar) < 1:
+            o = Option(short, None, 0)
+            options.append(o)
+            if tokens.error is DocoptExit:
+                o = Option(short, None, 0, True)
+        else:  # why copying is necessary here?
+            o = Option(short, similar[0].long,
+                       similar[0].argcount, similar[0].value)
+            value = None
+            if o.argcount != 0:
+                if left == '':
+                    if tokens.current() is None:
+                        raise tokens.error('%s requires argument' % short)
+                    value = tokens.move()
+                else:
+                    value = left
+                    left = ''
+            if tokens.error is DocoptExit:
+                o.value = value if value is not None else True
+        parsed.append(o)
+    return parsed
+
+
+def parse_pattern(source, options):
+    tokens = TokenStream(re.sub(r'([\[\]\(\)\|]|\.\.\.)', r' \1 ', source),
+                         DocoptLanguageError)
+    result = parse_expr(tokens, options)
+    if tokens.current() is not None:
+        raise tokens.error('unexpected ending: %r' % ' '.join(tokens))
+    return Required(*result)
+
+
+def parse_expr(tokens, options):
+    """expr ::= seq ( '|' seq )* ;"""
+    seq = parse_seq(tokens, options)
+    if tokens.current() != '|':
+        return seq
+    result = [Required(*seq)] if len(seq) > 1 else seq
+    while tokens.current() == '|':
+        tokens.move()
+        seq = parse_seq(tokens, options)
+        result += [Required(*seq)] if len(seq) > 1 else seq
+    return [Either(*result)] if len(result) > 1 else result
+
+
+def parse_seq(tokens, options):
+    """seq ::= ( atom [ '...' ] )* ;"""
+    result = []
+    while tokens.current() not in [None, ']', ')', '|']:
+        atom = parse_atom(tokens, options)
+        if tokens.current() == '...':
+            atom = [OneOrMore(*atom)]
+            tokens.move()
+        result += atom
+    return result
+
+
+def parse_atom(tokens, options):
+    """atom ::= '(' expr ')' | '[' expr ']' | 'options'
+             | long | shorts | argument | command ;
+    """
+    token = tokens.current()
+    result = []
+    if token in '([':
+        tokens.move()
+        matching, pattern = {'(': [')', Required], '[': [']', Optional]}[token]
+        result = pattern(*parse_expr(tokens, options))
+        if tokens.move() != matching:
+            raise tokens.error("unmatched '%s'" % token)
+        return [result]
+    elif token == 'options':
+        tokens.move()
+        return [AnyOptions()]
+    elif token.startswith('--') and token != '--':
+        return parse_long(tokens, options)
+    elif token.startswith('-') and token not in ('-', '--'):
+        return parse_shorts(tokens, options)
+    elif token.startswith('<') and token.endswith('>') or token.isupper():
+        return [Argument(tokens.move())]
+    else:
+        return [Command(tokens.move())]
+
+
+def parse_argv(tokens, options, options_first=False):
+    """Parse command-line argument vector.
+
+    If options_first:
+        argv ::= [ long | shorts ]* [ argument ]* [ '--' [ argument ]* ] ;
+    else:
+        argv ::= [ long | shorts | argument ]* [ '--' [ argument ]* ] ;
+
+    """
+    parsed = []
+    while tokens.current() is not None:
+        if tokens.current() == '--':
+            return parsed + [Argument(None, v) for v in tokens]
+        elif tokens.current().startswith('--'):
+            parsed += parse_long(tokens, options)
+        elif tokens.current().startswith('-') and tokens.current() != '-':
+            parsed += parse_shorts(tokens, options)
+        elif options_first:
+            return parsed + [Argument(None, v) for v in tokens]
+        else:
+            parsed.append(Argument(None, tokens.move()))
+    return parsed
+
+
+def parse_defaults(doc):
+    # in python < 2.7 you can't pass flags=re.MULTILINE
+    split = re.split('\n *(<\S+?>|-\S+?)', doc)[1:]
+    split = [s1 + s2 for s1, s2 in zip(split[::2], split[1::2])]
+    options = [Option.parse(s) for s in split if s.startswith('-')]
+    #arguments = [Argument.parse(s) for s in split if s.startswith('<')]
+    #return options, arguments
+    return options
+
+
+def printable_usage(doc):
+    # in python < 2.7 you can't pass flags=re.IGNORECASE
+    usage_split = re.split(r'([Uu][Ss][Aa][Gg][Ee]:)', doc)
+    if len(usage_split) < 3:
+        raise DocoptLanguageError('"usage:" (case-insensitive) not found.')
+    if len(usage_split) > 3:
+        raise DocoptLanguageError('More than one "usage:" (case-insensitive).')
+    return re.split(r'\n\s*\n', ''.join(usage_split[1:]))[0].strip()
+
+
+def formal_usage(printable_usage):
+    pu = printable_usage.split()[1:]  # split and drop "usage:"
+    return '( ' + ' '.join(') | (' if s == pu[0] else s for s in pu[1:]) + ' )'
+
+
+def extras(help, version, options, doc):
+    if help and any((o.name in ('-h', '--help')) and o.value for o in options):
+        print(doc.strip("\n"))
+        sys.exit()
+    if version and any(o.name == '--version' and o.value for o in options):
+        print(version)
+        sys.exit()
+
+
+class Dict(dict):
+    def __repr__(self):
+        return '{%s}' % ',\n '.join('%r: %r' % i for i in sorted(self.items()))
+
+
+def docopt(doc, argv=None, help=True, version=None, options_first=False):
+    """Parse `argv` based on command-line interface described in `doc`.
+
+    `docopt` creates your command-line interface based on its
+    description that you pass as `doc`. Such description can contain
+    --options, <positional-argument>, commands, which could be
+    [optional], (required), (mutually | exclusive) or repeated...
+
+    Parameters
+    ----------
+    doc : str
+        Description of your command-line interface.
+    argv : list of str, optional
+        Argument vector to be parsed. sys.argv[1:] is used if not
+        provided.
+    help : bool (default: True)
+        Set to False to disable automatic help on -h or --help
+        options.
+    version : any object
+        If passed, the object will be printed if --version is in
+        `argv`.
+    options_first : bool (default: False)
+        Set to True to require options preceed positional arguments,
+        i.e. to forbid options and positional arguments intermix.
+
+    Returns
+    -------
+    args : dict
+        A dictionary, where keys are names of command-line elements
+        such as e.g. "--verbose" and "<path>", and values are the
+        parsed values of those elements.
+
+    Example
+    -------
+    >>> from docopt import docopt
+    >>> doc = '''
+    Usage:
+        my_program tcp <host> <port> [--timeout=<seconds>]
+        my_program serial <port> [--baud=<n>] [--timeout=<seconds>]
+        my_program (-h | --help | --version)
+
+    Options:
+        -h, --help  Show this screen and exit.
+        --baud=<n>  Baudrate [default: 9600]
+    '''
+    >>> argv = ['tcp', '127.0.0.1', '80', '--timeout', '30']
+    >>> docopt(doc, argv)
+    {'--baud': '9600',
+     '--help': False,
+     '--timeout': '30',
+     '--version': False,
+     '<host>': '127.0.0.1',
+     '<port>': '80',
+     'serial': False,
+     'tcp': True}
+
+    See also
+    --------
+    * For video introduction see http://docopt.org
+    * Full documentation is available in README.rst as well as online
+      at https://github.com/docopt/docopt#readme
+
+    """
+    if argv is None:
+        argv = sys.argv[1:]
+    DocoptExit.usage = printable_usage(doc)
+    options = parse_defaults(doc)
+    pattern = parse_pattern(formal_usage(DocoptExit.usage), options)
+    # [default] syntax for argument is disabled
+    #for a in pattern.flat(Argument):
+    #    same_name = [d for d in arguments if d.name == a.name]
+    #    if same_name:
+    #        a.value = same_name[0].value
+    argv = parse_argv(TokenStream(argv, DocoptExit), list(options),
+                      options_first)
+    pattern_options = set(pattern.flat(Option))
+    for ao in pattern.flat(AnyOptions):
+        doc_options = parse_defaults(doc)
+        ao.children = list(set(doc_options) - pattern_options)
+        #if any_options:
+        #    ao.children += [Option(o.short, o.long, o.argcount)
+        #                    for o in argv if type(o) is Option]
+    extras(help, version, argv, doc)
+    matched, left, collected = pattern.fix().match(argv)
+    if matched and left == []:  # better error message if left?
+        return Dict((a.name, a.value) for a in (pattern.flat() + collected))
+    raise DocoptExit()

external/qp2-dependencies

@@ -1 +1 @@
-Subproject commit 90ee61f5041c7c94a0c605625a264860292813a0
+Subproject commit 242151e03d1d6bf042387226431d82d35845686a

include/f77_zmq.h

@@ -0,0 +1,617 @@
+      integer EADDRINUSE
+      integer EADDRNOTAVAIL
+      integer EAFNOSUPPORT
+      integer ECONNABORTED
+      integer ECONNREFUSED
+      integer ECONNRESET
+      integer EFSM
+      integer EHOSTUNREACH
+      integer EINPROGRESS
+      integer EMSGSIZE
+      integer EMTHREAD
+      integer ENETDOWN
+      integer ENETRESET
+      integer ENETUNREACH
+      integer ENOBUFS
+      integer ENOCOMPATPROTO
+      integer ENOTCONN
+      integer ENOTSOCK
+      integer ENOTSUP
+      integer EPROTONOSUPPORT
+      integer ETERM
+      integer ETIMEDOUT
+      integer ZMQ_AFFINITY
+      integer ZMQ_BACKLOG
+      integer ZMQ_BINDTODEVICE
+      integer ZMQ_BLOCKY
+      integer ZMQ_CHANNEL
+      integer ZMQ_CLIENT
+      integer ZMQ_CONFLATE
+      integer ZMQ_CONNECT_RID
+      integer ZMQ_CONNECT_ROUTING_ID
+      integer ZMQ_CONNECT_TIMEOUT
+      integer ZMQ_CURRENT_EVENT_VERSION
+      integer ZMQ_CURRENT_EVENT_VERSION_DRAFT
+      integer ZMQ_CURVE
+      integer ZMQ_CURVE_PUBLICKEY
+      integer ZMQ_CURVE_SECRETKEY
+      integer ZMQ_CURVE_SERVER
+      integer ZMQ_CURVE_SERVERKEY
+      integer ZMQ_DEALER
+      integer ZMQ_DEFINED_STDINT
+      integer ZMQ_DELAY_ATTACH_ON_CONNECT
+      integer ZMQ_DGRAM
+      integer ZMQ_DISCONNECT_MSG
+      integer ZMQ_DISH
+      integer ZMQ_DONTWAIT
+      integer ZMQ_EVENTS
+      integer ZMQ_EVENT_ACCEPTED
+      integer ZMQ_EVENT_ACCEPT_FAILED
+      integer ZMQ_EVENT_ALL
+      integer ZMQ_EVENT_ALL_V1
+      integer ZMQ_EVENT_ALL_V2
+      integer ZMQ_EVENT_BIND_FAILED
+      integer ZMQ_EVENT_CLOSED
+      integer ZMQ_EVENT_CLOSE_FAILED
+      integer ZMQ_EVENT_CONNECTED
+      integer ZMQ_EVENT_CONNECT_DELAYED
+      integer ZMQ_EVENT_CONNECT_RETRIED
+      integer ZMQ_EVENT_DISCONNECTED
+      integer ZMQ_EVENT_HANDSHAKE_FAILED_AUTH
+      integer ZMQ_EVENT_HANDSHAKE_FAILED_NO_DETAIL
+      integer ZMQ_EVENT_HANDSHAKE_FAILED_PROTOCOL
+      integer ZMQ_EVENT_HANDSHAKE_SUCCEEDED
+      integer ZMQ_EVENT_LISTENING
+      integer ZMQ_EVENT_MONITOR_STOPPED
+      integer ZMQ_EVENT_PIPES_STATS
+      integer ZMQ_FAIL_UNROUTABLE
+      integer ZMQ_FD
+      integer ZMQ_FORWARDER
+      integer ZMQ_GATHER
+      integer ZMQ_GROUP_MAX_LENGTH
+      integer ZMQ_GSSAPI
+      integer ZMQ_GSSAPI_NT_HOSTBASED
+      integer ZMQ_GSSAPI_NT_KRB5_PRINCIPAL
+      integer ZMQ_GSSAPI_NT_USER_NAME
+      integer ZMQ_GSSAPI_PLAINTEXT
+      integer ZMQ_GSSAPI_PRINCIPAL
+      integer ZMQ_GSSAPI_PRINCIPAL_NAMETYPE
+      integer ZMQ_GSSAPI_SERVER
+      integer ZMQ_GSSAPI_SERVICE_PRINCIPAL
+      integer ZMQ_GSSAPI_SERVICE_PRINCIPAL_NAMETYPE
+      integer ZMQ_HANDSHAKE_IVL
+      integer ZMQ_HAS_CAPABILITIES
+      integer ZMQ_HAUSNUMERO
+      integer ZMQ_HEARTBEAT_IVL
+      integer ZMQ_HEARTBEAT_TIMEOUT
+      integer ZMQ_HEARTBEAT_TTL
+      integer ZMQ_HELLO_MSG
+      integer ZMQ_IDENTITY
+      integer ZMQ_IMMEDIATE
+      integer ZMQ_INVERT_MATCHING
+      integer ZMQ_IN_BATCH_SIZE
+      integer ZMQ_IO_THREADS
+      integer ZMQ_IO_THREADS_DFLT
+      integer ZMQ_IPC_FILTER_GID
+      integer ZMQ_IPC_FILTER_PID
+      integer ZMQ_IPC_FILTER_UID
+      integer ZMQ_IPV4ONLY
+      integer ZMQ_IPV6
+      integer ZMQ_LAST_ENDPOINT
+      integer ZMQ_LINGER
+      integer ZMQ_LOOPBACK_FASTPATH
+      integer ZMQ_MAXMSGSIZE
+      integer ZMQ_MAX_MSGSZ
+      integer ZMQ_MAX_SOCKETS
+      integer ZMQ_MAX_SOCKETS_DFLT
+      integer ZMQ_MECHANISM
+      integer ZMQ_METADATA
+      integer ZMQ_MORE
+      integer ZMQ_MSG_T_SIZE
+      integer ZMQ_MULTICAST_HOPS
+      integer ZMQ_MULTICAST_LOOP
+      integer ZMQ_MULTICAST_MAXTPDU
+      integer ZMQ_NOBLOCK
+      integer ZMQ_NOTIFY_CONNECT
+      integer ZMQ_NOTIFY_DISCONNECT
+      integer ZMQ_NULL
+      integer ZMQ_ONLY_FIRST_SUBSCRIBE
+      integer ZMQ_OUT_BATCH_SIZE
+      integer ZMQ_PAIR
+      integer ZMQ_PEER
+      integer ZMQ_PLAIN
+      integer ZMQ_PLAIN_PASSWORD
+      integer ZMQ_PLAIN_SERVER
+      integer ZMQ_PLAIN_USERNAME
+      integer ZMQ_POLLERR
+      integer ZMQ_POLLIN
+      integer ZMQ_POLLITEMS_DFLT
+      integer ZMQ_POLLOUT
+      integer ZMQ_POLLPRI
+      integer ZMQ_PRIORITY
+      integer ZMQ_PROBE_ROUTER
+      integer ZMQ_PROTOCOL_ERROR_WS_UNSPECIFIED
+      integer ZMQ_PROTOCOL_ERROR_ZAP_BAD_REQUEST_ID
+      integer ZMQ_PROTOCOL_ERROR_ZAP_BAD_VERSION
+      integer ZMQ_PROTOCOL_ERROR_ZAP_INVALID_METADATA
+      integer ZMQ_PROTOCOL_ERROR_ZAP_INVALID_STATUS_CODE
+      integer ZMQ_PROTOCOL_ERROR_ZAP_MALFORMED_REPLY
+      integer ZMQ_PROTOCOL_ERROR_ZAP_UNSPECIFIED
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_CRYPTOGRAPHIC
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_INVALID_METADATA
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_INVALID_SEQUENCE
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_KEY_EXCHANGE
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_ERROR
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_HELLO
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_INITIATE
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_MESSAGE
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_READY
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_UNSPECIFIED
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_WELCOME
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_MECHANISM_MISMATCH
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_UNEXPECTED_COMMAND
+      integer ZMQ_PROTOCOL_ERROR_ZMTP_UNSPECIFIED
+      integer ZMQ_PTR
+      integer ZMQ_PUB
+      integer ZMQ_PULL
+      integer ZMQ_PUSH
+      integer ZMQ_QUEUE
+      integer ZMQ_RADIO
+      integer ZMQ_RATE
+      integer ZMQ_RCVBUF
+      integer ZMQ_RCVHWM
+      integer ZMQ_RCVMORE
+      integer ZMQ_RCVTIMEO
+      integer ZMQ_RECONNECT_IVL
+      integer ZMQ_RECONNECT_IVL_MAX
+      integer ZMQ_RECONNECT_STOP
+      integer ZMQ_RECONNECT_STOP_AFTER_DISCONNECT
+      integer ZMQ_RECONNECT_STOP_CONN_REFUSED
+      integer ZMQ_RECONNECT_STOP_HANDSHAKE_FAILED
+      integer ZMQ_RECOVERY_IVL
+      integer ZMQ_REP
+      integer ZMQ_REQ
+      integer ZMQ_REQ_CORRELATE
+      integer ZMQ_REQ_RELAXED
+      integer ZMQ_ROUTER
+      integer ZMQ_ROUTER_BEHAVIOR
+      integer ZMQ_ROUTER_HANDOVER
+      integer ZMQ_ROUTER_MANDATORY
+      integer ZMQ_ROUTER_NOTIFY
+      integer ZMQ_ROUTER_RAW
+      integer ZMQ_ROUTING_ID
+      integer ZMQ_SCATTER
+      integer ZMQ_SERVER
+      integer ZMQ_SHARED
+      integer ZMQ_SNDBUF
+      integer ZMQ_SNDHWM
+      integer ZMQ_SNDMORE
+      integer ZMQ_SNDTIMEO
+      integer ZMQ_SOCKET_LIMIT
+      integer ZMQ_SOCKS_PASSWORD
+      integer ZMQ_SOCKS_PROXY
+      integer ZMQ_SOCKS_USERNAME
+      integer ZMQ_SRCFD
+      integer ZMQ_STREAM
+      integer ZMQ_STREAMER
+      integer ZMQ_STREAM_NOTIFY
+      integer ZMQ_SUB
+      integer ZMQ_SUBSCRIBE
+      integer ZMQ_TCP_ACCEPT_FILTER
+      integer ZMQ_TCP_KEEPALIVE
+      integer ZMQ_TCP_KEEPALIVE_CNT
+      integer ZMQ_TCP_KEEPALIVE_IDLE
+      integer ZMQ_TCP_KEEPALIVE_INTVL
+      integer ZMQ_TCP_MAXRT
+      integer ZMQ_THREAD_AFFINITY_CPU_ADD
+      integer ZMQ_THREAD_AFFINITY_CPU_REMOVE
+      integer ZMQ_THREAD_NAME_PREFIX
+      integer ZMQ_THREAD_PRIORITY
+      integer ZMQ_THREAD_PRIORITY_DFLT
+      integer ZMQ_THREAD_SAFE
+      integer ZMQ_THREAD_SCHED_POLICY
+      integer ZMQ_THREAD_SCHED_POLICY_DFLT
+      integer ZMQ_TOS
+      integer ZMQ_TYPE
+      integer ZMQ_UNSUBSCRIBE
+      integer ZMQ_USE_FD
+      integer ZMQ_VERSION
+      integer ZMQ_VERSION_MAJOR
+      integer ZMQ_VERSION_MINOR
+      integer ZMQ_VERSION_PATCH
+      integer ZMQ_VMCI_BUFFER_MAX_SIZE
+      integer ZMQ_VMCI_BUFFER_MIN_SIZE
+      integer ZMQ_VMCI_BUFFER_SIZE
+      integer ZMQ_VMCI_CONNECT_TIMEOUT
+      integer ZMQ_WSS_CERT_PEM
+      integer ZMQ_WSS_HOSTNAME
+      integer ZMQ_WSS_KEY_PEM
+      integer ZMQ_WSS_TRUST_PEM
+      integer ZMQ_WSS_TRUST_SYSTEM
+      integer ZMQ_XPUB
+      integer ZMQ_XPUB_MANUAL
+      integer ZMQ_XPUB_MANUAL_LAST_VALUE
+      integer ZMQ_XPUB_NODROP
+      integer ZMQ_XPUB_VERBOSE
+      integer ZMQ_XPUB_VERBOSER
+      integer ZMQ_XPUB_WELCOME_MSG
+      integer ZMQ_XREP
+      integer ZMQ_XREQ
+      integer ZMQ_XSUB
+      integer ZMQ_ZAP_DOMAIN
+      integer ZMQ_ZAP_ENFORCE_DOMAIN
+      integer ZMQ_ZERO_COPY_RECV
+      parameter(EADDRINUSE=156384717)
+      parameter(EADDRNOTAVAIL=156384718)
+      parameter(EAFNOSUPPORT=156384723)
+      parameter(ECONNABORTED=156384725)
+      parameter(ECONNREFUSED=156384719)
+      parameter(ECONNRESET=156384726)
+      parameter(EFSM=156384763)
+      parameter(EHOSTUNREACH=156384729)
+      parameter(EINPROGRESS=156384720)
+      parameter(EMSGSIZE=156384722)
+      parameter(EMTHREAD=156384766)
+      parameter(ENETDOWN=156384716)
+      parameter(ENETRESET=156384730)
+      parameter(ENETUNREACH=156384724)
+      parameter(ENOBUFS=156384715)
+      parameter(ENOCOMPATPROTO=156384764)
+      parameter(ENOTCONN=156384727)
+      parameter(ENOTSOCK=156384721)
+      parameter(ENOTSUP=156384713)
+      parameter(EPROTONOSUPPORT=156384714)
+      parameter(ETERM=156384765)
+      parameter(ETIMEDOUT=156384728)
+      parameter(ZMQ_AFFINITY=4)
+      parameter(ZMQ_BACKLOG=19)
+      parameter(ZMQ_BINDTODEVICE=92)
+      parameter(ZMQ_BLOCKY=70)
+      parameter(ZMQ_CHANNEL=20)
+      parameter(ZMQ_CLIENT=13)
+      parameter(ZMQ_CONFLATE=54)
+      parameter(ZMQ_CONNECT_RID=61)
+      parameter(ZMQ_CONNECT_ROUTING_ID=61)
+      parameter(ZMQ_CONNECT_TIMEOUT=79)
+      parameter(ZMQ_CURRENT_EVENT_VERSION=1)
+      parameter(ZMQ_CURRENT_EVENT_VERSION_DRAFT=2)
+      parameter(ZMQ_CURVE=2)
+      parameter(ZMQ_CURVE_PUBLICKEY=48)
+      parameter(ZMQ_CURVE_SECRETKEY=49)
+      parameter(ZMQ_CURVE_SERVER=47)
+      parameter(ZMQ_CURVE_SERVERKEY=50)
+      parameter(ZMQ_DEALER=5)
+      parameter(ZMQ_DEFINED_STDINT=1)
+      parameter(ZMQ_DELAY_ATTACH_ON_CONNECT=39)
+      parameter(ZMQ_DGRAM=18)
+      parameter(ZMQ_DISCONNECT_MSG=111)
+      parameter(ZMQ_DISH=15)
+      parameter(ZMQ_DONTWAIT=1)
+      parameter(ZMQ_EVENTS=15)
+      parameter(ZMQ_EVENT_ACCEPTED=32)
+      parameter(ZMQ_EVENT_ACCEPT_FAILED=64)
+      parameter(ZMQ_EVENT_ALL=65535)
+      parameter(ZMQ_EVENT_ALL_V1=65535)
+      parameter(ZMQ_EVENT_ALL_V2=131071)
+      parameter(ZMQ_EVENT_BIND_FAILED=16)
+      parameter(ZMQ_EVENT_CLOSED=128)
+      parameter(ZMQ_EVENT_CLOSE_FAILED=256)
+      parameter(ZMQ_EVENT_CONNECTED=1)
+      parameter(ZMQ_EVENT_CONNECT_DELAYED=2)
+      parameter(ZMQ_EVENT_CONNECT_RETRIED=4)
+      parameter(ZMQ_EVENT_DISCONNECTED=512)
+      parameter(ZMQ_EVENT_HANDSHAKE_FAILED_AUTH=16384)
+      parameter(ZMQ_EVENT_HANDSHAKE_FAILED_NO_DETAIL=2048)
+      parameter(ZMQ_EVENT_HANDSHAKE_FAILED_PROTOCOL=8192)
+      parameter(ZMQ_EVENT_HANDSHAKE_SUCCEEDED=4096)
+      parameter(ZMQ_EVENT_LISTENING=8)
+      parameter(ZMQ_EVENT_MONITOR_STOPPED=1024)
+      parameter(ZMQ_EVENT_PIPES_STATS=65536)
+      parameter(ZMQ_FAIL_UNROUTABLE=33)
+      parameter(ZMQ_FD=14)
+      parameter(ZMQ_FORWARDER=2)
+      parameter(ZMQ_GATHER=16)
+      parameter(ZMQ_GROUP_MAX_LENGTH=255)
+      parameter(ZMQ_GSSAPI=3)
+      parameter(ZMQ_GSSAPI_NT_HOSTBASED=0)
+      parameter(ZMQ_GSSAPI_NT_KRB5_PRINCIPAL=2)
+      parameter(ZMQ_GSSAPI_NT_USER_NAME=1)
+      parameter(ZMQ_GSSAPI_PLAINTEXT=65)
+      parameter(ZMQ_GSSAPI_PRINCIPAL=63)
+      parameter(ZMQ_GSSAPI_PRINCIPAL_NAMETYPE=90)
+      parameter(ZMQ_GSSAPI_SERVER=62)
+      parameter(ZMQ_GSSAPI_SERVICE_PRINCIPAL=64)
+      parameter(ZMQ_GSSAPI_SERVICE_PRINCIPAL_NAMETYPE=91)
+      parameter(ZMQ_HANDSHAKE_IVL=66)
+      parameter(ZMQ_HAS_CAPABILITIES=1)
+      parameter(ZMQ_HAUSNUMERO=156384712)
+      parameter(ZMQ_HEARTBEAT_IVL=75)
+      parameter(ZMQ_HEARTBEAT_TIMEOUT=77)
+      parameter(ZMQ_HEARTBEAT_TTL=76)
+      parameter(ZMQ_HELLO_MSG=110)
+      parameter(ZMQ_IDENTITY=5)
+      parameter(ZMQ_IMMEDIATE=39)
+      parameter(ZMQ_INVERT_MATCHING=74)
+      parameter(ZMQ_IN_BATCH_SIZE=101)
+      parameter(ZMQ_IO_THREADS=1)
+      parameter(ZMQ_IO_THREADS_DFLT=1)
+      parameter(ZMQ_IPC_FILTER_GID=60)
+      parameter(ZMQ_IPC_FILTER_PID=58)
+      parameter(ZMQ_IPC_FILTER_UID=59)
+      parameter(ZMQ_IPV4ONLY=31)
+      parameter(ZMQ_IPV6=42)
+      parameter(ZMQ_LAST_ENDPOINT=32)
+      parameter(ZMQ_LINGER=17)
+      parameter(ZMQ_LOOPBACK_FASTPATH=94)
+      parameter(ZMQ_MAXMSGSIZE=22)
+      parameter(ZMQ_MAX_MSGSZ=5)
+      parameter(ZMQ_MAX_SOCKETS=2)
+      parameter(ZMQ_MAX_SOCKETS_DFLT=1023)
+      parameter(ZMQ_MECHANISM=43)
+      parameter(ZMQ_METADATA=95)
+      parameter(ZMQ_MORE=1)
+      parameter(ZMQ_MSG_T_SIZE=6)
+      parameter(ZMQ_MULTICAST_HOPS=25)
+      parameter(ZMQ_MULTICAST_LOOP=96)
+      parameter(ZMQ_MULTICAST_MAXTPDU=84)
+      parameter(ZMQ_NOBLOCK=1)
+      parameter(ZMQ_NOTIFY_CONNECT=1)
+      parameter(ZMQ_NOTIFY_DISCONNECT=2)
+      parameter(ZMQ_NULL=0)
+      parameter(ZMQ_ONLY_FIRST_SUBSCRIBE=108)
+      parameter(ZMQ_OUT_BATCH_SIZE=102)
+      parameter(ZMQ_PAIR=0)
+      parameter(ZMQ_PEER=19)
+      parameter(ZMQ_PLAIN=1)
+      parameter(ZMQ_PLAIN_PASSWORD=46)
+      parameter(ZMQ_PLAIN_SERVER=44)
+      parameter(ZMQ_PLAIN_USERNAME=45)
+      parameter(ZMQ_POLLERR=4)
+      parameter(ZMQ_POLLIN=1)
+      parameter(ZMQ_POLLITEMS_DFLT=16)
+      parameter(ZMQ_POLLOUT=2)
+      parameter(ZMQ_POLLPRI=8)
+      parameter(ZMQ_PRIORITY=112)
+      parameter(ZMQ_PROBE_ROUTER=51)
+      parameter(ZMQ_PROTOCOL_ERROR_WS_UNSPECIFIED=805306368)
+      parameter(ZMQ_PROTOCOL_ERROR_ZAP_BAD_REQUEST_ID=536870914)
+      parameter(ZMQ_PROTOCOL_ERROR_ZAP_BAD_VERSION=536870915)
+      parameter(ZMQ_PROTOCOL_ERROR_ZAP_INVALID_METADATA=536870917)
+      parameter(ZMQ_PROTOCOL_ERROR_ZAP_INVALID_STATUS_CODE=536870916)
+      parameter(ZMQ_PROTOCOL_ERROR_ZAP_MALFORMED_REPLY=536870913)
+      parameter(ZMQ_PROTOCOL_ERROR_ZAP_UNSPECIFIED=536870912)
+      parameter(ZMQ_PROTOCOL_ERROR_ZMTP_CRYPTOGRAPHIC=285212673)
+      parameter(ZMQ_PROTOCOL_ERROR_ZMTP_INVALID_METADATA=268435480)
+      parameter(ZMQ_PROTOCOL_ERROR_ZMTP_INVALID_SEQUENCE=268435458)
+      parameter(ZMQ_PROTOCOL_ERROR_ZMTP_KEY_EXCHANGE=268435459)
+      parameter(
+     & ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_ERROR=268435477)
+      parameter(
+     & ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_HELLO=268435475)
+      parameter(
+     & ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_INITIATE=268435476)
+      parameter(
+     & ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_MESSAGE=268435474)
+      parameter(
+     & ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_READY=268435478)
+      parameter(
+     & ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_UNSPECIFIED=268435473)
+      parameter(
+     & ZMQ_PROTOCOL_ERROR_ZMTP_MALFORMED_COMMAND_WELCOME=268435479)
+      parameter(ZMQ_PROTOCOL_ERROR_ZMTP_MECHANISM_MISMATCH=285212674)
+      parameter(ZMQ_PROTOCOL_ERROR_ZMTP_UNEXPECTED_COMMAND=268435457)
+      parameter(ZMQ_PROTOCOL_ERROR_ZMTP_UNSPECIFIED=268435456)
+      parameter(ZMQ_PTR=8)
+      parameter(ZMQ_PUB=1)
+      parameter(ZMQ_PULL=7)
+      parameter(ZMQ_PUSH=8)
+      parameter(ZMQ_QUEUE=3)
+      parameter(ZMQ_RADIO=14)
+      parameter(ZMQ_RATE=8)
+      parameter(ZMQ_RCVBUF=12)
+      parameter(ZMQ_RCVHWM=24)
+      parameter(ZMQ_RCVMORE=13)
+      parameter(ZMQ_RCVTIMEO=27)
+      parameter(ZMQ_RECONNECT_IVL=18)
+      parameter(ZMQ_RECONNECT_IVL_MAX=21)
+      parameter(ZMQ_RECONNECT_STOP=109)
+      parameter(ZMQ_RECONNECT_STOP_AFTER_DISCONNECT=3)
+      parameter(ZMQ_RECONNECT_STOP_CONN_REFUSED=1)
+      parameter(ZMQ_RECONNECT_STOP_HANDSHAKE_FAILED=2)
+      parameter(ZMQ_RECOVERY_IVL=9)
+      parameter(ZMQ_REP=4)
+      parameter(ZMQ_REQ=3)
+      parameter(ZMQ_REQ_CORRELATE=52)
+      parameter(ZMQ_REQ_RELAXED=53)
+      parameter(ZMQ_ROUTER=6)
+      parameter(ZMQ_ROUTER_BEHAVIOR=33)
+      parameter(ZMQ_ROUTER_HANDOVER=56)
+      parameter(ZMQ_ROUTER_MANDATORY=33)
+      parameter(ZMQ_ROUTER_NOTIFY=97)
+      parameter(ZMQ_ROUTER_RAW=41)
+      parameter(ZMQ_ROUTING_ID=5)
+      parameter(ZMQ_SCATTER=17)
+      parameter(ZMQ_SERVER=12)
+      parameter(ZMQ_SHARED=3)
+      parameter(ZMQ_SNDBUF=11)
+      parameter(ZMQ_SNDHWM=23)
+      parameter(ZMQ_SNDMORE=2)
+      parameter(ZMQ_SNDTIMEO=28)
+      parameter(ZMQ_SOCKET_LIMIT=3)
+      parameter(ZMQ_SOCKS_PASSWORD=100)
+      parameter(ZMQ_SOCKS_PROXY=68)
+      parameter(ZMQ_SOCKS_USERNAME=99)
+      parameter(ZMQ_SRCFD=2)
+      parameter(ZMQ_STREAM=11)
+      parameter(ZMQ_STREAMER=1)
+      parameter(ZMQ_STREAM_NOTIFY=73)
+      parameter(ZMQ_SUB=2)
+      parameter(ZMQ_SUBSCRIBE=6)
+      parameter(ZMQ_TCP_ACCEPT_FILTER=38)
+      parameter(ZMQ_TCP_KEEPALIVE=34)
+      parameter(ZMQ_TCP_KEEPALIVE_CNT=35)
+      parameter(ZMQ_TCP_KEEPALIVE_IDLE=36)
+      parameter(ZMQ_TCP_KEEPALIVE_INTVL=37)
+      parameter(ZMQ_TCP_MAXRT=80)
+      parameter(ZMQ_THREAD_AFFINITY_CPU_ADD=7)
+      parameter(ZMQ_THREAD_AFFINITY_CPU_REMOVE=8)
+      parameter(ZMQ_THREAD_NAME_PREFIX=9)
+      parameter(ZMQ_THREAD_PRIORITY=3)
+      parameter(ZMQ_THREAD_PRIORITY_DFLT=-1)
+      parameter(ZMQ_THREAD_SAFE=81)
+      parameter(ZMQ_THREAD_SCHED_POLICY=4)
+      parameter(ZMQ_THREAD_SCHED_POLICY_DFLT=-1)
+      parameter(ZMQ_TOS=57)
+      parameter(ZMQ_TYPE=16)
+      parameter(ZMQ_UNSUBSCRIBE=7)
+      parameter(ZMQ_USE_FD=89)
+      parameter(ZMQ_VERSION=40304)
+      parameter(ZMQ_VERSION_MAJOR=4)
+      parameter(ZMQ_VERSION_MINOR=3)
+      parameter(ZMQ_VERSION_PATCH=4)
+      parameter(ZMQ_VMCI_BUFFER_MAX_SIZE=87)
+      parameter(ZMQ_VMCI_BUFFER_MIN_SIZE=86)
+      parameter(ZMQ_VMCI_BUFFER_SIZE=85)
+      parameter(ZMQ_VMCI_CONNECT_TIMEOUT=88)
+      parameter(ZMQ_WSS_CERT_PEM=104)
+      parameter(ZMQ_WSS_HOSTNAME=106)
+      parameter(ZMQ_WSS_KEY_PEM=103)
+      parameter(ZMQ_WSS_TRUST_PEM=105)
+      parameter(ZMQ_WSS_TRUST_SYSTEM=107)
+      parameter(ZMQ_XPUB=9)
+      parameter(ZMQ_XPUB_MANUAL=71)
+      parameter(ZMQ_XPUB_MANUAL_LAST_VALUE=98)
+      parameter(ZMQ_XPUB_NODROP=69)
+      parameter(ZMQ_XPUB_VERBOSE=40)
+      parameter(ZMQ_XPUB_VERBOSER=78)
+      parameter(ZMQ_XPUB_WELCOME_MSG=72)
+      parameter(ZMQ_XREP=6)
+      parameter(ZMQ_XREQ=5)
+      parameter(ZMQ_XSUB=10)
+      parameter(ZMQ_ZAP_DOMAIN=55)
+      parameter(ZMQ_ZAP_ENFORCE_DOMAIN=93)
+      parameter(ZMQ_ZERO_COPY_RECV=10)
+      integer              f77_zmq_bind
+      external             f77_zmq_bind
+      integer              f77_zmq_close
+      external             f77_zmq_close
+      integer              f77_zmq_connect
+      external             f77_zmq_connect
+      integer              f77_zmq_ctx_destroy
+      external             f77_zmq_ctx_destroy
+      integer              f77_zmq_ctx_get
+      external             f77_zmq_ctx_get
+      integer*8            f77_zmq_ctx_new
+      external             f77_zmq_ctx_new
+      integer              f77_zmq_ctx_set
+      external             f77_zmq_ctx_set
+      integer              f77_zmq_ctx_shutdown
+      external             f77_zmq_ctx_shutdown
+      integer              f77_zmq_ctx_term
+      external             f77_zmq_ctx_term
+      integer              f77_zmq_disconnect
+      external             f77_zmq_disconnect
+      integer              f77_zmq_errno
+      external             f77_zmq_errno
+      integer              f77_zmq_getsockopt
+      external             f77_zmq_getsockopt
+      integer              f77_zmq_microsleep
+      external             f77_zmq_microsleep
+      integer              f77_zmq_msg_close
+      external             f77_zmq_msg_close
+      integer              f77_zmq_msg_copy
+      external             f77_zmq_msg_copy
+      integer              f77_zmq_msg_copy_from_data
+      external             f77_zmq_msg_copy_from_data
+      integer              f77_zmq_msg_copy_to_data
+      external             f77_zmq_msg_copy_to_data
+      integer              f77_zmq_msg_copy_to_data8
+      external             f77_zmq_msg_copy_to_data8
+      integer*8            f77_zmq_msg_data
+      external             f77_zmq_msg_data
+      integer*8            f77_zmq_msg_data_new
+      external             f77_zmq_msg_data_new
+      integer              f77_zmq_msg_destroy
+      external             f77_zmq_msg_destroy
+      integer              f77_zmq_msg_destroy_data
+      external             f77_zmq_msg_destroy_data
+      integer              f77_zmq_msg_get
+      external             f77_zmq_msg_get
+      character*(64)       f77_zmq_msg_gets
+      external             f77_zmq_msg_gets
+      integer              f77_zmq_msg_init
+      external             f77_zmq_msg_init
+      integer              f77_zmq_msg_init_data
+      external             f77_zmq_msg_init_data
+      integer              f77_zmq_msg_init_size
+      external             f77_zmq_msg_init_size
+      integer              f77_zmq_msg_more
+      external             f77_zmq_msg_more
+      integer              f77_zmq_msg_move
+      external             f77_zmq_msg_move
+      integer*8            f77_zmq_msg_new
+      external             f77_zmq_msg_new
+      integer              f77_zmq_msg_recv
+      external             f77_zmq_msg_recv
+      integer*8            f77_zmq_msg_recv8
+      external             f77_zmq_msg_recv8
+      integer              f77_zmq_msg_send
+      external             f77_zmq_msg_send
+      integer*8            f77_zmq_msg_send8
+      external             f77_zmq_msg_send8
+      integer              f77_zmq_msg_set
+      external             f77_zmq_msg_set
+      integer              f77_zmq_msg_size
+      external             f77_zmq_msg_size
+      integer*8            f77_zmq_msg_size8
+      external             f77_zmq_msg_size8
+      integer              f77_zmq_poll
+      external             f77_zmq_poll
+      integer              f77_zmq_pollitem_destroy
+      external             f77_zmq_pollitem_destroy
+      integer*8            f77_zmq_pollitem_new
+      external             f77_zmq_pollitem_new
+      integer              f77_zmq_pollitem_revents
+      external             f77_zmq_pollitem_revents
+      integer              f77_zmq_pollitem_set_events
+      external             f77_zmq_pollitem_set_events
+      integer              f77_zmq_pollitem_set_socket
+      external             f77_zmq_pollitem_set_socket
+      integer              f77_zmq_proxy
+      external             f77_zmq_proxy
+      integer              f77_zmq_proxy_steerable
+      external             f77_zmq_proxy_steerable
+      integer              f77_zmq_recv
+      external             f77_zmq_recv
+      integer*8            f77_zmq_recv8
+      external             f77_zmq_recv8
+      integer              f77_zmq_send
+      external             f77_zmq_send
+      integer*8            f77_zmq_send8
+      external             f77_zmq_send8
+      integer              f77_zmq_send_const
+      external             f77_zmq_send_const
+      integer*8            f77_zmq_send_const8
+      external             f77_zmq_send_const8
+      integer              f77_zmq_setsockopt
+      external             f77_zmq_setsockopt
+      integer*8            f77_zmq_socket
+      external             f77_zmq_socket
+      integer              f77_zmq_socket_monitor
+      external             f77_zmq_socket_monitor
+      character*(64)       f77_zmq_strerror
+      external             f77_zmq_strerror
+      integer              f77_zmq_term
+      external             f77_zmq_term
+      integer              f77_zmq_unbind
+      external             f77_zmq_unbind
+      integer              f77_zmq_version
+      external             f77_zmq_version
+      integer              pthread_create
+      external             pthread_create
+      integer              pthread_create_arg
+      external             pthread_create_arg
+      integer              pthread_detach
+      external             pthread_detach
+      integer              pthread_join
+      external             pthread_join

ocaml/Input_ao_two_e_eff_pot.ml

@@ -0,0 +1,113 @@
+(* =~=~ *)
+(* Init *)
+(* =~=~ *)
+
+open Qptypes;;
+open Qputils;;
+open Sexplib.Std;;
+
+module Ao_two_e_eff_pot : sig
+(* Generate type *)
+   type t = 
+     {
+       adjoint_tc_h                   : bool;
+       grad_squared                   : bool;
+     } [@@deriving sexp]
+   ;;
+  val read  : unit -> t option
+  val write : t-> unit
+  val to_string : t -> string
+  val to_rst : t -> Rst_string.t
+  val of_rst : Rst_string.t -> t option
+end = struct
+(* Generate type *)
+   type t = 
+     {
+       adjoint_tc_h                   : bool;
+       grad_squared                   : bool;
+     } [@@deriving sexp]
+   ;;
+
+  let get_default = Qpackage.get_ezfio_default "ao_two_e_eff_pot";;
+
+(* =~=~=~=~=~=~==~=~=~=~=~=~ *)
+(* Generate Special Function *)
+(* =~=~=~==~=~~=~=~=~=~=~=~=~ *)
+
+(* Read snippet for adjoint_tc_h *)
+  let read_adjoint_tc_h () =
+    if not (Ezfio.has_ao_two_e_eff_pot_adjoint_tc_h ()) then
+       get_default "adjoint_tc_h"
+       |> bool_of_string
+       |> Ezfio.set_ao_two_e_eff_pot_adjoint_tc_h
+    ;
+    Ezfio.get_ao_two_e_eff_pot_adjoint_tc_h ()
+  ;;
+(* Write snippet for adjoint_tc_h *)
+  let write_adjoint_tc_h =
+     Ezfio.set_ao_two_e_eff_pot_adjoint_tc_h
+  ;;
+
+(* Read snippet for grad_squared *)
+  let read_grad_squared () =
+    if not (Ezfio.has_ao_two_e_eff_pot_grad_squared ()) then
+       get_default "grad_squared"
+       |> bool_of_string
+       |> Ezfio.set_ao_two_e_eff_pot_grad_squared
+    ;
+    Ezfio.get_ao_two_e_eff_pot_grad_squared ()
+  ;;
+(* Write snippet for grad_squared *)
+  let write_grad_squared =
+     Ezfio.set_ao_two_e_eff_pot_grad_squared
+  ;;
+
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+(* Generate Global Function *)
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+
+(* Read all *)
+   let read() = 
+     Some
+     {
+       adjoint_tc_h                   = read_adjoint_tc_h ();
+       grad_squared                   = read_grad_squared ();
+     }
+   ;;
+(* Write all *)
+   let write{ 
+              adjoint_tc_h;
+              grad_squared;
+            } =
+     write_adjoint_tc_h                   adjoint_tc_h;
+     write_grad_squared                   grad_squared;
+   ;;
+(* to_string*)
+   let to_string b =
+     Printf.sprintf "
+   adjoint_tc_h = %s
+   grad_squared = %s
+   "
+       (string_of_bool b.adjoint_tc_h)
+       (string_of_bool b.grad_squared)
+   ;;
+(* to_rst*)
+   let to_rst b =
+     Printf.sprintf "
+   If |true|, you compute the adjoint of the transcorrelated Hamiltonian ::
+   
+     adjoint_tc_h = %s
+   
+   If |true|, you compute also the square of the gradient of the correlation factor ::
+   
+     grad_squared = %s
+   
+   "
+       (string_of_bool b.adjoint_tc_h)
+       (string_of_bool b.grad_squared)
+   |> Rst_string.of_string
+   ;;
+  include Generic_input_of_rst;;
+  let of_rst = of_rst t_of_sexp;;
+
+end

ocaml/Input_bi_ortho_mos.ml

@@ -0,0 +1,87 @@
+(* =~=~ *)
+(* Init *)
+(* =~=~ *)
+
+open Qptypes;;
+open Qputils;;
+open Sexplib.Std;;
+
+module Bi_ortho_mos : sig
+(* Generate type *)
+   type t = 
+     {
+       bi_ortho                       : bool;
+     } [@@deriving sexp]
+   ;;
+  val read  : unit -> t option
+  val write : t-> unit
+  val to_string : t -> string
+  val to_rst : t -> Rst_string.t
+  val of_rst : Rst_string.t -> t option
+end = struct
+(* Generate type *)
+   type t = 
+     {
+       bi_ortho                       : bool;
+     } [@@deriving sexp]
+   ;;
+
+  let get_default = Qpackage.get_ezfio_default "bi_ortho_mos";;
+
+(* =~=~=~=~=~=~==~=~=~=~=~=~ *)
+(* Generate Special Function *)
+(* =~=~=~==~=~~=~=~=~=~=~=~=~ *)
+
+(* Read snippet for bi_ortho *)
+  let read_bi_ortho () =
+    if not (Ezfio.has_bi_ortho_mos_bi_ortho ()) then
+       get_default "bi_ortho"
+       |> bool_of_string
+       |> Ezfio.set_bi_ortho_mos_bi_ortho
+    ;
+    Ezfio.get_bi_ortho_mos_bi_ortho ()
+  ;;
+(* Write snippet for bi_ortho *)
+  let write_bi_ortho =
+     Ezfio.set_bi_ortho_mos_bi_ortho
+  ;;
+
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+(* Generate Global Function *)
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+
+(* Read all *)
+   let read() = 
+     Some
+     {
+       bi_ortho                       = read_bi_ortho ();
+     }
+   ;;
+(* Write all *)
+   let write{ 
+              bi_ortho;
+            } =
+     write_bi_ortho                       bi_ortho;
+   ;;
+(* to_string*)
+   let to_string b =
+     Printf.sprintf "
+   bi_ortho = %s
+   "
+       (string_of_bool b.bi_ortho)
+   ;;
+(* to_rst*)
+   let to_rst b =
+     Printf.sprintf "
+   If |true|, the MO basis is assumed to be bi-orthonormal ::
+   
+     bi_ortho = %s
+   
+   "
+       (string_of_bool b.bi_ortho)
+   |> Rst_string.of_string
+   ;;
+  include Generic_input_of_rst;;
+  let of_rst = of_rst t_of_sexp;;
+
+end

ocaml/Input_cassd.ml

@@ -0,0 +1,113 @@
+(* =~=~ *)
+(* Init *)
+(* =~=~ *)
+
+open Qptypes;;
+open Qputils;;
+open Sexplib.Std;;
+
+module Cassd : sig
+(* Generate type *)
+   type t = 
+     {
+       do_ddci                        : bool;
+       do_only_1h1p                   : bool;
+     } [@@deriving sexp]
+   ;;
+  val read  : unit -> t option
+  val write : t-> unit
+  val to_string : t -> string
+  val to_rst : t -> Rst_string.t
+  val of_rst : Rst_string.t -> t option
+end = struct
+(* Generate type *)
+   type t = 
+     {
+       do_ddci                        : bool;
+       do_only_1h1p                   : bool;
+     } [@@deriving sexp]
+   ;;
+
+  let get_default = Qpackage.get_ezfio_default "cassd";;
+
+(* =~=~=~=~=~=~==~=~=~=~=~=~ *)
+(* Generate Special Function *)
+(* =~=~=~==~=~~=~=~=~=~=~=~=~ *)
+
+(* Read snippet for do_ddci *)
+  let read_do_ddci () =
+    if not (Ezfio.has_cassd_do_ddci ()) then
+       get_default "do_ddci"
+       |> bool_of_string
+       |> Ezfio.set_cassd_do_ddci
+    ;
+    Ezfio.get_cassd_do_ddci ()
+  ;;
+(* Write snippet for do_ddci *)
+  let write_do_ddci =
+     Ezfio.set_cassd_do_ddci
+  ;;
+
+(* Read snippet for do_only_1h1p *)
+  let read_do_only_1h1p () =
+    if not (Ezfio.has_cassd_do_only_1h1p ()) then
+       get_default "do_only_1h1p"
+       |> bool_of_string
+       |> Ezfio.set_cassd_do_only_1h1p
+    ;
+    Ezfio.get_cassd_do_only_1h1p ()
+  ;;
+(* Write snippet for do_only_1h1p *)
+  let write_do_only_1h1p =
+     Ezfio.set_cassd_do_only_1h1p
+  ;;
+
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+(* Generate Global Function *)
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+
+(* Read all *)
+   let read() = 
+     Some
+     {
+       do_ddci                        = read_do_ddci ();
+       do_only_1h1p                   = read_do_only_1h1p ();
+     }
+   ;;
+(* Write all *)
+   let write{ 
+              do_ddci;
+              do_only_1h1p;
+            } =
+     write_do_ddci                        do_ddci;
+     write_do_only_1h1p                   do_only_1h1p;
+   ;;
+(* to_string*)
+   let to_string b =
+     Printf.sprintf "
+   do_ddci = %s
+   do_only_1h1p = %s
+   "
+       (string_of_bool b.do_ddci)
+       (string_of_bool b.do_only_1h1p)
+   ;;
+(* to_rst*)
+   let to_rst b =
+     Printf.sprintf "
+   If true, remove purely inactive double excitations ::
+   
+     do_ddci = %s
+   
+   If true, do only one hole/one particle excitations ::
+   
+     do_only_1h1p = %s
+   
+   "
+       (string_of_bool b.do_ddci)
+       (string_of_bool b.do_only_1h1p)
+   |> Rst_string.of_string
+   ;;
+  include Generic_input_of_rst;;
+  let of_rst = of_rst t_of_sexp;;
+
+end

ocaml/Input_cipsi_deb.ml

@@ -0,0 +1,243 @@
+(* =~=~ *)
+(* Init *)
+(* =~=~ *)
+
+open Qptypes;;
+open Qputils;;
+open Sexplib.Std;;
+
+module Cipsi_deb : sig
+(* Generate type *)
+   type t = 
+     {
+       pert_2rdm                      : bool;
+       save_wf_after_selection        : bool;
+       seniority_max                  : int;
+       excitation_ref                 : int;
+       excitation_max                 : int;
+       excitation_alpha_max           : int;
+       excitation_beta_max            : int;
+     } [@@deriving sexp]
+   ;;
+  val read  : unit -> t option
+  val write : t-> unit
+  val to_string : t -> string
+  val to_rst : t -> Rst_string.t
+  val of_rst : Rst_string.t -> t option
+end = struct
+(* Generate type *)
+   type t = 
+     {
+       pert_2rdm                      : bool;
+       save_wf_after_selection        : bool;
+       seniority_max                  : int;
+       excitation_ref                 : int;
+       excitation_max                 : int;
+       excitation_alpha_max           : int;
+       excitation_beta_max            : int;
+     } [@@deriving sexp]
+   ;;
+
+  let get_default = Qpackage.get_ezfio_default "cipsi_deb";;
+
+(* =~=~=~=~=~=~==~=~=~=~=~=~ *)
+(* Generate Special Function *)
+(* =~=~=~==~=~~=~=~=~=~=~=~=~ *)
+
+(* Read snippet for excitation_alpha_max *)
+  let read_excitation_alpha_max () =
+    if not (Ezfio.has_cipsi_deb_excitation_alpha_max ()) then
+       get_default "excitation_alpha_max"
+       |> int_of_string
+       |> Ezfio.set_cipsi_deb_excitation_alpha_max
+    ;
+    Ezfio.get_cipsi_deb_excitation_alpha_max ()
+  ;;
+(* Write snippet for excitation_alpha_max *)
+  let write_excitation_alpha_max =
+     Ezfio.set_cipsi_deb_excitation_alpha_max
+  ;;
+
+(* Read snippet for excitation_beta_max *)
+  let read_excitation_beta_max () =
+    if not (Ezfio.has_cipsi_deb_excitation_beta_max ()) then
+       get_default "excitation_beta_max"
+       |> int_of_string
+       |> Ezfio.set_cipsi_deb_excitation_beta_max
+    ;
+    Ezfio.get_cipsi_deb_excitation_beta_max ()
+  ;;
+(* Write snippet for excitation_beta_max *)
+  let write_excitation_beta_max =
+     Ezfio.set_cipsi_deb_excitation_beta_max
+  ;;
+
+(* Read snippet for excitation_max *)
+  let read_excitation_max () =
+    if not (Ezfio.has_cipsi_deb_excitation_max ()) then
+       get_default "excitation_max"
+       |> int_of_string
+       |> Ezfio.set_cipsi_deb_excitation_max
+    ;
+    Ezfio.get_cipsi_deb_excitation_max ()
+  ;;
+(* Write snippet for excitation_max *)
+  let write_excitation_max =
+     Ezfio.set_cipsi_deb_excitation_max
+  ;;
+
+(* Read snippet for excitation_ref *)
+  let read_excitation_ref () =
+    if not (Ezfio.has_cipsi_deb_excitation_ref ()) then
+       get_default "excitation_ref"
+       |> int_of_string
+       |> Ezfio.set_cipsi_deb_excitation_ref
+    ;
+    Ezfio.get_cipsi_deb_excitation_ref ()
+  ;;
+(* Write snippet for excitation_ref *)
+  let write_excitation_ref =
+     Ezfio.set_cipsi_deb_excitation_ref
+  ;;
+
+(* Read snippet for pert_2rdm *)
+  let read_pert_2rdm () =
+    if not (Ezfio.has_cipsi_deb_pert_2rdm ()) then
+       get_default "pert_2rdm"
+       |> bool_of_string
+       |> Ezfio.set_cipsi_deb_pert_2rdm
+    ;
+    Ezfio.get_cipsi_deb_pert_2rdm ()
+  ;;
+(* Write snippet for pert_2rdm *)
+  let write_pert_2rdm =
+     Ezfio.set_cipsi_deb_pert_2rdm
+  ;;
+
+(* Read snippet for save_wf_after_selection *)
+  let read_save_wf_after_selection () =
+    if not (Ezfio.has_cipsi_deb_save_wf_after_selection ()) then
+       get_default "save_wf_after_selection"
+       |> bool_of_string
+       |> Ezfio.set_cipsi_deb_save_wf_after_selection
+    ;
+    Ezfio.get_cipsi_deb_save_wf_after_selection ()
+  ;;
+(* Write snippet for save_wf_after_selection *)
+  let write_save_wf_after_selection =
+     Ezfio.set_cipsi_deb_save_wf_after_selection
+  ;;
+
+(* Read snippet for seniority_max *)
+  let read_seniority_max () =
+    if not (Ezfio.has_cipsi_deb_seniority_max ()) then
+       get_default "seniority_max"
+       |> int_of_string
+       |> Ezfio.set_cipsi_deb_seniority_max
+    ;
+    Ezfio.get_cipsi_deb_seniority_max ()
+  ;;
+(* Write snippet for seniority_max *)
+  let write_seniority_max =
+     Ezfio.set_cipsi_deb_seniority_max
+  ;;
+
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+(* Generate Global Function *)
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+
+(* Read all *)
+   let read() = 
+     Some
+     {
+       pert_2rdm                      = read_pert_2rdm ();
+       save_wf_after_selection        = read_save_wf_after_selection ();
+       seniority_max                  = read_seniority_max ();
+       excitation_ref                 = read_excitation_ref ();
+       excitation_max                 = read_excitation_max ();
+       excitation_alpha_max           = read_excitation_alpha_max ();
+       excitation_beta_max            = read_excitation_beta_max ();
+     }
+   ;;
+(* Write all *)
+   let write{ 
+              pert_2rdm;
+              save_wf_after_selection;
+              seniority_max;
+              excitation_ref;
+              excitation_max;
+              excitation_alpha_max;
+              excitation_beta_max;
+            } =
+     write_pert_2rdm                      pert_2rdm;
+     write_save_wf_after_selection        save_wf_after_selection;
+     write_seniority_max                  seniority_max;
+     write_excitation_ref                 excitation_ref;
+     write_excitation_max                 excitation_max;
+     write_excitation_alpha_max           excitation_alpha_max;
+     write_excitation_beta_max            excitation_beta_max;
+   ;;
+(* to_string*)
+   let to_string b =
+     Printf.sprintf "
+   pert_2rdm = %s
+   save_wf_after_selection = %s
+   seniority_max = %s
+   excitation_ref = %s
+   excitation_max = %s
+   excitation_alpha_max = %s
+   excitation_beta_max = %s
+   "
+       (string_of_bool b.pert_2rdm)
+       (string_of_bool b.save_wf_after_selection)
+       (string_of_int b.seniority_max)
+       (string_of_int b.excitation_ref)
+       (string_of_int b.excitation_max)
+       (string_of_int b.excitation_alpha_max)
+       (string_of_int b.excitation_beta_max)
+   ;;
+(* to_rst*)
+   let to_rst b =
+     Printf.sprintf "
+   If true, computes the one- and two-body rdms with perturbation theory ::
+   
+     pert_2rdm = %s
+   
+   If true, saves the wave function after the selection, before the diagonalization ::
+   
+     save_wf_after_selection = %s
+   
+   Maximum number of allowed open shells. Using -1 selects all determinants ::
+   
+     seniority_max = %s
+   
+   1: Hartree-Fock determinant, 2:All determinants of the dominant configuration ::
+   
+     excitation_ref = %s
+   
+   Maximum number of excitation with respect to the Hartree-Fock determinant. Using -1 selects all determinants ::
+   
+     excitation_max = %s
+   
+   Maximum number of excitation for alpha determinants with respect to the Hartree-Fock determinant. Using -1 selects all determinants ::
+   
+     excitation_alpha_max = %s
+   
+   Maximum number of excitation for beta determinants with respect to the Hartree-Fock determinant. Using -1 selects all determinants ::
+   
+     excitation_beta_max = %s
+   
+   "
+       (string_of_bool b.pert_2rdm)
+       (string_of_bool b.save_wf_after_selection)
+       (string_of_int b.seniority_max)
+       (string_of_int b.excitation_ref)
+       (string_of_int b.excitation_max)
+       (string_of_int b.excitation_alpha_max)
+       (string_of_int b.excitation_beta_max)
+   |> Rst_string.of_string
+   ;;
+  include Generic_input_of_rst;;
+  let of_rst = of_rst t_of_sexp;;
+
+end

ocaml/Input_tc_h_clean.ml

@@ -0,0 +1,351 @@
+(* =~=~ *)
+(* Init *)
+(* =~=~ *)
+
+open Qptypes;;
+open Qputils;;
+open Sexplib.Std;;
+
+module Tc_h_clean : sig
+(* Generate type *)
+   type t = 
+     {
+       read_rl_eigv                   : bool;
+       comp_left_eigv                 : bool;
+       three_body_h_tc                : bool;
+       pure_three_body_h_tc           : bool;
+       double_normal_ord              : bool;
+       core_tc_op                     : bool;
+       full_tc_h_solver               : bool;
+       thresh_it_dav                  : Threshold.t;
+       max_it_dav                     : int;
+       thresh_psi_r                   : Threshold.t;
+       thresh_psi_r_norm              : bool;
+     } [@@deriving sexp]
+   ;;
+  val read  : unit -> t option
+  val write : t-> unit
+  val to_string : t -> string
+  val to_rst : t -> Rst_string.t
+  val of_rst : Rst_string.t -> t option
+end = struct
+(* Generate type *)
+   type t = 
+     {
+       read_rl_eigv                   : bool;
+       comp_left_eigv                 : bool;
+       three_body_h_tc                : bool;
+       pure_three_body_h_tc           : bool;
+       double_normal_ord              : bool;
+       core_tc_op                     : bool;
+       full_tc_h_solver               : bool;
+       thresh_it_dav                  : Threshold.t;
+       max_it_dav                     : int;
+       thresh_psi_r                   : Threshold.t;
+       thresh_psi_r_norm              : bool;
+     } [@@deriving sexp]
+   ;;
+
+  let get_default = Qpackage.get_ezfio_default "tc_h_clean";;
+
+(* =~=~=~=~=~=~==~=~=~=~=~=~ *)
+(* Generate Special Function *)
+(* =~=~=~==~=~~=~=~=~=~=~=~=~ *)
+
+(* Read snippet for comp_left_eigv *)
+  let read_comp_left_eigv () =
+    if not (Ezfio.has_tc_h_clean_comp_left_eigv ()) then
+       get_default "comp_left_eigv"
+       |> bool_of_string
+       |> Ezfio.set_tc_h_clean_comp_left_eigv
+    ;
+    Ezfio.get_tc_h_clean_comp_left_eigv ()
+  ;;
+(* Write snippet for comp_left_eigv *)
+  let write_comp_left_eigv =
+     Ezfio.set_tc_h_clean_comp_left_eigv
+  ;;
+
+(* Read snippet for core_tc_op *)
+  let read_core_tc_op () =
+    if not (Ezfio.has_tc_h_clean_core_tc_op ()) then
+       get_default "core_tc_op"
+       |> bool_of_string
+       |> Ezfio.set_tc_h_clean_core_tc_op
+    ;
+    Ezfio.get_tc_h_clean_core_tc_op ()
+  ;;
+(* Write snippet for core_tc_op *)
+  let write_core_tc_op =
+     Ezfio.set_tc_h_clean_core_tc_op
+  ;;
+
+(* Read snippet for double_normal_ord *)
+  let read_double_normal_ord () =
+    if not (Ezfio.has_tc_h_clean_double_normal_ord ()) then
+       get_default "double_normal_ord"
+       |> bool_of_string
+       |> Ezfio.set_tc_h_clean_double_normal_ord
+    ;
+    Ezfio.get_tc_h_clean_double_normal_ord ()
+  ;;
+(* Write snippet for double_normal_ord *)
+  let write_double_normal_ord =
+     Ezfio.set_tc_h_clean_double_normal_ord
+  ;;
+
+(* Read snippet for full_tc_h_solver *)
+  let read_full_tc_h_solver () =
+    if not (Ezfio.has_tc_h_clean_full_tc_h_solver ()) then
+       get_default "full_tc_h_solver"
+       |> bool_of_string
+       |> Ezfio.set_tc_h_clean_full_tc_h_solver
+    ;
+    Ezfio.get_tc_h_clean_full_tc_h_solver ()
+  ;;
+(* Write snippet for full_tc_h_solver *)
+  let write_full_tc_h_solver =
+     Ezfio.set_tc_h_clean_full_tc_h_solver
+  ;;
+
+(* Read snippet for max_it_dav *)
+  let read_max_it_dav () =
+    if not (Ezfio.has_tc_h_clean_max_it_dav ()) then
+       get_default "max_it_dav"
+       |> int_of_string
+       |> Ezfio.set_tc_h_clean_max_it_dav
+    ;
+    Ezfio.get_tc_h_clean_max_it_dav ()
+  ;;
+(* Write snippet for max_it_dav *)
+  let write_max_it_dav =
+     Ezfio.set_tc_h_clean_max_it_dav
+  ;;
+
+(* Read snippet for pure_three_body_h_tc *)
+  let read_pure_three_body_h_tc () =
+    if not (Ezfio.has_tc_h_clean_pure_three_body_h_tc ()) then
+       get_default "pure_three_body_h_tc"
+       |> bool_of_string
+       |> Ezfio.set_tc_h_clean_pure_three_body_h_tc
+    ;
+    Ezfio.get_tc_h_clean_pure_three_body_h_tc ()
+  ;;
+(* Write snippet for pure_three_body_h_tc *)
+  let write_pure_three_body_h_tc =
+     Ezfio.set_tc_h_clean_pure_three_body_h_tc
+  ;;
+
+(* Read snippet for read_rl_eigv *)
+  let read_read_rl_eigv () =
+    if not (Ezfio.has_tc_h_clean_read_rl_eigv ()) then
+       get_default "read_rl_eigv"
+       |> bool_of_string
+       |> Ezfio.set_tc_h_clean_read_rl_eigv
+    ;
+    Ezfio.get_tc_h_clean_read_rl_eigv ()
+  ;;
+(* Write snippet for read_rl_eigv *)
+  let write_read_rl_eigv =
+     Ezfio.set_tc_h_clean_read_rl_eigv
+  ;;
+
+(* Read snippet for three_body_h_tc *)
+  let read_three_body_h_tc () =
+    if not (Ezfio.has_tc_h_clean_three_body_h_tc ()) then
+       get_default "three_body_h_tc"
+       |> bool_of_string
+       |> Ezfio.set_tc_h_clean_three_body_h_tc
+    ;
+    Ezfio.get_tc_h_clean_three_body_h_tc ()
+  ;;
+(* Write snippet for three_body_h_tc *)
+  let write_three_body_h_tc =
+     Ezfio.set_tc_h_clean_three_body_h_tc
+  ;;
+
+(* Read snippet for thresh_it_dav *)
+  let read_thresh_it_dav () =
+    if not (Ezfio.has_tc_h_clean_thresh_it_dav ()) then
+       get_default "thresh_it_dav"
+       |> float_of_string
+       |> Ezfio.set_tc_h_clean_thresh_it_dav
+    ;
+    Ezfio.get_tc_h_clean_thresh_it_dav ()
+      |> Threshold.of_float
+  ;;
+(* Write snippet for thresh_it_dav *)
+  let write_thresh_it_dav var = 
+    Threshold.to_float var
+    |> Ezfio.set_tc_h_clean_thresh_it_dav
+  ;;
+
+(* Read snippet for thresh_psi_r *)
+  let read_thresh_psi_r () =
+    if not (Ezfio.has_tc_h_clean_thresh_psi_r ()) then
+       get_default "thresh_psi_r"
+       |> float_of_string
+       |> Ezfio.set_tc_h_clean_thresh_psi_r
+    ;
+    Ezfio.get_tc_h_clean_thresh_psi_r ()
+      |> Threshold.of_float
+  ;;
+(* Write snippet for thresh_psi_r *)
+  let write_thresh_psi_r var = 
+    Threshold.to_float var
+    |> Ezfio.set_tc_h_clean_thresh_psi_r
+  ;;
+
+(* Read snippet for thresh_psi_r_norm *)
+  let read_thresh_psi_r_norm () =
+    if not (Ezfio.has_tc_h_clean_thresh_psi_r_norm ()) then
+       get_default "thresh_psi_r_norm"
+       |> bool_of_string
+       |> Ezfio.set_tc_h_clean_thresh_psi_r_norm
+    ;
+    Ezfio.get_tc_h_clean_thresh_psi_r_norm ()
+  ;;
+(* Write snippet for thresh_psi_r_norm *)
+  let write_thresh_psi_r_norm =
+     Ezfio.set_tc_h_clean_thresh_psi_r_norm
+  ;;
+
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+(* Generate Global Function *)
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+
+(* Read all *)
+   let read() = 
+     Some
+     {
+       read_rl_eigv                   = read_read_rl_eigv ();
+       comp_left_eigv                 = read_comp_left_eigv ();
+       three_body_h_tc                = read_three_body_h_tc ();
+       pure_three_body_h_tc           = read_pure_three_body_h_tc ();
+       double_normal_ord              = read_double_normal_ord ();
+       core_tc_op                     = read_core_tc_op ();
+       full_tc_h_solver               = read_full_tc_h_solver ();
+       thresh_it_dav                  = read_thresh_it_dav ();
+       max_it_dav                     = read_max_it_dav ();
+       thresh_psi_r                   = read_thresh_psi_r ();
+       thresh_psi_r_norm              = read_thresh_psi_r_norm ();
+     }
+   ;;
+(* Write all *)
+   let write{ 
+              read_rl_eigv;
+              comp_left_eigv;
+              three_body_h_tc;
+              pure_three_body_h_tc;
+              double_normal_ord;
+              core_tc_op;
+              full_tc_h_solver;
+              thresh_it_dav;
+              max_it_dav;
+              thresh_psi_r;
+              thresh_psi_r_norm;
+            } =
+     write_read_rl_eigv                   read_rl_eigv;
+     write_comp_left_eigv                 comp_left_eigv;
+     write_three_body_h_tc                three_body_h_tc;
+     write_pure_three_body_h_tc           pure_three_body_h_tc;
+     write_double_normal_ord              double_normal_ord;
+     write_core_tc_op                     core_tc_op;
+     write_full_tc_h_solver               full_tc_h_solver;
+     write_thresh_it_dav                  thresh_it_dav;
+     write_max_it_dav                     max_it_dav;
+     write_thresh_psi_r                   thresh_psi_r;
+     write_thresh_psi_r_norm              thresh_psi_r_norm;
+   ;;
+(* to_string*)
+   let to_string b =
+     Printf.sprintf "
+   read_rl_eigv = %s
+   comp_left_eigv = %s
+   three_body_h_tc = %s
+   pure_three_body_h_tc = %s
+   double_normal_ord = %s
+   core_tc_op = %s
+   full_tc_h_solver = %s
+   thresh_it_dav = %s
+   max_it_dav = %s
+   thresh_psi_r = %s
+   thresh_psi_r_norm = %s
+   "
+       (string_of_bool b.read_rl_eigv)
+       (string_of_bool b.comp_left_eigv)
+       (string_of_bool b.three_body_h_tc)
+       (string_of_bool b.pure_three_body_h_tc)
+       (string_of_bool b.double_normal_ord)
+       (string_of_bool b.core_tc_op)
+       (string_of_bool b.full_tc_h_solver)
+       (Threshold.to_string b.thresh_it_dav)
+       (string_of_int b.max_it_dav)
+       (Threshold.to_string b.thresh_psi_r)
+       (string_of_bool b.thresh_psi_r_norm)
+   ;;
+(* to_rst*)
+   let to_rst b =
+     Printf.sprintf "
+   If |true|, read the right/left eigenvectors from ezfio ::
+   
+     read_rl_eigv = %s
+   
+   If |true|, computes also the left-eigenvector ::
+   
+     comp_left_eigv = %s
+   
+   If |true|, three-body terms are included ::
+   
+     three_body_h_tc = %s
+   
+   If |true|, pure triple excitation three-body terms are included ::
+   
+     pure_three_body_h_tc = %s
+   
+   If |true|, contracted double excitation three-body terms are included ::
+   
+     double_normal_ord = %s
+   
+   If |true|, takes the usual Hamiltonian for core orbitals (assumed to be doubly occupied) ::
+   
+     core_tc_op = %s
+   
+   If |true|, you diagonalize the full TC H matrix ::
+   
+     full_tc_h_solver = %s
+   
+   Thresholds on the energy for iterative Davidson used in TC ::
+   
+     thresh_it_dav = %s
+   
+   nb max of iteration in Davidson used in TC ::
+   
+     max_it_dav = %s
+   
+   Thresholds on the coefficients of the right-eigenvector. Used for PT2 computation. ::
+   
+     thresh_psi_r = %s
+   
+   If |true|, you prune the WF to compute the PT1 coef based on the norm. If False, the pruning is done through the amplitude on the right-coefficient. ::
+   
+     thresh_psi_r_norm = %s
+   
+   "
+       (string_of_bool b.read_rl_eigv)
+       (string_of_bool b.comp_left_eigv)
+       (string_of_bool b.three_body_h_tc)
+       (string_of_bool b.pure_three_body_h_tc)
+       (string_of_bool b.double_normal_ord)
+       (string_of_bool b.core_tc_op)
+       (string_of_bool b.full_tc_h_solver)
+       (Threshold.to_string b.thresh_it_dav)
+       (string_of_int b.max_it_dav)
+       (Threshold.to_string b.thresh_psi_r)
+       (string_of_bool b.thresh_psi_r_norm)
+   |> Rst_string.of_string
+   ;;
+  include Generic_input_of_rst;;
+  let of_rst = of_rst t_of_sexp;;
+
+end

ocaml/Input_tc_scf.ml

@@ -0,0 +1,143 @@
+(* =~=~ *)
+(* Init *)
+(* =~=~ *)
+
+open Qptypes;;
+open Qputils;;
+open Sexplib.Std;;
+
+module Tc_scf : sig
+(* Generate type *)
+   type t = 
+     {
+       bi_ortho                       : bool;
+       thresh_tcscf                   : Threshold.t;
+       n_it_tcscf_max                 : Strictly_positive_int.t;
+     } [@@deriving sexp]
+   ;;
+  val read  : unit -> t option
+  val write : t-> unit
+  val to_string : t -> string
+  val to_rst : t -> Rst_string.t
+  val of_rst : Rst_string.t -> t option
+end = struct
+(* Generate type *)
+   type t = 
+     {
+       bi_ortho                       : bool;
+       thresh_tcscf                   : Threshold.t;
+       n_it_tcscf_max                 : Strictly_positive_int.t;
+     } [@@deriving sexp]
+   ;;
+
+  let get_default = Qpackage.get_ezfio_default "tc_scf";;
+
+(* =~=~=~=~=~=~==~=~=~=~=~=~ *)
+(* Generate Special Function *)
+(* =~=~=~==~=~~=~=~=~=~=~=~=~ *)
+
+(* Read snippet for bi_ortho *)
+  let read_bi_ortho () =
+    if not (Ezfio.has_tc_scf_bi_ortho ()) then
+       get_default "bi_ortho"
+       |> bool_of_string
+       |> Ezfio.set_tc_scf_bi_ortho
+    ;
+    Ezfio.get_tc_scf_bi_ortho ()
+  ;;
+(* Write snippet for bi_ortho *)
+  let write_bi_ortho =
+     Ezfio.set_tc_scf_bi_ortho
+  ;;
+
+(* Read snippet for n_it_tcscf_max *)
+  let read_n_it_tcscf_max () =
+    if not (Ezfio.has_tc_scf_n_it_tcscf_max ()) then
+       get_default "n_it_tcscf_max"
+       |> int_of_string
+       |> Ezfio.set_tc_scf_n_it_tcscf_max
+    ;
+    Ezfio.get_tc_scf_n_it_tcscf_max ()
+      |> Strictly_positive_int.of_int
+  ;;
+(* Write snippet for n_it_tcscf_max *)
+  let write_n_it_tcscf_max var = 
+    Strictly_positive_int.to_int var
+    |> Ezfio.set_tc_scf_n_it_tcscf_max
+  ;;
+
+(* Read snippet for thresh_tcscf *)
+  let read_thresh_tcscf () =
+    if not (Ezfio.has_tc_scf_thresh_tcscf ()) then
+       get_default "thresh_tcscf"
+       |> float_of_string
+       |> Ezfio.set_tc_scf_thresh_tcscf
+    ;
+    Ezfio.get_tc_scf_thresh_tcscf ()
+      |> Threshold.of_float
+  ;;
+(* Write snippet for thresh_tcscf *)
+  let write_thresh_tcscf var = 
+    Threshold.to_float var
+    |> Ezfio.set_tc_scf_thresh_tcscf
+  ;;
+
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+(* Generate Global Function *)
+(* =~=~=~=~=~=~=~=~=~=~=~=~ *)
+
+(* Read all *)
+   let read() = 
+     Some
+     {
+       bi_ortho                       = read_bi_ortho ();
+       thresh_tcscf                   = read_thresh_tcscf ();
+       n_it_tcscf_max                 = read_n_it_tcscf_max ();
+     }
+   ;;
+(* Write all *)
+   let write{ 
+              bi_ortho;
+              thresh_tcscf;
+              n_it_tcscf_max;
+            } =
+     write_bi_ortho                       bi_ortho;
+     write_thresh_tcscf                   thresh_tcscf;
+     write_n_it_tcscf_max                 n_it_tcscf_max;
+   ;;
+(* to_string*)
+   let to_string b =
+     Printf.sprintf "
+   bi_ortho = %s
+   thresh_tcscf = %s
+   n_it_tcscf_max = %s
+   "
+       (string_of_bool b.bi_ortho)
+       (Threshold.to_string b.thresh_tcscf)
+       (Strictly_positive_int.to_string b.n_it_tcscf_max)
+   ;;
+(* to_rst*)
+   let to_rst b =
+     Printf.sprintf "
+   If |true|, the MO basis is assumed to be bi-orthonormal ::
+   
+     bi_ortho = %s
+   
+   Threshold on the convergence of the Hartree Fock energy. ::
+   
+     thresh_tcscf = %s
+   
+   Maximum number of SCF iterations ::
+   
+     n_it_tcscf_max = %s
+   
+   "
+       (string_of_bool b.bi_ortho)
+       (Threshold.to_string b.thresh_tcscf)
+       (Strictly_positive_int.to_string b.n_it_tcscf_max)
+   |> Rst_string.of_string
+   ;;
+  include Generic_input_of_rst;;
+  let of_rst = of_rst t_of_sexp;;
+
+end

ocaml/qp_create_ezfio.ml

@@ -681,10 +681,8 @@ let () =
   let open Command_line in
   begin
     "Creates an EZFIO directory from a standard xyz file or from a z-matrix file in Gaussian format.  The basis set is defined as a single string if all the atoms are taken from the same basis set, otherwise specific elements can be defined as follows:
-
     -b \"cc-pcvdz | H:cc-pvdz | C:6-31g\"
     -b \"cc-pvtz | 1,H:sto-3g | 3,H:6-31g\"
-
 If a file with the same name as the basis set exists, this file will be read.  Otherwise, the basis set is obtained from the database.
 "   |> set_description_doc ;
     set_header_doc (Sys.argv.(0) ^ " - Quantum Package command");

src/ao_basis/EZFIO.cfg

@@ -17,7 +17,7 @@ interface: ezfio, provider
 [ao_prim_num_max]
 type: integer
 doc: Maximum number of primitives
-default: =maxval(ao_basis.ao_prim_num)
+#default: =maxval(ao_basis.ao_prim_num)
 interface: ezfio
 
 [ao_nucl]
@@ -36,13 +36,13 @@ interface: ezfio, provider
 type: double precision
 doc: Primitive coefficients, read from input. Those should not be used directly, as the MOs are expressed on the basis of **normalized** AOs.
 size: (ao_basis.ao_num,ao_basis.ao_prim_num_max)
-interface: ezfio, provider
+interface: ezfio
 
 [ao_expo]
 type: double precision
 doc: Exponents for each primitive of each |AO|
 size: (ao_basis.ao_num,ao_basis.ao_prim_num_max)
-interface: ezfio, provider
+interface: ezfio
 
 [ao_md5]
 type: character*(32)
@@ -67,3 +67,4 @@ doc: Use normalized primitive functions
 interface: ezfio, provider
 default: true
 
+

src/ao_basis/aos.irp.f

@@ -1,11 +1,3 @@
-BEGIN_PROVIDER [ integer, ao_prim_num_max ]
- implicit none
- BEGIN_DOC
- ! Max number of primitives.
- END_DOC
- ao_prim_num_max = maxval(ao_prim_num)
-END_PROVIDER
-
 BEGIN_PROVIDER [ integer, ao_shell, (ao_num) ]
  implicit none
  BEGIN_DOC
@@ -23,6 +15,32 @@ BEGIN_PROVIDER [ integer, ao_shell, (ao_num) ]
 
 END_PROVIDER
 
+
+ BEGIN_PROVIDER [ double precision, ao_coef , (ao_num,ao_prim_num_max) ]
+&BEGIN_PROVIDER [ double precision, ao_expo , (ao_num,ao_prim_num_max) ]
+ implicit none
+ BEGIN_DOC
+! Primitive coefficients and exponents for each atomic orbital. Copied from shell info.
+ END_DOC
+
+ integer :: i, l
+ do i=1,ao_num
+   l = ao_shell(i)
+   ao_coef(i,:) = shell_coef(l,:)
+   ao_expo(i,:) = shell_expo(l,:)
+ end do
+
+END_PROVIDER
+
+
+BEGIN_PROVIDER [ integer, ao_prim_num_max ]
+ implicit none
+ BEGIN_DOC
+ ! Max number of primitives.
+ END_DOC
+ ao_prim_num_max = shell_prim_num_max
+END_PROVIDER
+
 BEGIN_PROVIDER [ integer, ao_first_of_shell, (shell_num) ]
  implicit none
  BEGIN_DOC
@@ -44,20 +62,20 @@ END_PROVIDER
   BEGIN_DOC
   ! Coefficients including the |AO| normalization
   END_DOC
+
+  do i=1,ao_num
+    l = ao_shell(i)
+    ao_coef_normalized(i,:) = shell_coef(l,:) * shell_normalization_factor(l)
+  end do
+
   double precision               :: norm,overlap_x,overlap_y,overlap_z,C_A(3), c
   integer                        :: l, powA(3), nz
   integer                        :: i,j,k
   nz=100
-  C_A(1) = 0.d0
+  C_A = 0.d0
-  C_A(2) = 0.d0
-  C_A(3) = 0.d0
-  ao_coef_normalized = 0.d0
 
   do i=1,ao_num
 
-!    powA(1) = ao_power(i,1) +  ao_power(i,2) +  ao_power(i,3)
-!    powA(2) = 0
-!    powA(3) = 0
     powA(1) = ao_power(i,1)
     powA(2) = ao_power(i,2)
     powA(3) = ao_power(i,3)
@@ -67,18 +85,9 @@ END_PROVIDER
       do j=1,ao_prim_num(i)
         call overlap_gaussian_xyz(C_A,C_A,ao_expo(i,j),ao_expo(i,j), &
            powA,powA,overlap_x,overlap_y,overlap_z,norm,nz)
-        ao_coef_normalized(i,j) = ao_coef(i,j)/dsqrt(norm)
+        ao_coef_normalized(i,j) = ao_coef_normalized(i,j)/dsqrt(norm)
-      enddo
-    else
-      do j=1,ao_prim_num(i)
-        ao_coef_normalized(i,j) = ao_coef(i,j)
       enddo
     endif
-
-    powA(1) = ao_power(i,1)
-    powA(2) = ao_power(i,2)
-    powA(3) = ao_power(i,3)
-
     ! Normalization of the contracted basis functions
     if (ao_normalized) then
       norm = 0.d0

src/ao_basis/aos_in_r.irp.f

@@ -12,21 +12,21 @@ double precision function ao_value(i,r)
  integer :: power_ao(3)
  double precision :: accu,dx,dy,dz,r2
  num_ao = ao_nucl(i)
-! power_ao(1:3)= ao_power(i,1:3)
+ power_ao(1:3)= ao_power(i,1:3)
-! center_ao(1:3) = nucl_coord(num_ao,1:3)
+ center_ao(1:3) = nucl_coord(num_ao,1:3)
-! dx = (r(1) - center_ao(1))
+ dx = (r(1) - center_ao(1))
-! dy = (r(2) - center_ao(2))
+ dy = (r(2) - center_ao(2))
-! dz = (r(3) - center_ao(3))
+ dz = (r(3) - center_ao(3))
-! r2 = dx*dx + dy*dy + dz*dz
+ r2 = dx*dx + dy*dy + dz*dz
-! dx = dx**power_ao(1)
+ dx = dx**power_ao(1)
-! dy = dy**power_ao(2)
+ dy = dy**power_ao(2)
-! dz = dz**power_ao(3)
+ dz = dz**power_ao(3)
 
  accu = 0.d0
-! do m=1,ao_prim_num(i)
+ do m=1,ao_prim_num(i)
-!   beta = ao_expo_ordered_transp(m,i)
+   beta = ao_expo_ordered_transp(m,i)
-!   accu += ao_coef_normalized_ordered_transp(m,i) * dexp(-beta*r2)
+   accu += ao_coef_normalized_ordered_transp(m,i) * dexp(-beta*r2)
-! enddo
+ enddo
  ao_value = accu * dx * dy * dz
 
 end

src/ao_basis/spherical_to_cartesian.irp.f

@@ -1,7 +1,7 @@
 ! Spherical to cartesian transformation matrix obtained with
 ! Horton (http://theochem.github.com/horton/, 2015)
 
-! First index is the index of the cartesian AO, obtained by ao_power_index
+! First index is the index of the carteisan AO, obtained by ao_power_index
 ! Second index is the index of the spherical AO
 
 BEGIN_PROVIDER [ double precision, cart_to_sphe_0, (1,1) ]

src/ao_many_one_e_ints/NEED

@@ -0,0 +1,5 @@
+ao_one_e_ints
+ao_two_e_ints
+becke_numerical_grid
+mo_one_e_ints
+dft_utils_in_r

src/ao_many_one_e_ints/README.rst

@@ -0,0 +1,25 @@
+==================
+ao_many_one_e_ints
+==================
+
+This module contains A LOT of one-electron integrals of the type 
+A_ij( r ) = \int dr' phi_i(r') w(r,r') phi_j(r') 
+where r is a point in real space. 
+
++) ao_gaus_gauss.irp.f: w(r,r') is a exp(-(r-r')^2)  , and can be multiplied by x/y/z
++) ao_erf_gauss.irp.f : w(r,r') is a exp(-(r-r')^2) erf(mu * |r-r'|)/|r-r'| , and can be multiplied by x/y/z
++) ao_erf_gauss_grad.irp.f: w(r,r') is a exp(-(r-r')^2) erf(mu * |r-r'|)/|r-r'| , and can be multiplied by x/y/z, but evaluated with also one gradient of an AO function. 
+
+Fit of a Slater function and corresponding integrals
+----------------------------------------------------
+The file fit_slat_gauss.irp.f contains many useful providers/routines to fit a Slater function with 20 gaussian. 
++) coef_fit_slat_gauss : coefficients of the gaussians to fit e^(-x)
++) expo_fit_slat_gauss : exponents of the gaussians to fit e^(-x)
+
+Integrals involving Slater functions : stg_gauss_int.irp.f
+
+Taylor expansion of full correlation factor
+-------------------------------------------
+In taylor_exp.irp.f you might find interesting integrals of the type 
+\int dr' exp( e^{-alpha |r-r|' - beta |r-r'|^2}) phi_i(r') phi_j(r') 
+evaluated as a Taylor expansion of the exponential. 

src/ao_many_one_e_ints/ao_erf_gauss.irp.f

@@ -0,0 +1,269 @@
+
+subroutine phi_j_erf_mu_r_xyz_phi(i,j,mu_in, C_center, xyz_ints)
+ implicit none
+ BEGIN_DOC
+! xyz_ints(1/2/3) = int dr phi_j(r) [erf(mu  |r - C|)/|r-C|]  x/y/z phi_i(r)
+!
+! where phi_i and phi_j are AOs
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in) :: mu_in, C_center(3)
+ double precision, intent(out):: xyz_ints(3)
+ integer :: num_A,power_A(3), num_b, power_B(3),power_B_tmp(3)
+ double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
+ integer :: n_pt_in,l,m,mm
+ xyz_ints = 0.d0
+ if(ao_overlap_abs(j,i).lt.1.d-12)then
+  return
+ endif
+ n_pt_in = n_pt_max_integrals
+ ! j 
+ num_A = ao_nucl(j)
+ power_A(1:3)= ao_power(j,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ ! i 
+ num_B = ao_nucl(i)
+ power_B(1:3)= ao_power(i,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+
+ do l=1,ao_prim_num(j)
+  alpha = ao_expo_ordered_transp(l,j)
+  do m=1,ao_prim_num(i)
+    beta = ao_expo_ordered_transp(m,i)
+    do mm = 1, 3
+     ! (x phi_i ) * phi_j 
+     ! x * (x - B_x)^b_x = b_x (x - B_x)^b_x + 1 * (x - B_x)^{b_x+1}
+     !
+     ! first contribution :: B_x (x - B_x)^b_x :: usual integral multiplied by B_x
+     power_B_tmp = power_B
+     contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B_tmp,alpha,beta,C_center,n_pt_in,mu_in)  
+     xyz_ints(mm) += contrib * B_center(mm) * ao_coef_normalized_ordered_transp(l,j)             &
+                                            * ao_coef_normalized_ordered_transp(m,i) 
+     ! second contribution :: 1 * (x - B_x)^(b_x+1) :: integral with b_x=>b_x+1 
+     power_B_tmp(mm) += 1
+     contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B_tmp,alpha,beta,C_center,n_pt_in,mu_in)  
+     xyz_ints(mm) += contrib * 1.d0        * ao_coef_normalized_ordered_transp(l,j)             &
+                                           * ao_coef_normalized_ordered_transp(m,i) 
+    enddo
+  enddo
+ enddo
+end
+
+
+double precision function phi_j_erf_mu_r_phi(i,j,mu_in, C_center)
+ implicit none
+ BEGIN_DOC
+! phi_j_erf_mu_r_phi  = int dr phi_j(r) [erf(mu  |r - C|)/|r-C|]  phi_i(r)
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in) :: mu_in, C_center(3)
+ integer :: num_A,power_A(3), num_b, power_B(3)
+ double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
+ integer :: n_pt_in,l,m
+ phi_j_erf_mu_r_phi = 0.d0
+ if(ao_overlap_abs(j,i).lt.1.d-12)then
+  return
+ endif
+ n_pt_in = n_pt_max_integrals
+ ! j 
+ num_A = ao_nucl(j)
+ power_A(1:3)= ao_power(j,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ ! i 
+ num_B = ao_nucl(i)
+ power_B(1:3)= ao_power(i,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+
+ do l=1,ao_prim_num(j)
+  alpha = ao_expo_ordered_transp(l,j)
+  do m=1,ao_prim_num(i)
+    beta = ao_expo_ordered_transp(m,i)
+    contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)  
+    phi_j_erf_mu_r_phi += contrib *  ao_coef_normalized_ordered_transp(l,j)             &
+                                  *  ao_coef_normalized_ordered_transp(m,i) 
+  enddo
+ enddo
+end
+
+
+
+subroutine erfc_mu_gauss_xyz_ij_ao(i,j,mu, C_center, delta,gauss_ints)
+ implicit none
+ BEGIN_DOC
+  ! gauss_ints(m) =   \int dr exp(-delta (r - C)^2 ) x/y/z * ( 1 - erf(mu |r-r'|))/ |r-r'| * AO_i(r') * AO_j(r')
+  !
+  ! with m = 1 ==> x, m = 2, m = 3 ==> z
+  !
+  !      m = 4 ==> no x/y/z
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in) :: mu, C_center(3),delta
+ double precision, intent(out):: gauss_ints(4)
+
+ integer :: num_A,power_A(3), num_b, power_B(3)
+ double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
+ double precision :: xyz_ints(4)
+ integer :: n_pt_in,l,m,mm
+ gauss_ints = 0.d0
+ if(ao_overlap_abs(j,i).lt.1.d-12)then
+  return
+ endif
+ n_pt_in = n_pt_max_integrals
+ ! j 
+ num_A = ao_nucl(j)
+ power_A(1:3)= ao_power(j,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ ! i 
+ num_B = ao_nucl(i)
+ power_B(1:3)= ao_power(i,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+
+ gauss_ints = 0.d0
+ do l=1,ao_prim_num(j)
+  alpha = ao_expo_ordered_transp(l,j)
+  do m=1,ao_prim_num(i)
+    beta = ao_expo_ordered_transp(m,i)
+    call erfc_mu_gauss_xyz(C_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in,xyz_ints)
+    do mm = 1, 4
+     gauss_ints(mm) += xyz_ints(mm)  * ao_coef_normalized_ordered_transp(l,j)             &
+                                     * ao_coef_normalized_ordered_transp(m,i) 
+    enddo
+  enddo
+ enddo
+end
+
+subroutine erf_mu_gauss_ij_ao(i,j,mu, C_center, delta,gauss_ints)
+ implicit none
+ BEGIN_DOC
+  ! gauss_ints(m) =   \int dr exp(-delta (r - C)^2 )  * erf(mu |r-r'|)/ |r-r'| * AO_i(r') * AO_j(r')
+  !
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in) :: mu, C_center(3),delta
+ double precision, intent(out):: gauss_ints
+
+ integer :: num_A,power_A(3), num_b, power_B(3)
+ double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
+ double precision :: integral , erf_mu_gauss
+ integer :: n_pt_in,l,m,mm
+ gauss_ints = 0.d0
+ if(ao_overlap_abs(j,i).lt.1.d-12)then
+  return
+ endif
+ n_pt_in = n_pt_max_integrals
+ ! j 
+ num_A = ao_nucl(j)
+ power_A(1:3)= ao_power(j,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ ! i 
+ num_B = ao_nucl(i)
+ power_B(1:3)= ao_power(i,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+
+ do l=1,ao_prim_num(j)
+  alpha = ao_expo_ordered_transp(l,j)
+  do m=1,ao_prim_num(i)
+    beta = ao_expo_ordered_transp(m,i)
+    if(dabs(ao_coef_normalized_ordered_transp(l,j) * ao_coef_normalized_ordered_transp(m,i)).lt.1.d-12)cycle
+    integral = erf_mu_gauss(C_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in)
+    gauss_ints += integral * ao_coef_normalized_ordered_transp(l,j)             &
+                           * ao_coef_normalized_ordered_transp(m,i) 
+  enddo
+ enddo
+end
+
+
+subroutine NAI_pol_x_mult_erf_ao(i_ao,j_ao,mu_in,C_center,ints)
+ implicit none
+  BEGIN_DOC
+  ! Computes the following integral :
+  ! $\int_{-\infty}^{infty} dr x * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
+  !
+  ! $\int_{-\infty}^{infty} dr y * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
+  !
+  ! $\int_{-\infty}^{infty} dr z * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
+  END_DOC
+ include 'utils/constants.include.F'                                                                                                                                  
+ integer, intent(in) :: i_ao,j_ao
+ double precision, intent(in) :: mu_in, C_center(3)
+ double precision, intent(out):: ints(3)
+ double precision               :: A_center(3), B_center(3),integral, alpha,beta
+ double precision               :: NAI_pol_mult_erf
+ integer                        :: i,j,num_A,num_B, power_A(3), power_B(3), n_pt_in, power_xA(3),m
+ ints = 0.d0
+ if(ao_overlap_abs(j_ao,i_ao).lt.1.d-12)then
+  return
+ endif
+ num_A = ao_nucl(i_ao)
+ power_A(1:3)= ao_power(i_ao,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ num_B = ao_nucl(j_ao)
+ power_B(1:3)= ao_power(j_ao,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+ n_pt_in = n_pt_max_integrals
+
+
+ do i = 1, ao_prim_num(i_ao)
+  alpha = ao_expo_ordered_transp(i,i_ao)
+   do m = 1, 3
+    power_xA = power_A
+    ! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
+    power_xA(m) += 1
+    do j = 1, ao_prim_num(j_ao)
+      beta = ao_expo_ordered_transp(j,j_ao)
+      ! First term = (x-Ax)**(ax+1)
+      integral =  NAI_pol_mult_erf(A_center,B_center,power_xA,power_B,alpha,beta,C_center,n_pt_in,mu_in)
+      ints(m) += integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
+      ! Second term = Ax * (x-Ax)**(ax)
+      integral =  NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
+      ints(m) += A_center(m) * integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
+    enddo
+  enddo
+ enddo
+end
+
+subroutine NAI_pol_x_specify_mult_erf_ao(i_ao,j_ao,mu_in,C_center,m,ints)
+ implicit none
+  BEGIN_DOC
+  ! Computes the following integral :
+  ! $\int_{-\infty}^{infty} dr X(m) * \chi_i(r) \chi_j(r) \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
+  !
+  ! if m == 1 X(m) = x, m == 1 X(m) = y, m == 1 X(m) = z
+  END_DOC
+ include 'utils/constants.include.F'                                                                                                                                  
+ integer, intent(in) :: i_ao,j_ao,m
+ double precision, intent(in) :: mu_in, C_center(3)
+ double precision, intent(out):: ints
+ double precision               :: A_center(3), B_center(3),integral, alpha,beta
+ double precision               :: NAI_pol_mult_erf
+ integer                        :: i,j,num_A,num_B, power_A(3), power_B(3), n_pt_in, power_xA(3)
+ ints = 0.d0
+ if(ao_overlap_abs(j_ao,i_ao).lt.1.d-12)then
+  return
+ endif
+ num_A = ao_nucl(i_ao)
+ power_A(1:3)= ao_power(i_ao,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ num_B = ao_nucl(j_ao)
+ power_B(1:3)= ao_power(j_ao,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+ n_pt_in = n_pt_max_integrals
+
+
+ do i = 1, ao_prim_num(i_ao)
+  alpha = ao_expo_ordered_transp(i,i_ao)
+    power_xA = power_A
+    ! x * phi_i(r) = x * (x-Ax)**ax = (x-Ax)**(ax+1) + Ax * (x-Ax)**ax
+    power_xA(m) += 1
+    do j = 1, ao_prim_num(j_ao)
+      beta = ao_expo_ordered_transp(j,j_ao)
+      ! First term = (x-Ax)**(ax+1)
+      integral =  NAI_pol_mult_erf(A_center,B_center,power_xA,power_B,alpha,beta,C_center,n_pt_in,mu_in)
+      ints += integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
+      ! Second term = Ax * (x-Ax)**(ax)
+      integral =  NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
+      ints += A_center(m) * integral * ao_coef_normalized_ordered_transp(j,j_ao)*ao_coef_normalized_ordered_transp(i,i_ao)
+    enddo
+ enddo
+end
+

src/ao_many_one_e_ints/ao_erf_gauss_grad.irp.f

@@ -0,0 +1,150 @@
+subroutine phi_j_erf_mu_r_dxyz_phi(i,j,mu_in, C_center, dxyz_ints)
+ implicit none
+ BEGIN_DOC
+! dxyz_ints(1/2/3) = int dr phi_i(r) [erf(mu  |r - C|)/|r-C|]  d/d(x/y/z) phi_i(r)
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in) :: mu_in, C_center(3)
+ double precision, intent(out):: dxyz_ints(3)
+ integer :: num_A,power_A(3), num_b, power_B(3),power_B_tmp(3)
+ double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf,coef,thr
+ integer :: n_pt_in,l,m,mm
+ thr = 1.d-12
+ dxyz_ints = 0.d0
+ if(ao_overlap_abs(j,i).lt.thr)then
+  return
+ endif
+
+ n_pt_in = n_pt_max_integrals
+ ! j 
+ num_A = ao_nucl(j)
+ power_A(1:3)= ao_power(j,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ ! i 
+ num_B = ao_nucl(i)
+ power_B(1:3)= ao_power(i,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+
+ do l=1,ao_prim_num(j)
+  alpha = ao_expo_ordered_transp(l,j)
+  do m=1,ao_prim_num(i)
+    beta = ao_expo_ordered_transp(m,i)
+    coef = ao_coef_normalized_ordered_transp(l,j) * ao_coef_normalized_ordered_transp(m,i) 
+    if(dabs(coef).lt.thr)cycle
+    do mm = 1, 3
+     ! (d/dx phi_i ) * phi_j 
+     ! d/dx * (x - B_x)^b_x exp(-beta * (x -B_x)^2)= [b_x * (x - B_x)^(b_x - 1) - 2 beta * (x - B_x)^(b_x + 1)] exp(-beta * (x -B_x)^2)
+     !
+     ! first contribution :: b_x (x - B_x)^(b_x-1) :: integral with b_x=>b_x-1 multiplied by b_x
+     power_B_tmp = power_B
+     power_B_tmp(mm) += -1
+     contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B_tmp,alpha,beta,C_center,n_pt_in,mu_in)  
+     dxyz_ints(mm) += contrib * dble(power_B(mm)) * coef 
+                                                  
+     ! second contribution ::  - 2 beta * (x - B_x)^(b_x + 1) :: integral with b_x=> b_x+1 multiplied by -2 * beta
+     power_B_tmp = power_B
+     power_B_tmp(mm) += 1
+     contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B_tmp,alpha,beta,C_center,n_pt_in,mu_in)  
+     dxyz_ints(mm) += contrib * (-2.d0 * beta )  * coef 
+                                                 
+    enddo
+  enddo
+ enddo
+end
+
+
+
+
+subroutine phi_j_erf_mu_r_dxyz_phi_bis(i,j,mu_in, C_center, dxyz_ints)
+ implicit none
+ BEGIN_DOC
+! dxyz_ints(1/2/3) = int dr phi_j(r) [erf(mu  |r - C|)/|r-C|]  d/d(x/y/z) phi_i(r)
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in) :: mu_in, C_center(3)
+ double precision, intent(out):: dxyz_ints(3)
+ integer :: num_A,power_A(3), num_b, power_B(3),power_B_tmp(3)
+ double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
+ double precision :: thr, coef
+ integer :: n_pt_in,l,m,mm,kk
+ thr = 1.d-12
+ dxyz_ints = 0.d0
+ if(ao_overlap_abs(j,i).lt.thr)then
+  return
+ endif
+
+ n_pt_in = n_pt_max_integrals
+ ! j == A 
+ num_A = ao_nucl(j)
+ power_A(1:3)= ao_power(j,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ ! i == B
+ num_B = ao_nucl(i)
+ power_B(1:3)= ao_power(i,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+
+ dxyz_ints = 0.d0
+ do l=1,ao_prim_num(j)
+  alpha = ao_expo_ordered_transp(l,j)
+  do m=1,ao_prim_num(i)
+    beta = ao_expo_ordered_transp(m,i)
+    do kk = 1, 2 ! loop over the extra terms induced by the d/dx/y/z * AO(i)
+     do mm = 1, 3
+      power_B_tmp = power_B
+      power_B_tmp(mm) = power_ord_grad_transp(kk,mm,i)
+      coef = ao_coef_normalized_ordered_transp(l,j) * ao_coef_ord_grad_transp(kk,mm,m,i) 
+      if(dabs(coef).lt.thr)cycle
+      contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B_tmp,alpha,beta,C_center,n_pt_in,mu_in)  
+      dxyz_ints(mm) += contrib * coef 
+     enddo
+    enddo
+  enddo
+ enddo
+end
+
+subroutine phi_j_erf_mu_r_xyz_dxyz_phi(i,j,mu_in, C_center, dxyz_ints)
+ implicit none
+ BEGIN_DOC
+! dxyz_ints(1/2/3) = int dr phi_j(r) x/y/z [erf(mu  |r - C|)/|r-C|]  d/d(x/y/z) phi_i(r)
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in) :: mu_in, C_center(3)
+ double precision, intent(out):: dxyz_ints(3)
+ integer :: num_A,power_A(3), num_b, power_B(3),power_B_tmp(3)
+ double precision :: alpha, beta, A_center(3), B_center(3),contrib,NAI_pol_mult_erf
+ double precision :: thr, coef
+ integer :: n_pt_in,l,m,mm,kk
+ thr = 1.d-12
+ dxyz_ints = 0.d0
+ if(ao_overlap_abs(j,i).lt.thr)then
+  return
+ endif
+
+ n_pt_in = n_pt_max_integrals
+ ! j == A 
+ num_A = ao_nucl(j)
+ power_A(1:3)= ao_power(j,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ ! i == B
+ num_B = ao_nucl(i)
+ power_B(1:3)= ao_power(i,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+
+ dxyz_ints = 0.d0
+ do l=1,ao_prim_num(j)
+  alpha = ao_expo_ordered_transp(l,j)
+  do m=1,ao_prim_num(i)
+    beta = ao_expo_ordered_transp(m,i)
+    do kk = 1, 4 ! loop over the extra terms induced by the x/y/z * d dx/y/z AO(i)
+     do mm = 1, 3
+      power_B_tmp = power_B
+      power_B_tmp(mm) = power_ord_xyz_grad_transp(kk,mm,i)
+      coef = ao_coef_normalized_ordered_transp(l,j) * ao_coef_ord_xyz_grad_transp(kk,mm,m,i) 
+      if(dabs(coef).lt.thr)cycle
+      contrib = NAI_pol_mult_erf(A_center,B_center,power_A,power_B_tmp,alpha,beta,C_center,n_pt_in,mu_in)  
+      dxyz_ints(mm) += contrib * coef 
+     enddo
+    enddo
+  enddo
+ enddo
+end

src/ao_many_one_e_ints/ao_gaus_gauss.irp.f

@@ -0,0 +1,137 @@
+subroutine overlap_gauss_xyz_r12_ao(D_center,delta,i,j,gauss_ints)
+ implicit none
+ BEGIN_DOC
+! gauss_ints(m) = \int dr AO_i(r) AO_j(r) x/y/z e^{-delta |r-D_center|^2}
+!
+! with m == 1 ==> x, m == 2 ==> y, m == 3 ==> z
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in)  :: D_center(3), delta
+ double precision, intent(out) :: gauss_ints(3)
+
+ integer :: num_a,num_b,power_A(3), power_B(3),l,k,m
+ double precision :: A_center(3), B_center(3),overlap_gauss_r12,alpha,beta,gauss_ints_tmp(3)
+ gauss_ints = 0.d0
+ if(ao_overlap_abs(j,i).lt.1.d-12)then
+  return
+ endif
+ num_A = ao_nucl(i)
+ power_A(1:3)= ao_power(i,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ num_B = ao_nucl(j)
+ power_B(1:3)= ao_power(j,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+ do l=1,ao_prim_num(i)
+  alpha = ao_expo_ordered_transp(l,i)     
+  do k=1,ao_prim_num(j)
+   beta = ao_expo_ordered_transp(k,j)     
+   call overlap_gauss_xyz_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,gauss_ints_tmp)
+   do m = 1, 3
+    gauss_ints(m) += gauss_ints_tmp(m) *  ao_coef_normalized_ordered_transp(l,i)             &
+                                       *  ao_coef_normalized_ordered_transp(k,j) 
+   enddo
+  enddo 
+ enddo
+end
+
+
+
+double precision function overlap_gauss_xyz_r12_ao_specific(D_center,delta,i,j,mx)
+ implicit none
+ BEGIN_DOC
+! \int dr AO_i(r) AO_j(r) x/y/z e^{-delta |r-D_center|^2}
+!
+! with mx == 1 ==> x, mx == 2 ==> y, mx == 3 ==> z
+ END_DOC
+ integer, intent(in) :: i,j,mx
+ double precision, intent(in)  :: D_center(3), delta
+
+ integer :: num_a,num_b,power_A(3), power_B(3),l,k
+ double precision :: gauss_int
+ double precision :: A_center(3), B_center(3),overlap_gauss_r12,alpha,beta
+ double precision :: overlap_gauss_xyz_r12_specific
+ overlap_gauss_xyz_r12_ao_specific = 0.d0
+ if(ao_overlap_abs(j,i).lt.1.d-12)then
+  return
+ endif
+ num_A = ao_nucl(i)
+ power_A(1:3)= ao_power(i,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ num_B = ao_nucl(j)
+ power_B(1:3)= ao_power(j,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+ do l=1,ao_prim_num(i)
+  alpha = ao_expo_ordered_transp(l,i)     
+  do k=1,ao_prim_num(j)
+   beta = ao_expo_ordered_transp(k,j)     
+   gauss_int = overlap_gauss_xyz_r12_specific(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,mx)
+   overlap_gauss_xyz_r12_ao_specific = gauss_int *  ao_coef_normalized_ordered_transp(l,i)             &
+                                                 *  ao_coef_normalized_ordered_transp(k,j) 
+  enddo 
+ enddo
+end
+
+
+subroutine overlap_gauss_r12_all_ao(D_center,delta,aos_ints)
+ implicit none
+ double precision, intent(in) :: D_center(3), delta
+ double precision, intent(out):: aos_ints(ao_num,ao_num)
+
+ integer :: num_a,num_b,power_A(3), power_B(3),l,k,i,j
+ double precision :: A_center(3), B_center(3),overlap_gauss_r12,alpha,beta,analytical_j
+ aos_ints = 0.d0
+ do i = 1, ao_num
+  do j = 1, ao_num
+   if(ao_overlap_abs(j,i).lt.1.d-12)cycle
+   num_A = ao_nucl(i)
+   power_A(1:3)= ao_power(i,1:3)
+   A_center(1:3) = nucl_coord(num_A,1:3)
+   num_B = ao_nucl(j)
+   power_B(1:3)= ao_power(j,1:3)
+   B_center(1:3) = nucl_coord(num_B,1:3)
+   do l=1,ao_prim_num(i)
+    alpha = ao_expo_ordered_transp(l,i)     
+    do k=1,ao_prim_num(j)
+     beta = ao_expo_ordered_transp(k,j)     
+     analytical_j = overlap_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta)
+     aos_ints(j,i) += analytical_j *  ao_coef_normalized_ordered_transp(l,i)             &
+                                   *  ao_coef_normalized_ordered_transp(k,j) 
+    enddo 
+   enddo
+  enddo
+ enddo
+end
+
+double precision function overlap_gauss_r12_ao(D_center,delta,i,j)
+ implicit none
+ BEGIN_DOC
+! \int dr AO_i(r) AO_j(r) e^{-delta |r-D_center|^2}
+ END_DOC
+ integer, intent(in) :: i,j
+ double precision, intent(in) :: D_center(3), delta
+
+ integer :: num_a,num_b,power_A(3), power_B(3),l,k
+ double precision :: A_center(3), B_center(3),overlap_gauss_r12,alpha,beta,analytical_j
+ overlap_gauss_r12_ao = 0.d0
+ if(ao_overlap_abs(j,i).lt.1.d-12)then
+  return
+ endif
+ ! TODO :: PUT CYCLES IN LOOPS
+ num_A = ao_nucl(i)
+ power_A(1:3)= ao_power(i,1:3)
+ A_center(1:3) = nucl_coord(num_A,1:3)
+ num_B = ao_nucl(j)
+ power_B(1:3)= ao_power(j,1:3)
+ B_center(1:3) = nucl_coord(num_B,1:3)
+ do l=1,ao_prim_num(i)
+  alpha = ao_expo_ordered_transp(l,i)     
+  do k=1,ao_prim_num(j)
+   beta = ao_expo_ordered_transp(k,j)     
+   analytical_j = overlap_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta)
+   overlap_gauss_r12_ao += analytical_j *  ao_coef_normalized_ordered_transp(l,i)             &
+                                        *  ao_coef_normalized_ordered_transp(k,j) 
+  enddo 
+ enddo
+end
+
+

src/ao_many_one_e_ints/fit_slat_gauss.irp.f

@@ -0,0 +1,94 @@
+ BEGIN_PROVIDER [integer, n_max_fit_slat]
+ implicit none
+ BEGIN_DOC
+! number of gaussian to fit exp(-x)
+!
+! I took 20 gaussians from the program bassto.f
+ END_DOC
+ n_max_fit_slat = 20
+ END_PROVIDER
+
+ BEGIN_PROVIDER [double precision, coef_fit_slat_gauss, (n_max_fit_slat)]
+&BEGIN_PROVIDER [double precision, expo_fit_slat_gauss, (n_max_fit_slat)]
+ implicit none
+  include 'constants.include.F'
+ BEGIN_DOC
+ ! fit the exp(-x) as 
+ !
+ ! \sum_{i = 1, n_max_fit_slat} coef_fit_slat_gauss(i) * exp(-expo_fit_slat_gauss(i) * x**2)
+ !
+ ! The coefficient are taken from the program bassto.f
+ END_DOC
+
+
+      expo_fit_slat_gauss(01)=30573.77073000000
+      coef_fit_slat_gauss(01)=0.00338925525
+      expo_fit_slat_gauss(02)=5608.45238100000
+      coef_fit_slat_gauss(02)=0.00536433869
+      expo_fit_slat_gauss(03)=1570.95673400000
+      coef_fit_slat_gauss(03)=0.00818702846
+      expo_fit_slat_gauss(04)=541.39785110000
+      coef_fit_slat_gauss(04)=0.01202047655
+      expo_fit_slat_gauss(05)=212.43469630000
+      coef_fit_slat_gauss(05)=0.01711289568
+      expo_fit_slat_gauss(06)=91.31444574000
+      coef_fit_slat_gauss(06)=0.02376001022
+      expo_fit_slat_gauss(07)=42.04087246000
+      coef_fit_slat_gauss(07)=0.03229121736
+      expo_fit_slat_gauss(08)=20.43200443000
+      coef_fit_slat_gauss(08)=0.04303646818
+      expo_fit_slat_gauss(09)=10.37775161000
+      coef_fit_slat_gauss(09)=0.05624657578
+      expo_fit_slat_gauss(10)=5.46880754500
+      coef_fit_slat_gauss(10)=0.07192311571
+      expo_fit_slat_gauss(11)=2.97373529200
+      coef_fit_slat_gauss(11)=0.08949389001
+      expo_fit_slat_gauss(12)=1.66144190200
+      coef_fit_slat_gauss(12)=0.10727599240
+      expo_fit_slat_gauss(13)=0.95052560820
+      coef_fit_slat_gauss(13)=0.12178961750
+      expo_fit_slat_gauss(14)=0.55528683970
+      coef_fit_slat_gauss(14)=0.12740141870
+      expo_fit_slat_gauss(15)=0.33043360020
+      coef_fit_slat_gauss(15)=0.11759168160
+      expo_fit_slat_gauss(16)=0.19982303230
+      coef_fit_slat_gauss(16)=0.08953504394
+      expo_fit_slat_gauss(17)=0.12246840760
+      coef_fit_slat_gauss(17)=0.05066721317
+      expo_fit_slat_gauss(18)=0.07575825322
+      coef_fit_slat_gauss(18)=0.01806363869
+      expo_fit_slat_gauss(19)=0.04690146243
+      coef_fit_slat_gauss(19)=0.00305632563
+      expo_fit_slat_gauss(20)=0.02834749861
+      coef_fit_slat_gauss(20)=0.00013317513
+
+
+
+END_PROVIDER 
+
+double precision function slater_fit_gam(x,gam)
+ implicit none
+ double precision, intent(in) :: x,gam
+ BEGIN_DOC
+! fit of the function exp(-gam * x) with gaussian functions 
+ END_DOC
+ integer :: i
+ slater_fit_gam = 0.d0
+ do i = 1, n_max_fit_slat
+  slater_fit_gam += coef_fit_slat_gauss(i) * dexp(-expo_fit_slat_gauss(i) * gam * gam * x * x)
+ enddo
+end
+
+subroutine expo_fit_slater_gam(gam,expos)
+ implicit none
+ BEGIN_DOC
+! returns the array of the exponents of the gaussians to fit exp(-gam*x)
+ END_DOC
+ double precision, intent(in)  :: gam
+ double precision, intent(out) :: expos(n_max_fit_slat)
+ integer :: i
+ do i = 1, n_max_fit_slat
+  expos(i) = expo_fit_slat_gauss(i) * gam * gam
+ enddo
+end
+

src/ao_many_one_e_ints/grad_related_ints.irp.f

@@ -0,0 +1,342 @@
+BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu, ( ao_num, ao_num,n_points_final_grid)]
+ implicit none
+ BEGIN_DOC
+! int dr phi_i(r) phi_j(r) (erf(mu(R) |r - R| - 1)/|r - R|
+ END_DOC
+ integer :: i,j,ipoint
+ double precision :: mu,r(3),NAI_pol_mult_erf_ao
+ double precision :: int_mu, int_coulomb
+ provide mu_erf final_grid_points 
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ !$OMP PARALLEL                  &
+ !$OMP DEFAULT (NONE)            &
+ !$OMP PRIVATE (i,j,ipoint,mu,r,int_mu,int_coulomb) & 
+ !$OMP SHARED (ao_num,n_points_final_grid,v_ij_erf_rk_cst_mu,final_grid_points,mu_erf)
+ !$OMP DO SCHEDULE (dynamic)
+ do ipoint = 1, n_points_final_grid
+   do i = 1, ao_num
+    do j = i, ao_num
+     mu = mu_erf
+     r(1) = final_grid_points(1,ipoint)
+     r(2) = final_grid_points(2,ipoint)
+     r(3) = final_grid_points(3,ipoint)
+     int_mu = NAI_pol_mult_erf_ao(i,j,mu,r)
+     int_coulomb = NAI_pol_mult_erf_ao(i,j,1.d+9,r)
+     v_ij_erf_rk_cst_mu(j,i,ipoint)= (int_mu - int_coulomb )
+   enddo
+  enddo
+ enddo
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+ do ipoint = 1, n_points_final_grid
+  do i = 1, ao_num
+   do j = 1, i-1
+     v_ij_erf_rk_cst_mu(j,i,ipoint)= v_ij_erf_rk_cst_mu(i,j,ipoint)
+    enddo
+   enddo
+  enddo
+
+ call wall_time(wall1)
+ print*,'wall time for v_ij_erf_rk_cst_mu  ',wall1 - wall0
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu_transp, (n_points_final_grid, ao_num, ao_num)]
+ implicit none
+ BEGIN_DOC
+! int dr phi_i(r) phi_j(r) (erf(mu(R) |r - R| - 1)/|r - R|
+ END_DOC
+ integer :: i,j,ipoint
+ double precision :: mu,r(3),NAI_pol_mult_erf_ao
+ double precision :: int_mu, int_coulomb
+ provide mu_erf final_grid_points 
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ !$OMP PARALLEL                  &
+ !$OMP DEFAULT (NONE)            &
+ !$OMP PRIVATE (i,j,ipoint,mu,r,int_mu,int_coulomb) & 
+ !$OMP SHARED (ao_num,n_points_final_grid,v_ij_erf_rk_cst_mu_transp,final_grid_points,mu_erf)
+ !$OMP DO SCHEDULE (dynamic)
+ do i = 1, ao_num
+  do j = i, ao_num
+   do ipoint = 1, n_points_final_grid
+     mu = mu_erf 
+     r(1) = final_grid_points(1,ipoint)
+     r(2) = final_grid_points(2,ipoint)
+     r(3) = final_grid_points(3,ipoint)
+     int_mu = NAI_pol_mult_erf_ao(i,j,mu,r)
+     int_coulomb = NAI_pol_mult_erf_ao(i,j,1.d+9,r)
+     v_ij_erf_rk_cst_mu_transp(ipoint,j,i)= (int_mu - int_coulomb )
+   enddo
+  enddo
+ enddo
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+ do i = 1, ao_num
+  do j = 1, i-1
+   do ipoint = 1, n_points_final_grid
+     v_ij_erf_rk_cst_mu_transp(ipoint,j,i)= v_ij_erf_rk_cst_mu_transp(ipoint,i,j)
+    enddo
+   enddo
+  enddo
+
+ call wall_time(wall1)
+ print*,'wall time for v_ij_erf_rk_cst_mu_transp  ',wall1 - wall0
+END_PROVIDER 
+
+
+BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_tmp, (3,ao_num, ao_num,n_points_final_grid)]
+ implicit none
+ BEGIN_DOC
+! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
+ END_DOC
+ integer :: i,j,ipoint,m
+ double precision :: mu,r(3),ints(3),ints_coulomb(3)
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ !$OMP PARALLEL                  &
+ !$OMP DEFAULT (NONE)            &
+ !$OMP PRIVATE (i,j,ipoint,mu,r,ints,m,ints_coulomb) & 
+ !$OMP SHARED (ao_num,n_points_final_grid,x_v_ij_erf_rk_cst_mu_tmp,final_grid_points,mu_erf)
+ !$OMP DO SCHEDULE (dynamic)
+ do ipoint = 1, n_points_final_grid
+  do i = 1, ao_num
+   do j = i, ao_num
+    mu = mu_erf
+    r(1) = final_grid_points(1,ipoint)
+    r(2) = final_grid_points(2,ipoint)
+    r(3) = final_grid_points(3,ipoint)
+    call NAI_pol_x_mult_erf_ao(i,j,mu,r,ints)
+    call NAI_pol_x_mult_erf_ao(i,j,1.d+9,r,ints_coulomb)
+    do m = 1, 3
+     x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint) = ( ints(m) - ints_coulomb(m))
+    enddo
+   enddo
+  enddo
+ enddo
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+ do ipoint = 1, n_points_final_grid
+  do i = 1, ao_num
+   do j = 1, i-1
+    do m = 1, 3
+     x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint)= x_v_ij_erf_rk_cst_mu_tmp(m,i,j,ipoint)
+    enddo
+   enddo
+  enddo
+ enddo
+ call wall_time(wall1)
+ print*,'wall time for x_v_ij_erf_rk_cst_mu_tmp',wall1 - wall0
+
+
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu, (ao_num, ao_num,n_points_final_grid,3)]
+ implicit none
+ BEGIN_DOC
+! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
+ END_DOC
+ integer :: i,j,ipoint,m
+ double precision :: mu,r(3),ints,ints_coulomb
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ do ipoint = 1, n_points_final_grid
+  do i = 1, ao_num
+   do j = 1, ao_num
+    do m = 1, 3
+     x_v_ij_erf_rk_cst_mu(j,i,ipoint,m)= x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint)
+    enddo
+   enddo
+  enddo
+ enddo
+
+ call wall_time(wall1)
+ print*,'wall time for x_v_ij_erf_rk_cst_mu',wall1 - wall0
+
+END_PROVIDER 
+
+
+BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_transp, (ao_num, ao_num,3,n_points_final_grid)]
+ implicit none
+ BEGIN_DOC
+! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
+ END_DOC
+ integer :: i,j,ipoint,m
+ double precision :: mu,r(3),ints,ints_coulomb
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ do ipoint = 1, n_points_final_grid
+  do m = 1, 3
+   do i = 1, ao_num
+    do j = 1, ao_num
+     x_v_ij_erf_rk_cst_mu_transp(j,i,m,ipoint)= x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint)
+    enddo
+   enddo
+  enddo
+ enddo
+ call wall_time(wall1)
+ print*,'wall time for x_v_ij_erf_rk_cst_mu_transp',wall1 - wall0
+
+
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_transp_bis, (n_points_final_grid,ao_num, ao_num,3)]
+ implicit none
+ BEGIN_DOC
+! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
+ END_DOC
+ integer :: i,j,ipoint,m
+ double precision :: mu,r(3),ints,ints_coulomb
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ do m = 1, 3
+  do i = 1, ao_num
+   do j = 1, ao_num
+    do ipoint = 1, n_points_final_grid
+     x_v_ij_erf_rk_cst_mu_transp_bis(ipoint,j,i,m)= x_v_ij_erf_rk_cst_mu_tmp(m,j,i,ipoint)
+    enddo
+   enddo
+  enddo
+ enddo
+ call wall_time(wall1)
+ print*,'wall time for x_v_ij_erf_rk_cst_mu_transp',wall1 - wall0
+
+
+END_PROVIDER 
+
+
+BEGIN_PROVIDER [ double precision, d_dx_v_ij_erf_rk_cst_mu_tmp, (3,n_points_final_grid,ao_num, ao_num)]
+ implicit none
+ BEGIN_DOC
+! d_dx_v_ij_erf_rk_cst_mu_tmp(m,R,j,i) = int dr phi_j(r)) (erf(mu(R) |r - R|) - 1)/|r - R| d/dx (phi_i(r) 
+!
+! with m == 1 -> d/dx , m == 2 -> d/dy , m == 3 -> d/dz
+ END_DOC
+ integer :: i,j,ipoint,m
+ double precision :: mu,r(3),ints(3),ints_coulomb(3)
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ !$OMP PARALLEL                  &
+ !$OMP DEFAULT (NONE)            &
+ !$OMP PRIVATE (i,j,ipoint,mu,r,ints,m,ints_coulomb) & 
+ !$OMP SHARED (ao_num,n_points_final_grid,d_dx_v_ij_erf_rk_cst_mu_tmp,final_grid_points,mu_erf)
+ !$OMP DO SCHEDULE (dynamic)
+ do i = 1, ao_num
+  do j = 1, ao_num
+   do ipoint = 1, n_points_final_grid
+    mu = mu_erf 
+    r(1) = final_grid_points(1,ipoint)
+    r(2) = final_grid_points(2,ipoint)
+    r(3) = final_grid_points(3,ipoint)
+    call phi_j_erf_mu_r_dxyz_phi(j,i,mu, r, ints)
+    call phi_j_erf_mu_r_dxyz_phi(j,i,1.d+9, r, ints_coulomb)
+    do m = 1, 3
+     d_dx_v_ij_erf_rk_cst_mu_tmp(m,ipoint,j,i) = ( ints(m) - ints_coulomb(m))
+    enddo
+   enddo
+  enddo
+ enddo
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+ call wall_time(wall1)
+ print*,'wall time for d_dx_v_ij_erf_rk_cst_mu_tmp',wall1 - wall0
+
+
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, d_dx_v_ij_erf_rk_cst_mu, (n_points_final_grid,ao_num, ao_num,3)]
+ implicit none
+ BEGIN_DOC
+! d_dx_v_ij_erf_rk_cst_mu_tmp(j,i,R,m) = int dr phi_j(r)) (erf(mu(R) |r - R|) - 1)/|r - R| d/dx (phi_i(r) 
+!
+! with m == 1 -> d/dx , m == 2 -> d/dy , m == 3 -> d/dz
+ END_DOC
+ integer :: i,j,ipoint,m
+ double precision :: mu,r(3),ints,ints_coulomb
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ do i = 1, ao_num
+  do j = 1, ao_num
+   do m = 1, 3
+    do ipoint = 1, n_points_final_grid
+     d_dx_v_ij_erf_rk_cst_mu(ipoint,j,i,m)= d_dx_v_ij_erf_rk_cst_mu_tmp(m,ipoint,j,i)
+    enddo
+   enddo
+  enddo
+ enddo
+
+ call wall_time(wall1)
+ print*,'wall time for d_dx_v_ij_erf_rk_cst_mu',wall1 - wall0
+
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, x_d_dx_v_ij_erf_rk_cst_mu_tmp, (3,n_points_final_grid,ao_num, ao_num)]
+ implicit none
+ BEGIN_DOC
+! x_d_dx_v_ij_erf_rk_cst_mu_tmp(m,j,i,R) = int dr x phi_j(r)) (erf(mu(R) |r - R|) - 1)/|r - R| d/dx (phi_i(r) 
+!
+! with m == 1 -> d/dx , m == 2 -> d/dy , m == 3 -> d/dz
+ END_DOC
+ integer :: i,j,ipoint,m
+ double precision :: mu,r(3),ints(3),ints_coulomb(3)
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ !$OMP PARALLEL                  &
+ !$OMP DEFAULT (NONE)            &
+ !$OMP PRIVATE (i,j,ipoint,mu,r,ints,m,ints_coulomb) & 
+ !$OMP SHARED (ao_num,n_points_final_grid,x_d_dx_v_ij_erf_rk_cst_mu_tmp,final_grid_points,mu_erf)
+ !$OMP DO SCHEDULE (dynamic)
+ do i = 1, ao_num
+  do j = 1, ao_num
+   do ipoint = 1, n_points_final_grid
+    mu = mu_erf
+    r(1) = final_grid_points(1,ipoint)
+    r(2) = final_grid_points(2,ipoint)
+    r(3) = final_grid_points(3,ipoint)
+    call phi_j_erf_mu_r_xyz_dxyz_phi(j,i,mu, r, ints)
+    call phi_j_erf_mu_r_xyz_dxyz_phi(j,i,1.d+9, r, ints_coulomb)
+    do m = 1, 3
+     x_d_dx_v_ij_erf_rk_cst_mu_tmp(m,ipoint,j,i) = ( ints(m) - ints_coulomb(m))
+    enddo
+   enddo
+  enddo
+ enddo
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+ call wall_time(wall1)
+ print*,'wall time for x_d_dx_v_ij_erf_rk_cst_mu_tmp',wall1 - wall0
+
+
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, x_d_dx_v_ij_erf_rk_cst_mu, (n_points_final_grid,ao_num, ao_num,3)]
+ implicit none
+ BEGIN_DOC
+! x_d_dx_v_ij_erf_rk_cst_mu_tmp(j,i,R,m) = int dr x phi_j(r)) (erf(mu(R) |r - R|) - 1)/|r - R| d/dx (phi_i(r) 
+!
+! with m == 1 -> d/dx , m == 2 -> d/dy , m == 3 -> d/dz
+ END_DOC
+ integer :: i,j,ipoint,m
+ double precision :: mu,r(3),ints,ints_coulomb
+ double precision :: wall0, wall1
+ call wall_time(wall0)
+ do i = 1, ao_num
+  do j = 1, ao_num
+   do ipoint = 1, n_points_final_grid
+    do m = 1, 3
+     x_d_dx_v_ij_erf_rk_cst_mu(ipoint,j,i,m)= x_d_dx_v_ij_erf_rk_cst_mu_tmp(m,ipoint,j,i)
+    enddo
+   enddo
+  enddo
+ enddo
+
+ call wall_time(wall1)
+ print*,'wall time for x_d_dx_v_ij_erf_rk_cst_mu',wall1 - wall0
+
+END_PROVIDER 
+

src/ao_many_one_e_ints/prim_int_erf_gauss.irp.f

@@ -0,0 +1,195 @@
+double precision function NAI_pol_mult_erf_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
+  BEGIN_DOC
+  ! Computes the following integral R^3 :
+  !
+  ! .. math::
+  ! 
+  !   \int dr  (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !   \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$ exp(-delta (r - D)^2 ).
+  !
+  END_DOC
+
+ implicit none
+  include 'constants.include.F'
+ double precision, intent(in)    :: D_center(3), delta  ! pure gaussian "D" 
+ double precision, intent(in)    :: C_center(3),mu      ! coulomb center "C" and "mu" in the erf(mu*x)/x function
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3)
+
+ double precision  :: NAI_pol_mult_erf
+ ! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
+ double precision  :: A_new(0:max_dim,3)! new polynom 
+ double precision  :: A_center_new(3)   ! new center
+ integer           :: iorder_a_new(3)   ! i_order(i) = order of the new polynom ==> should be equal to power_A
+ double precision  :: alpha_new         ! new exponent
+ double precision  :: fact_a_new        ! constant factor
+ double precision  :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr
+ integer           :: d(3),i,lx,ly,lz,iorder_tmp(3)
+ thr = 1.d-10
+ d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 )  == 0
+
+ ! New gaussian/polynom defined by :: new pol new center new expo   cst fact new order                                
+ call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , & 
+                                      delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
+ ! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
+ accu = 0.d0
+ do lx = 0, iorder_a_new(1)
+  coefx = A_new(lx,1)
+  if(dabs(coefx).lt.thr)cycle
+  iorder_tmp(1) = lx
+  do ly = 0, iorder_a_new(2)
+   coefy = A_new(ly,2)
+   coefxy = coefx * coefy 
+   if(dabs(coefxy).lt.thr)cycle
+   iorder_tmp(2) = ly
+   do lz = 0, iorder_a_new(3)
+    coefz = A_new(lz,3)
+    coefxyz = coefxy * coefz 
+    if(dabs(coefxyz).lt.thr)cycle
+    iorder_tmp(3) = lz
+    accu += coefxyz * NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B,alpha_new,beta,C_center,n_pt_max_integrals,mu)
+   enddo
+  enddo
+ enddo
+ NAI_pol_mult_erf_gauss_r12 = fact_a_new * accu 
+end
+
+subroutine erfc_mu_gauss_xyz(D_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in,xyz_ints)
+  BEGIN_DOC
+  ! Computes the following integral :
+  !
+  ! .. math::
+  ! 
+  !   \int dr exp(-delta (r - D)^2 ) x/y/z * (1 - erf(mu |r-r'|))/ |r-r'| * (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !
+  !   xyz_ints(1) = x , xyz_ints(2) = y, xyz_ints(3) = z, xyz_ints(4) = x^0 
+  END_DOC
+
+ implicit none
+  include 'constants.include.F'
+ double precision, intent(in)    :: D_center(3), delta,mu  ! pure gaussian "D" and mu parameter
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3),n_pt_in
+ double precision, intent(out)   :: xyz_ints(4)
+
+ double precision  :: NAI_pol_mult_erf
+ ! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
+ double precision  :: A_new(0:max_dim,3)! new polynom 
+ double precision  :: A_center_new(3)   ! new center
+ integer           :: iorder_a_new(3)   ! i_order(i) = order of the new polynom ==> should be equal to power_A
+ double precision  :: alpha_new         ! new exponent
+ double precision  :: fact_a_new        ! constant factor
+ double precision  :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr,contrib,contrib_inf,mu_inf
+ integer           :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,mm
+ integer           :: power_B_tmp(3)
+ dim1=100
+ mu_inf = 1.d+10
+ thr = 1.d-10
+ d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 )  == 0
+
+ ! New gaussian/polynom defined by :: new pol new center new expo   cst fact new order                                
+ call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , & 
+                                      delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
+ ! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
+ xyz_ints = 0.d0
+ do lx = 0, iorder_a_new(1)
+  coefx = A_new(lx,1)
+  if(dabs(coefx).lt.thr)cycle
+  iorder_tmp(1) = lx
+  do ly = 0, iorder_a_new(2)
+   coefy = A_new(ly,2)
+   coefxy = coefx * coefy 
+   if(dabs(coefxy).lt.thr)cycle
+   iorder_tmp(2) = ly
+   do lz = 0, iorder_a_new(3)
+    coefz = A_new(lz,3)
+    coefxyz = coefxy * coefz 
+    if(dabs(coefxyz).lt.thr)cycle
+    iorder_tmp(3) = lz
+     power_B_tmp = power_B
+     contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)  
+     contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)  
+     xyz_ints(4) += (contrib_inf - contrib) * coefxyz ! usual term with no x/y/z 
+                                      
+     do mm = 1, 3 
+      ! (x phi_i ) * phi_j 
+      ! x * (x - B_x)^b_x = B_x (x - B_x)^b_x + 1 * (x - B_x)^{b_x+1}
+      
+      !
+      ! first contribution :: B_x (x - B_x)^b_x :: usual integral multiplied by B_x
+      power_B_tmp = power_B
+      contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)  
+      contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)  
+      xyz_ints(mm) += (contrib_inf - contrib) * B_center(mm) * coefxyz 
+                                                       
+      !
+      ! second contribution :: (x - B_x)^(b_x+1) :: integral with b_x=>b_x+1 
+      power_B_tmp(mm) += 1
+      contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu)  
+      contrib_inf = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B_tmp,alpha_new,beta,D_center,n_pt_in,mu_inf)  
+      xyz_ints(mm) += (contrib_inf -  contrib) * coefxyz     
+     enddo
+   enddo
+  enddo
+ enddo
+ xyz_ints *= fact_a_new 
+end
+
+
+double precision function erf_mu_gauss(D_center,delta,mu,A_center,B_center,power_A,power_B,alpha,beta,n_pt_in)
+  BEGIN_DOC
+  ! Computes the following integral :
+  !
+  ! .. math::
+  ! 
+  !   \int dr exp(-delta (r - D)^2 ) erf(mu*|r-r'|)/ |r-r'| * (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !
+  END_DOC
+
+ implicit none
+  include 'constants.include.F'
+ double precision, intent(in)    :: D_center(3), delta,mu  ! pure gaussian "D" and mu parameter
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3),n_pt_in
+
+ double precision  :: NAI_pol_mult_erf
+ ! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
+ double precision  :: A_new(0:max_dim,3)! new polynom 
+ double precision  :: A_center_new(3)   ! new center
+ integer           :: iorder_a_new(3)   ! i_order(i) = order of the new polynom ==> should be equal to power_A
+ double precision  :: alpha_new         ! new exponent
+ double precision  :: fact_a_new        ! constant factor
+ double precision  :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr,contrib,contrib_inf,mu_inf
+ integer           :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,mm
+ dim1=100
+ mu_inf = 1.d+10
+ thr = 1.d-10
+ d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 )  == 0
+
+ ! New gaussian/polynom defined by :: new pol new center new expo   cst fact new order                                
+ call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , & 
+                                      delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
+ ! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
+ erf_mu_gauss = 0.d0
+ do lx = 0, iorder_a_new(1)
+  coefx = A_new(lx,1)
+  if(dabs(coefx).lt.thr)cycle
+  iorder_tmp(1) = lx
+  do ly = 0, iorder_a_new(2)
+   coefy = A_new(ly,2)
+   coefxy = coefx * coefy 
+   if(dabs(coefxy).lt.thr)cycle
+   iorder_tmp(2) = ly
+   do lz = 0, iorder_a_new(3)
+    coefz = A_new(lz,3)
+    coefxyz = coefxy * coefz 
+    if(dabs(coefxyz).lt.thr)cycle
+    iorder_tmp(3) = lz
+    contrib = NAI_pol_mult_erf(A_center_new,B_center,iorder_tmp,power_B,alpha_new,beta,D_center,n_pt_in,mu)
+    erf_mu_gauss += contrib * coefxyz     
+   enddo
+  enddo
+ enddo
+ erf_mu_gauss *= fact_a_new 
+end
+

src/ao_many_one_e_ints/prim_int_gauss_gauss.irp.f

@@ -0,0 +1,191 @@
+
+double precision function overlap_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta)
+  BEGIN_DOC
+  ! Computes the following integral :
+  !
+  ! .. math::
+  ! 
+  !   \int dr exp(-delta (r - D)^2 ) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !
+  END_DOC
+
+ implicit none
+  include 'constants.include.F'
+ double precision, intent(in)    :: D_center(3), delta  ! pure gaussian "D" 
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3)
+
+ double precision  :: overlap_x,overlap_y,overlap_z,overlap
+ ! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
+ double precision  :: A_new(0:max_dim,3)! new polynom 
+ double precision  :: A_center_new(3)   ! new center
+ integer           :: iorder_a_new(3)   ! i_order(i) = order of the new polynom ==> should be equal to power_A
+ double precision  :: alpha_new         ! new exponent
+ double precision  :: fact_a_new        ! constant factor
+ double precision  :: accu,coefx,coefy,coefz,coefxy,coefxyz,thr
+ integer           :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1
+ dim1=100
+ thr = 1.d-10
+ d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 )  == 0
+
+ ! New gaussian/polynom defined by :: new pol new center new expo   cst fact new order                                
+ call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , & 
+                                      delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
+ ! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
+ accu = 0.d0
+ do lx = 0, iorder_a_new(1)
+  coefx = A_new(lx,1)
+  if(dabs(coefx).lt.thr)cycle
+  iorder_tmp(1) = lx
+  do ly = 0, iorder_a_new(2)
+   coefy = A_new(ly,2)
+   coefxy = coefx * coefy 
+   if(dabs(coefxy).lt.thr)cycle
+   iorder_tmp(2) = ly
+   do lz = 0, iorder_a_new(3)
+    coefz = A_new(lz,3)
+    coefxyz = coefxy * coefz 
+    if(dabs(coefxyz).lt.thr)cycle
+    iorder_tmp(3) = lz
+    call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B,overlap_x,overlap_y,overlap_z,overlap,dim1)
+    accu += coefxyz * overlap
+   enddo
+  enddo
+ enddo
+ overlap_gauss_r12 = fact_a_new * accu 
+end
+
+
+subroutine overlap_gauss_xyz_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,gauss_ints)
+  BEGIN_DOC
+  ! Computes the following integral :
+  !
+  ! .. math::
+  ! 
+  !   gauss_ints(m) = \int dr exp(-delta (r - D)^2 ) * x/y/z (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !
+  ! with m == 1 ==> x, m == 2 ==> y, m == 3 ==> z
+  END_DOC
+
+ implicit none
+  include 'constants.include.F'
+ double precision, intent(in)    :: D_center(3), delta  ! pure gaussian "D" 
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3)
+ double precision, intent(out)   :: gauss_ints(3)
+
+ double precision  :: overlap_x,overlap_y,overlap_z,overlap
+ ! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
+ double precision  :: A_new(0:max_dim,3)! new polynom 
+ double precision  :: A_center_new(3)   ! new center
+ integer           :: iorder_a_new(3)   ! i_order(i) = order of the new polynom ==> should be equal to power_A
+ integer           :: power_B_new(3)
+ double precision  :: alpha_new         ! new exponent
+ double precision  :: fact_a_new        ! constant factor
+ double precision  :: coefx,coefy,coefz,coefxy,coefxyz,thr
+ integer           :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,m
+ dim1=100
+ thr = 1.d-10
+ d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 )  == 0
+
+ ! New gaussian/polynom defined by :: new pol new center new expo   cst fact new order                                
+ call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , & 
+                                      delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
+ ! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
+ gauss_ints = 0.d0
+ do lx = 0, iorder_a_new(1)
+  coefx = A_new(lx,1)
+  if(dabs(coefx).lt.thr)cycle
+  iorder_tmp(1) = lx
+  do ly = 0, iorder_a_new(2)
+   coefy = A_new(ly,2)
+   coefxy = coefx * coefy 
+   if(dabs(coefxy).lt.thr)cycle
+   iorder_tmp(2) = ly
+   do lz = 0, iorder_a_new(3)
+    coefz = A_new(lz,3)
+    coefxyz = coefxy * coefz 
+    if(dabs(coefxyz).lt.thr)cycle
+    iorder_tmp(3) = lz
+    do m = 1, 3
+     ! change (x-Bx)^bx --> (x-Bx)^(bx+1) + Bx(x-Bx)^bx
+     power_B_new = power_B
+     power_B_new(m) += 1 ! (x-Bx)^(bx+1)
+     call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B_new,overlap_x,overlap_y,overlap_z,overlap,dim1)
+     gauss_ints(m) += coefxyz * overlap
+
+     power_B_new = power_B
+     call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B_new,overlap_x,overlap_y,overlap_z,overlap,dim1)
+     gauss_ints(m) += coefxyz * overlap * B_center(m) ! Bx (x-Bx)^(bx)
+    enddo
+   enddo
+  enddo
+ enddo
+ gauss_ints *= fact_a_new
+end
+
+double precision function overlap_gauss_xyz_r12_specific(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,mx)
+  BEGIN_DOC
+  ! Computes the following integral :
+  !
+  ! .. math::
+  ! 
+  !    \int dr exp(-delta (r - D)^2 ) * x/y/z (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !
+  ! with mx == 1 ==> x, mx == 2 ==> y, mx == 3 ==> z
+  END_DOC
+
+ implicit none
+  include 'constants.include.F'
+ double precision, intent(in)    :: D_center(3), delta  ! pure gaussian "D" 
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3),mx
+
+ double precision  :: overlap_x,overlap_y,overlap_z,overlap
+ ! First you multiply the usual gaussian "A" with the gaussian exp(-delta (r - D)^2 )
+ double precision  :: A_new(0:max_dim,3)! new polynom 
+ double precision  :: A_center_new(3)   ! new center
+ integer           :: iorder_a_new(3)   ! i_order(i) = order of the new polynom ==> should be equal to power_A
+ integer           :: power_B_new(3)
+ double precision  :: alpha_new         ! new exponent
+ double precision  :: fact_a_new        ! constant factor
+ double precision  :: coefx,coefy,coefz,coefxy,coefxyz,thr
+ integer           :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1,m
+ dim1=100
+ thr = 1.d-10
+ d = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 )  == 0
+
+ ! New gaussian/polynom defined by :: new pol new center new expo   cst fact new order                                
+ call give_explicit_poly_and_gaussian(A_new , A_center_new , alpha_new, fact_a_new , iorder_a_new , & 
+                                      delta,alpha,d,power_A,D_center,A_center,n_pt_max_integrals)
+ ! The new gaussian exp(-delta (r - D)^2 ) (x-A_x)^a \exp(-\alpha (x-A_x)^2
+ overlap_gauss_xyz_r12_specific = 0.d0
+ do lx = 0, iorder_a_new(1)
+  coefx = A_new(lx,1)
+  if(dabs(coefx).lt.thr)cycle
+  iorder_tmp(1) = lx
+  do ly = 0, iorder_a_new(2)
+   coefy = A_new(ly,2)
+   coefxy = coefx * coefy 
+   if(dabs(coefxy).lt.thr)cycle
+   iorder_tmp(2) = ly
+   do lz = 0, iorder_a_new(3)
+    coefz = A_new(lz,3)
+    coefxyz = coefxy * coefz 
+    if(dabs(coefxyz).lt.thr)cycle
+    iorder_tmp(3) = lz
+    m = mx
+    ! change (x-Bx)^bx --> (x-Bx)^(bx+1) + Bx(x-Bx)^bx
+    power_B_new = power_B
+    power_B_new(m) += 1 ! (x-Bx)^(bx+1)
+    call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B_new,overlap_x,overlap_y,overlap_z,overlap,dim1)
+    overlap_gauss_xyz_r12_specific += coefxyz * overlap
+
+    power_B_new = power_B
+    call overlap_gaussian_xyz(A_center_new,B_center,alpha_new,beta,iorder_tmp,power_B_new,overlap_x,overlap_y,overlap_z,overlap,dim1)
+    overlap_gauss_xyz_r12_specific += coefxyz * overlap * B_center(m) ! Bx (x-Bx)^(bx)
+   enddo
+  enddo
+ enddo
+ overlap_gauss_xyz_r12_specific *= fact_a_new
+end

src/ao_many_one_e_ints/stg_gauss_int.irp.f

@@ -0,0 +1,121 @@
+double precision function ovlp_stg_gauss_int_phi_ij(D_center,gam,delta,A_center,B_center,power_A,power_B,alpha,beta)
+  BEGIN_DOC
+  ! Computes the following integral : 
+  !
+  ! .. math::
+  ! 
+  !   \int dr exp(-gam (r - D)) exp(-delta * (r -D)^2) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !
+  END_DOC
+
+ implicit none
+ double precision, intent(in)    :: D_center(3), gam ! pure Slater "D" in r-r_D
+ double precision, intent(in)    :: delta            ! gaussian        in r-r_D
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3)
+
+ integer :: i
+ double precision :: integral,gama_gauss
+ double precision, allocatable :: expos_slat(:)
+ allocate(expos_slat(n_max_fit_slat))
+ double precision :: overlap_gauss_r12
+ ovlp_stg_gauss_int_phi_ij = 0.d0
+ call expo_fit_slater_gam(gam,expos_slat)
+ do i = 1, n_max_fit_slat
+  gama_gauss = expos_slat(i)+delta 
+  integral = overlap_gauss_r12(D_center,gama_gauss,A_center,B_center,power_A,power_B,alpha,beta)
+  ovlp_stg_gauss_int_phi_ij += coef_fit_slat_gauss(i) * integral
+ enddo
+end
+
+
+double precision function erf_mu_stg_gauss_int_phi_ij(D_center,gam,delta,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
+  BEGIN_DOC
+  ! Computes the following integral : 
+  !
+  ! .. math::
+  ! 
+  !   \int dr exp(-gam(r - D)-delta(r - D)^2) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !   \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
+  !
+  END_DOC
+
+ implicit none
+  include 'constants.include.F'
+ double precision, intent(in)    :: D_center(3), gam ! pure Slater "D" in r-r_D
+ double precision, intent(in)    :: delta            ! gaussian        in r-r_D
+ double precision, intent(in)    :: C_center(3),mu      ! coulomb center "C" and "mu" in the erf(mu*x)/x function
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3)
+
+ integer :: i
+ double precision :: NAI_pol_mult_erf_gauss_r12
+ double precision :: integral,gama_gauss
+ double precision, allocatable :: expos_slat(:)
+ allocate(expos_slat(n_max_fit_slat))
+ erf_mu_stg_gauss_int_phi_ij = 0.d0
+ call expo_fit_slater_gam(gam,expos_slat)
+ do i = 1, n_max_fit_slat
+  gama_gauss = expos_slat(i) + delta
+  integral = NAI_pol_mult_erf_gauss_r12(D_center,gama_gauss,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
+  erf_mu_stg_gauss_int_phi_ij += coef_fit_slat_gauss(i) * integral
+ enddo
+end
+
+double precision function overlap_stg_gauss(D_center,gam,A_center,B_center,power_A,power_B,alpha,beta)
+  BEGIN_DOC
+  ! Computes the following integral : 
+  !
+  ! .. math::
+  ! 
+  !   \int dr exp(-gam (r - D)) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !
+  END_DOC
+
+ implicit none
+ double precision, intent(in)    :: D_center(3), gam ! pure Slater "D" 
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3)
+ 
+ integer :: i
+ double precision :: expos_slat(n_max_fit_slat),integral,delta
+ double precision :: overlap_gauss_r12
+ overlap_stg_gauss = 0.d0
+ call expo_fit_slater_gam(gam,expos_slat)
+ do i = 1, n_max_fit_slat
+  delta = expos_slat(i) 
+  integral = overlap_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta)
+  overlap_stg_gauss += coef_fit_slat_gauss(i) * integral
+ enddo
+end
+
+double precision function erf_mu_stg_gauss(D_center,gam,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
+  BEGIN_DOC
+  ! Computes the following integral : 
+  !
+  ! .. math::
+  ! 
+  !   \int dr exp(-gam(r - D)) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !   \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
+  !
+  END_DOC
+
+ implicit none
+  include 'constants.include.F'
+ double precision, intent(in)    :: D_center(3), gam    ! pure Slater "D" 
+ double precision, intent(in)    :: C_center(3),mu      ! coulomb center "C" and "mu" in the erf(mu*x)/x function
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3)
+
+ 
+ integer :: i
+ double precision :: expos_slat(n_max_fit_slat),integral,delta
+ double precision :: NAI_pol_mult_erf_gauss_r12
+ erf_mu_stg_gauss = 0.d0
+ call expo_fit_slater_gam(gam,expos_slat)
+ do i = 1, n_max_fit_slat
+  delta = expos_slat(i) 
+  integral = NAI_pol_mult_erf_gauss_r12(D_center,delta,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
+  erf_mu_stg_gauss += coef_fit_slat_gauss(i) * integral
+ enddo
+end

src/ao_many_one_e_ints/taylor_exp.irp.f

@@ -0,0 +1,101 @@
+double precision function exp_dl(x,n)
+ implicit none
+ double precision, intent(in) :: x
+ integer         , intent(in) :: n
+ integer :: i
+ exp_dl = 1.d0
+ do i = 1, n
+  exp_dl += fact_inv(i) * x**dble(i)
+ enddo
+end
+
+subroutine exp_dl_rout(x,n, array)
+ implicit none
+ double precision, intent(in) :: x
+ integer         , intent(in) :: n
+ double precision, intent(out)::  array(0:n)
+ integer :: i
+ double precision :: accu
+ accu = 1.d0
+ array(0) = 1.d0
+ do i = 1, n
+  accu += fact_inv(i) * x**dble(i)
+  array(i) = accu
+ enddo
+end
+
+subroutine exp_dl_ovlp_stg_phi_ij(zeta,D_center,gam,delta,A_center,B_center,power_A,power_B,alpha,beta,n_taylor,array_ints,integral_taylor,exponent_exp)
+  BEGIN_DOC
+  ! Computes the following integrals : 
+  !
+  ! .. math::
+  ! 
+  !   array(i) = \int dr EXP{exponent_exp * [exp(-gam*i (r - D)) exp(-delta*i * (r -D)^2)] (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !
+  !
+  ! and gives back the Taylor expansion of the exponential in integral_taylor
+  END_DOC
+
+ implicit none
+ double precision, intent(in)    :: zeta             ! prefactor of the argument of the exp(-zeta*x)
+ integer, intent(in)             :: n_taylor         ! order of the Taylor expansion of the exponential
+ double precision, intent(in)    :: D_center(3), gam ! pure Slater "D" in r-r_D
+ double precision, intent(in)    :: delta            ! gaussian        in r-r_D
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ double precision, intent(in)    :: exponent_exp
+ integer, intent(in)             :: power_A(3),power_B(3)
+ double precision, intent(out)   :: array_ints(0:n_taylor),integral_taylor
+
+ integer :: i,dim1
+ double precision :: delta_exp,gam_exp,ovlp_stg_gauss_int_phi_ij
+ double precision :: overlap_x,overlap_y,overlap_z,overlap
+ dim1=100
+ call overlap_gaussian_xyz(A_center,B_center,alpha,beta,power_A,power_B,overlap_x,overlap_y,overlap_z,overlap,dim1)
+ array_ints(0) = overlap
+ integral_taylor = array_ints(0)
+ do i = 1, n_taylor
+  delta_exp = dble(i) * delta
+  gam_exp   = dble(i) * gam
+  array_ints(i) = ovlp_stg_gauss_int_phi_ij(D_center,gam_exp,delta_exp,A_center,B_center,power_A,power_B,alpha,beta)
+  integral_taylor += (-zeta*exponent_exp)**dble(i) * fact_inv(i) * array_ints(i)
+ enddo
+
+end
+
+subroutine exp_dl_erf_stg_phi_ij(zeta,D_center,gam,delta,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu,n_taylor,array_ints,integral_taylor)
+  BEGIN_DOC
+  ! Computes the following integrals : 
+  !
+  ! .. math::
+  ! 
+  !   array(i) = \int dr exp(-gam*i (r - D)) exp(-delta*i * (r -D)^2) (x-A_x)^a (x-B_x)^b \exp(-\alpha (x-A_x)^2 - \beta (x-B_x)^2 )
+  !   \frac{\erf(\mu | r - R_C | )}{ | r - R_C | }$.
+  !
+  !
+  ! and gives back the Taylor expansion of the exponential in integral_taylor
+  END_DOC
+
+ implicit none
+ integer, intent(in)             :: n_taylor         ! order of the Taylor expansion of the exponential
+ double precision, intent(in)    :: zeta             ! prefactor of the argument of the exp(-zeta*x)
+ double precision, intent(in)    :: D_center(3), gam ! pure Slater "D" in r-r_D
+ double precision, intent(in)    :: delta            ! gaussian        in r-r_D
+ double precision, intent(in)    :: C_center(3),mu      ! coulomb center "C" and "mu" in the erf(mu*x)/x function
+ double precision, intent(in)    :: A_center(3),B_center(3),alpha,beta ! gaussian/polynoms "A" and "B"
+ integer, intent(in)             :: power_A(3),power_B(3)
+ double precision, intent(out)   :: array_ints(0:n_taylor),integral_taylor
+
+ integer :: i,dim1
+ double precision :: delta_exp,gam_exp,NAI_pol_mult_erf,erf_mu_stg_gauss_int_phi_ij
+ dim1=100
+ 
+ array_ints(0) = NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_max_integrals,mu)
+ integral_taylor = array_ints(0)
+ do i = 1, n_taylor
+  delta_exp = dble(i) * delta
+  gam_exp   = dble(i) * gam
+  array_ints(i) = erf_mu_stg_gauss_int_phi_ij(D_center,gam_exp,delta_exp,A_center,B_center,power_A,power_B,alpha,beta,C_center,mu)
+  integral_taylor += (-zeta)**dble(i) * fact_inv(i) * array_ints(i)
+ enddo
+
+end

src/ao_many_one_e_ints/xyz_grad_xyz_ao_pol.irp.f

@@ -0,0 +1,343 @@
+ BEGIN_PROVIDER [double precision, coef_xyz_ao, (2,3,ao_num)]
+&BEGIN_PROVIDER [integer, power_xyz_ao, (2,3,ao_num)]
+ implicit none
+ BEGIN_DOC
+! coefficient for the basis function :: (x * phi_i(r), y * phi_i(r), * z_phi(r))
+!
+! x * (x - A_x)^a_x = A_x (x - A_x)^a_x + 1 * (x - A_x)^{a_x+1}
+ END_DOC
+ integer :: i,j,k,num_ao,power_ao(1:3)
+ double precision :: center_ao(1:3)
+ do i = 1, ao_num
+  power_ao(1:3)= ao_power(i,1:3) 
+  num_ao = ao_nucl(i)
+  center_ao(1:3) = nucl_coord(num_ao,1:3)
+  do j = 1, 3
+   coef_xyz_ao(1,j,i) = center_ao(j) ! A_x (x - A_x)^a_x
+   power_xyz_ao(1,j,i)= power_ao(j)
+   coef_xyz_ao(2,j,i) = 1.d0         ! 1 * (x - A_x)^a_{x+1}
+   power_xyz_ao(2,j,i)= power_ao(j) + 1
+  enddo
+ enddo
+END_PROVIDER 
+
+ BEGIN_PROVIDER [ double precision, ao_coef_ord_grad_transp, (2,3,ao_prim_num_max,ao_num) ]
+&BEGIN_PROVIDER [ integer, power_ord_grad_transp, (2,3,ao_num) ]
+  implicit none
+  BEGIN_DOC
+  ! grad AO in terms of polynoms and coefficients 
+  ! 
+  ! WARNING !!!! SOME polynoms might be negative !!!!! 
+  !
+  ! WHEN IT IS THE CASE, coefficients are ZERO 
+  END_DOC
+  integer                        :: i,j,power_ao(3), m,kk
+  do j=1, ao_num
+    power_ao(1:3)= ao_power(j,1:3) 
+    do m = 1, 3
+     power_ord_grad_transp(1,m,j) = power_ao(m) - 1
+     power_ord_grad_transp(2,m,j) = power_ao(m) + 1
+    enddo
+    do i=1, ao_prim_num_max
+     do m = 1, 3
+       ao_coef_ord_grad_transp(1,m,i,j) = ao_coef_normalized_ordered(j,i) * dble(power_ao(m)) ! a_x * c_i 
+       ao_coef_ord_grad_transp(2,m,i,j) = -2.d0 * ao_coef_normalized_ordered(j,i) * ao_expo_ordered_transp(i,j) ! -2 * c_i * alpha_i 
+       do kk = 1, 2
+        if(power_ord_grad_transp(kk,m,j).lt.0)then
+         ao_coef_ord_grad_transp(kk,m,i,j) = 0.d0
+        endif
+       enddo
+     enddo
+    enddo
+  enddo
+
+END_PROVIDER
+
+ BEGIN_PROVIDER [ double precision, ao_coef_ord_xyz_grad_transp, (4,3,ao_prim_num_max,ao_num) ]
+&BEGIN_PROVIDER [ integer, power_ord_xyz_grad_transp, (4,3,ao_num) ]
+  implicit none
+  BEGIN_DOC
+  ! x * d/dx of an AO in terms of polynoms and coefficients 
+  !
+  ! WARNING !!!! SOME polynoms might be negative !!!!! 
+  !
+  ! WHEN IT IS THE CASE, coefficients are ZERO 
+  END_DOC
+  integer                        :: i,j,power_ao(3), m,num_ao,kk
+  double precision :: center_ao(1:3)
+  do j=1, ao_num
+   power_ao(1:3)= ao_power(j,1:3) 
+   num_ao = ao_nucl(j)
+   center_ao(1:3) = nucl_coord(num_ao,1:3)
+   do m = 1, 3
+     power_ord_xyz_grad_transp(1,m,j)   = power_ao(m) - 1
+     power_ord_xyz_grad_transp(2,m,j)   = power_ao(m)
+     power_ord_xyz_grad_transp(3,m,j)   = power_ao(m) + 1
+     power_ord_xyz_grad_transp(4,m,j)   = power_ao(m) + 2
+     do kk = 1, 4
+      if(power_ord_xyz_grad_transp(kk,m,j).lt.0)then
+       power_ord_xyz_grad_transp(kk,m,j) = -1
+      endif
+     enddo
+   enddo
+   do i=1, ao_prim_num_max
+    do m = 1, 3
+     ao_coef_ord_xyz_grad_transp(1,m,i,j) = dble(power_ao(m)) * ao_coef_normalized_ordered(j,i) * center_ao(m)
+     ao_coef_ord_xyz_grad_transp(2,m,i,j) = dble(power_ao(m)) * ao_coef_normalized_ordered(j,i) 
+     ao_coef_ord_xyz_grad_transp(3,m,i,j) = -2.d0 * ao_coef_normalized_ordered(j,i) * ao_expo_ordered_transp(i,j) * center_ao(m)
+     ao_coef_ord_xyz_grad_transp(4,m,i,j) = -2.d0 * ao_coef_normalized_ordered(j,i) * ao_expo_ordered_transp(i,j) 
+     do kk = 1, 4
+      if(power_ord_xyz_grad_transp(kk,m,j).lt.0)then
+       ao_coef_ord_xyz_grad_transp(kk,m,i,j) = 0.d0
+      endif
+     enddo
+    enddo
+   enddo
+  enddo
+
+END_PROVIDER
+
+subroutine xyz_grad_phi_ao(r,i_ao,xyz_grad_phi)
+ implicit none
+ integer, intent(in) :: i_ao
+ double precision, intent(in) :: r(3)
+ double precision, intent(out):: xyz_grad_phi(3) ! x * d/dx phi i, y * d/dy phi_i, z * d/dz phi_
+ double precision :: center_ao(3),beta
+ double precision :: accu(3,4),dr(3),r2,pol_usual(3)
+ integer :: m,power_ao(3),num_ao,j_prim
+ power_ao(1:3)= ao_power(i_ao,1:3) 
+ num_ao = ao_nucl(i_ao)
+ center_ao(1:3) = nucl_coord(num_ao,1:3)
+ dr(1) = (r(1) - center_ao(1))
+ dr(2) = (r(2) - center_ao(2))
+ dr(3) = (r(3) - center_ao(3))
+ r2 = 0.d0
+ do m = 1, 3
+  r2 += dr(m)*dr(m)
+ enddo
+ ! computes the gaussian part 
+ accu = 0.d0
+ do j_prim =1,ao_prim_num(i_ao)
+   beta = ao_expo_ordered_transp(j_prim,i_ao)
+   if(dabs(beta*r2).gt.50.d0)cycle
+   do m = 1, 3
+    accu(m,1) += ao_coef_ord_xyz_grad_transp(1,m,j_prim,i_ao) * dexp(-beta*r2) 
+    accu(m,2) += ao_coef_ord_xyz_grad_transp(2,m,j_prim,i_ao) * dexp(-beta*r2) 
+    accu(m,3) += ao_coef_ord_xyz_grad_transp(3,m,j_prim,i_ao) * dexp(-beta*r2) 
+    accu(m,4) += ao_coef_ord_xyz_grad_transp(4,m,j_prim,i_ao) * dexp(-beta*r2) 
+   enddo
+ enddo
+ ! computes the polynom part
+ pol_usual = 0.d0
+ pol_usual(1) = dr(2)**dble(power_ao(2)) * dr(3)**dble(power_ao(3)) 
+ pol_usual(2) = dr(1)**dble(power_ao(1)) * dr(3)**dble(power_ao(3)) 
+ pol_usual(3) = dr(1)**dble(power_ao(1)) * dr(2)**dble(power_ao(2)) 
+
+ xyz_grad_phi = 0.d0
+ do m = 1, 3
+  xyz_grad_phi(m) += accu(m,2) * pol_usual(m) * dr(m)**dble(power_ord_xyz_grad_transp(2,m,i_ao))
+  xyz_grad_phi(m) += accu(m,3) * pol_usual(m) * dr(m)**dble(power_ord_xyz_grad_transp(3,m,i_ao))
+  xyz_grad_phi(m) += accu(m,4) * pol_usual(m) * dr(m)**dble(power_ord_xyz_grad_transp(4,m,i_ao))
+  if(power_ord_xyz_grad_transp(1,m,i_ao).lt.0)cycle
+  xyz_grad_phi(m) += accu(m,1) * pol_usual(m) * dr(m)**dble(power_ord_xyz_grad_transp(1,m,i_ao))
+ enddo
+end
+
+subroutine grad_phi_ao(r,i_ao,grad_xyz_phi)
+ implicit none
+ integer, intent(in) :: i_ao
+ double precision, intent(in) :: r(3)
+ double precision, intent(out):: grad_xyz_phi(3) ! x * phi i, y * phi_i, z * phi_
+ double precision :: center_ao(3),beta
+ double precision :: accu(3,2),dr(3),r2,pol_usual(3)
+ integer :: m,power_ao(3),num_ao,j_prim
+ power_ao(1:3)= ao_power(i_ao,1:3) 
+ num_ao = ao_nucl(i_ao)
+ center_ao(1:3) = nucl_coord(num_ao,1:3)
+ dr(1) = (r(1) - center_ao(1))
+ dr(2) = (r(2) - center_ao(2))
+ dr(3) = (r(3) - center_ao(3))
+ r2 = 0.d0
+ do m = 1, 3
+  r2 += dr(m)*dr(m)
+ enddo
+ ! computes the gaussian part 
+ accu = 0.d0
+ do j_prim =1,ao_prim_num(i_ao)
+   beta = ao_expo_ordered_transp(j_prim,i_ao)
+   if(dabs(beta*r2).gt.50.d0)cycle
+   do m = 1, 3
+    accu(m,1) += ao_coef_ord_grad_transp(1,m,j_prim,i_ao) * dexp(-beta*r2) 
+    accu(m,2) += ao_coef_ord_grad_transp(2,m,j_prim,i_ao) * dexp(-beta*r2) 
+   enddo
+ enddo
+ ! computes the polynom part
+ pol_usual = 0.d0
+ pol_usual(1) = dr(2)**dble(power_ao(2)) * dr(3)**dble(power_ao(3)) 
+ pol_usual(2) = dr(1)**dble(power_ao(1)) * dr(3)**dble(power_ao(3)) 
+ pol_usual(3) = dr(1)**dble(power_ao(1)) * dr(2)**dble(power_ao(2)) 
+ do m = 1, 3
+  grad_xyz_phi(m)  = accu(m,2) * pol_usual(m) * dr(m)**dble(power_ord_grad_transp(2,m,i_ao))
+  if(power_ao(m)==0)cycle
+  grad_xyz_phi(m) += accu(m,1) * pol_usual(m) * dr(m)**dble(power_ord_grad_transp(1,m,i_ao))
+ enddo
+end
+
+subroutine xyz_phi_ao(r,i_ao,xyz_phi)
+ implicit none
+ integer, intent(in) :: i_ao
+ double precision, intent(in) :: r(3)
+ double precision, intent(out):: xyz_phi(3) ! x * phi i, y * phi_i, z * phi_i
+ double precision :: center_ao(3),beta
+ double precision :: accu,dr(3),r2,pol_usual(3)
+ integer :: m,power_ao(3),num_ao
+ power_ao(1:3)= ao_power(i_ao,1:3) 
+ num_ao = ao_nucl(i_ao)
+ center_ao(1:3) = nucl_coord(num_ao,1:3)
+ dr(1) = (r(1) - center_ao(1))
+ dr(2) = (r(2) - center_ao(2))
+ dr(3) = (r(3) - center_ao(3))
+ r2 = 0.d0
+ do m = 1, 3
+  r2 += dr(m)*dr(m)
+ enddo
+ ! computes the gaussian part 
+ accu = 0.d0
+ do m=1,ao_prim_num(i_ao)
+   beta = ao_expo_ordered_transp(m,i_ao)
+   if(dabs(beta*r2).gt.50.d0)cycle
+   accu += ao_coef_normalized_ordered_transp(m,i_ao) * dexp(-beta*r2)
+ enddo
+ ! computes the polynom part
+ pol_usual = 0.d0
+ pol_usual(1) = dr(2)**dble(power_ao(2)) * dr(3)**dble(power_ao(3)) 
+ pol_usual(2) = dr(1)**dble(power_ao(1)) * dr(3)**dble(power_ao(3)) 
+ pol_usual(3) = dr(1)**dble(power_ao(1)) * dr(2)**dble(power_ao(2)) 
+ do m = 1, 3
+  xyz_phi(m) = accu * pol_usual(m) * dr(m)**(dble(power_ao(m))) * ( coef_xyz_ao(1,m,i_ao) + coef_xyz_ao(2,m,i_ao) * dr(m) )
+ enddo
+end
+
+
+subroutine test_pol_xyz
+ implicit none
+ integer :: ipoint,i,j,m,jpoint
+ double precision :: r1(3),derf_mu_x
+ double precision :: weight1,r12,xyz_phi(3),grad_phi(3),xyz_grad_phi(3)
+ double precision, allocatable :: aos_array(:),aos_grad_array(:,:)
+ double precision :: num_xyz_phi(3),num_grad_phi(3),num_xyz_grad_phi(3)
+ double precision :: accu_xyz_phi(3),accu_grad_phi(3),accu_xyz_grad_phi(3)
+ double precision :: meta_accu_xyz_phi(3),meta_accu_grad_phi(3),meta_accu_xyz_grad_phi(3)
+ allocate(aos_array(ao_num),aos_grad_array(3,ao_num))
+ meta_accu_xyz_phi     = 0.d0
+ meta_accu_grad_phi    = 0.d0
+ meta_accu_xyz_grad_phi= 0.d0
+ do i = 1, ao_num
+  accu_xyz_phi     = 0.d0
+  accu_grad_phi    = 0.d0
+  accu_xyz_grad_phi= 0.d0
+
+  do ipoint = 1, n_points_final_grid
+   r1(:) = final_grid_points(:,ipoint)
+   weight1 = final_weight_at_r_vector(ipoint)
+   call give_all_aos_and_grad_at_r(r1,aos_array,aos_grad_array)
+   do m = 1, 3
+    num_xyz_phi(m)      = r1(m) *  aos_array(i)  
+    num_grad_phi(m)     = aos_grad_array(m,i)  
+    num_xyz_grad_phi(m) = r1(m) *  aos_grad_array(m,i) 
+   enddo
+   call xyz_phi_ao(r1,i,xyz_phi)
+   call grad_phi_ao(r1,i,grad_phi)
+   call xyz_grad_phi_ao(r1,i,xyz_grad_phi)
+   do m = 1, 3
+    accu_xyz_phi(m)      += weight1 * dabs(num_xyz_phi(m)      -  xyz_phi(m)     )
+    accu_grad_phi(m)     += weight1 * dabs(num_grad_phi(m)     -  grad_phi(m)    )
+    accu_xyz_grad_phi(m) += weight1 * dabs(num_xyz_grad_phi(m) -  xyz_grad_phi(m))
+   enddo
+  enddo
+  print*,''
+  print*,''
+  print*,'i,',i
+  print*,''
+  do m = 1, 3
+!    print*, 'm, accu_xyz_phi(m)  ' ,m, accu_xyz_phi(m)  
+!    print*, 'm, accu_grad_phi(m) ' ,m, accu_grad_phi(m)         
+    print*, 'm, accu_xyz_grad_phi' ,m, accu_xyz_grad_phi(m)
+  enddo
+  do m = 1, 3
+   meta_accu_xyz_phi(m) += dabs(accu_xyz_phi(m))
+   meta_accu_grad_phi(m) += dabs(accu_grad_phi(m))
+   meta_accu_xyz_grad_phi(m) += dabs(accu_xyz_grad_phi(m))
+  enddo
+ enddo
+  do m = 1, 3
+!    print*, 'm, meta_accu_xyz_phi(m)  ' ,m, meta_accu_xyz_phi(m)  
+!    print*, 'm, meta_accu_grad_phi(m) ' ,m, meta_accu_grad_phi(m)         
+    print*, 'm, meta_accu_xyz_grad_phi' ,m, meta_accu_xyz_grad_phi(m)
+  enddo
+
+
+
+end
+
+subroutine test_ints_semi_bis
+ implicit none
+ integer :: ipoint,i,j,m
+ double precision :: r1(3), aos_grad_array_r1(3, ao_num), aos_array_r1(ao_num)
+ double precision :: C_center(3), weight1,mu_in,r12,derf_mu_x,dxyz_ints(3),NAI_pol_mult_erf_ao
+ double precision :: ao_mat(ao_num,ao_num),ao_xmat(3,ao_num,ao_num),accu1, accu2(3)
+ mu_in = 0.5d0
+ C_center = 0.d0
+ C_center(1) = 0.25d0
+ C_center(3) = 1.12d0
+ C_center(2) = -1.d0
+ ao_mat = 0.d0
+ ao_xmat = 0.d0
+ do ipoint = 1, n_points_final_grid
+  r1(1) = final_grid_points(1,ipoint)
+  r1(2) = final_grid_points(2,ipoint)
+  r1(3) = final_grid_points(3,ipoint)
+  call give_all_aos_and_grad_at_r(r1,aos_array_r1,aos_grad_array_r1)
+  weight1 = final_weight_at_r_vector(ipoint)
+  r12 = (r1(1) - C_center(1))**2.d0 + (r1(2) - C_center(2))**2.d0 + (r1(3) - C_center(3))**2.d0 
+  r12 = dsqrt(r12)
+  do i = 1, ao_num
+   do j = 1, ao_num
+    ao_mat(j,i)  += aos_array_r1(i) * aos_array_r1(j) * weight1 * derf_mu_x(mu_in,r12)
+    do m = 1, 3
+     ao_xmat(m,j,i) += r1(m) * aos_array_r1(j) * aos_grad_array_r1(m,i) * weight1 * derf_mu_x(mu_in,r12)
+    enddo
+   enddo
+  enddo
+ enddo
+
+ accu1 = 0.d0
+ accu2 = 0.d0
+ accu1relat = 0.d0
+ accu2relat = 0.d0
+ double precision :: accu1relat, accu2relat(3)
+ double precision :: contrib(3)
+ do i = 1, ao_num
+  do j = 1, ao_num
+   call phi_j_erf_mu_r_xyz_dxyz_phi(i,j,mu_in, C_center, dxyz_ints)
+   print*,''
+   print*,'i,j',i,j
+   print*,dxyz_ints(:)
+   print*,ao_xmat(:,j,i)
+   do m = 1, 3
+    contrib(m) = dabs(ao_xmat(m,j,i) - dxyz_ints(m))
+    accu2(m) += contrib(m)
+    if(dabs(ao_xmat(m,j,i)).gt.1.d-10)then
+     accu2relat(m) += dabs(ao_xmat(m,j,i) - dxyz_ints(m))/dabs(ao_xmat(m,j,i))
+    endif
+   enddo
+    print*,contrib
+  enddo
+   print*,''
+ enddo
+ print*,'accu2relat = '
+ print*, accu2relat /dble(ao_num * ao_num)
+
+end
+
+

src/ao_one_e_ints/NEED

@@ -1,2 +1,3 @@
 ao_basis
 pseudo
+cosgtos_ao_int

src/ao_one_e_ints/ao_overlap.irp.f

@@ -1,27 +1,47 @@
- BEGIN_PROVIDER [ double precision, ao_overlap,(ao_num,ao_num) ]
+
-&BEGIN_PROVIDER [ double precision, ao_overlap_x,(ao_num,ao_num) ]
+! ---
-&BEGIN_PROVIDER [ double precision, ao_overlap_y,(ao_num,ao_num) ]
+
-&BEGIN_PROVIDER [ double precision, ao_overlap_z,(ao_num,ao_num) ]
+ BEGIN_PROVIDER [ double precision, ao_overlap  , (ao_num, ao_num) ]
-  implicit none
+&BEGIN_PROVIDER [ double precision, ao_overlap_x, (ao_num, ao_num) ]
+&BEGIN_PROVIDER [ double precision, ao_overlap_y, (ao_num, ao_num) ]
+&BEGIN_PROVIDER [ double precision, ao_overlap_z, (ao_num, ao_num) ]
+
   BEGIN_DOC
-! Overlap between atomic basis functions:
+  ! Overlap between atomic basis functions:
-!
+  !
-! :math:`\int \chi_i(r) \chi_j(r) dr`
+  ! :math:`\int \chi_i(r) \chi_j(r) dr`
   END_DOC
-  integer :: i,j,n,l
+
-  double precision :: f
+  implicit none
-  integer :: dim1
+  integer          :: i, j, n, l, dim1, power_A(3), power_B(3)
   double precision :: overlap, overlap_x, overlap_y, overlap_z
   double precision :: alpha, beta, c
   double precision :: A_center(3), B_center(3)
-  integer :: power_A(3), power_B(3)
+
   ao_overlap   = 0.d0
   ao_overlap_x = 0.d0
   ao_overlap_y = 0.d0
   ao_overlap_z = 0.d0
-  if (read_ao_integrals_overlap) then
+
+  if(read_ao_integrals_overlap) then
+
     call ezfio_get_ao_one_e_ints_ao_integrals_overlap(ao_overlap(1:ao_num, 1:ao_num))
     print *,  'AO overlap integrals read from disk'
+
+  else
+
+    if(use_cosgtos) then
+      !print*, ' use_cosgtos for ao_overlap ?', use_cosgtos
+
+      do j = 1, ao_num
+        do i = 1, ao_num
+          ao_overlap  (i,j) = ao_overlap_cosgtos  (i,j) 
+          ao_overlap_x(i,j) = ao_overlap_cosgtos_x(i,j)
+          ao_overlap_y(i,j) = ao_overlap_cosgtos_y(i,j)
+          ao_overlap_z(i,j) = ao_overlap_cosgtos_z(i,j)
+        enddo
+      enddo
+
     else
 
       dim1=100
@@ -69,7 +89,11 @@
       enddo
       enddo
       !$OMP END PARALLEL DO
+
     endif
+
+  endif
+
   if (write_ao_integrals_overlap) then
      call ezfio_set_ao_one_e_ints_ao_integrals_overlap(ao_overlap(1:ao_num, 1:ao_num))
      print *,  'AO overlap integrals written to disk'
@@ -77,6 +101,8 @@
 
 END_PROVIDER
 
+! ---
+
 BEGIN_PROVIDER [ double precision, ao_overlap_imag, (ao_num, ao_num) ]
  implicit none
  BEGIN_DOC
@@ -85,6 +111,8 @@ BEGIN_PROVIDER [ double precision, ao_overlap_imag, (ao_num, ao_num) ]
  ao_overlap_imag = 0.d0
 END_PROVIDER
 
+! ---
+
 BEGIN_PROVIDER [ complex*16, ao_overlap_complex, (ao_num, ao_num) ]
   implicit none
   BEGIN_DOC
@@ -98,37 +126,39 @@ BEGIN_PROVIDER [ complex*16, ao_overlap_complex, (ao_num, ao_num) ]
   enddo
 END_PROVIDER
 
+! ---
 
+BEGIN_PROVIDER [ double precision, ao_overlap_abs, (ao_num, ao_num) ]
 
-
-BEGIN_PROVIDER [ double precision, ao_overlap_abs,(ao_num,ao_num) ]
-  implicit none
   BEGIN_DOC
-! Overlap between absolute values of atomic basis functions:
+  ! Overlap between absolute values of atomic basis functions:
-!
+  !
-! :math:`\int |\chi_i(r)| |\chi_j(r)| dr`
+  ! :math:`\int |\chi_i(r)| |\chi_j(r)| dr`
   END_DOC
-  integer :: i,j,n,l
+
-  double precision :: f
+  implicit none
-  integer :: dim1
+  integer          :: i, j, n, l, dim1, power_A(3), power_B(3)
-  double precision :: overlap, overlap_x, overlap_y, overlap_z
+  double precision :: overlap_x, overlap_y, overlap_z
   double precision :: alpha, beta
   double precision :: A_center(3), B_center(3)
-  integer :: power_A(3), power_B(3)
   double precision :: lower_exp_val, dx
-  if (is_periodic) then
+
-    do j=1,ao_num
+  if(is_periodic) then
-      do i= 1,ao_num
+
-        ao_overlap_abs(i,j)= cdabs(ao_overlap_complex(i,j))
+    do j = 1, ao_num
+      do i = 1, ao_num
+        ao_overlap_abs(i,j) = cdabs(ao_overlap_complex(i,j))
       enddo
     enddo
+
   else
+
     dim1=100
     lower_exp_val = 40.d0
     !$OMP PARALLEL DO SCHEDULE(GUIDED)                               &
         !$OMP DEFAULT(NONE)                                          &
         !$OMP PRIVATE(A_center,B_center,power_A,power_B,             &
-        !$OMP  overlap_x,overlap_y, overlap_z, overlap,              &
+        !$OMP  overlap_x,overlap_y, overlap_z,                       &
         !$OMP  alpha, beta,i,j,dx)                                   &
         !$OMP SHARED(nucl_coord,ao_power,ao_prim_num,                &
         !$OMP  ao_overlap_abs,ao_num,ao_coef_normalized_ordered_transp,ao_nucl,&
@@ -161,9 +191,13 @@ BEGIN_PROVIDER [ double precision, ao_overlap_abs,(ao_num,ao_num) ]
       enddo
     enddo
     !$OMP END PARALLEL DO
+
   endif
+
 END_PROVIDER
 
+! ---
+
 BEGIN_PROVIDER [ double precision, S_inv,(ao_num,ao_num) ]
  implicit none
  BEGIN_DOC

src/ao_one_e_ints/kin_ao_ints.irp.f

@@ -1,7 +1,10 @@
- BEGIN_PROVIDER [ double precision, ao_deriv2_x,(ao_num,ao_num) ]
+
-&BEGIN_PROVIDER [ double precision, ao_deriv2_y,(ao_num,ao_num) ]
+! ---
-&BEGIN_PROVIDER [ double precision, ao_deriv2_z,(ao_num,ao_num) ]
+
-  implicit none
+ BEGIN_PROVIDER [ double precision, ao_deriv2_x, (ao_num, ao_num) ]
+&BEGIN_PROVIDER [ double precision, ao_deriv2_y, (ao_num, ao_num) ]
+&BEGIN_PROVIDER [ double precision, ao_deriv2_z, (ao_num, ao_num) ]
+
   BEGIN_DOC
   ! Second derivative matrix elements in the |AO| basis.
   !
@@ -11,15 +14,28 @@
   !   \langle \chi_i(x,y,z) | \frac{\partial^2}{\partial x^2} |\chi_j (x,y,z) \rangle
   !
   END_DOC
-  integer :: i,j,n,l
+
-  double precision :: f
+  implicit none
-  integer :: dim1
+  integer          :: i, j, n, l, dim1, power_A(3), power_B(3)
   double precision :: overlap, overlap_y, overlap_z
   double precision :: overlap_x0, overlap_y0, overlap_z0
   double precision :: alpha, beta, c
   double precision :: A_center(3), B_center(3)
-  integer :: power_A(3), power_B(3)
   double precision :: d_a_2,d_2
+
+  if(use_cosgtos) then
+    !print*, 'use_cosgtos for ao_kinetic_integrals ?', use_cosgtos
+
+    do j = 1, ao_num
+      do i = 1, ao_num
+        ao_deriv2_x(i,j) = ao_deriv2_cosgtos_x(i,j)
+        ao_deriv2_y(i,j) = ao_deriv2_cosgtos_y(i,j)
+        ao_deriv2_z(i,j) = ao_deriv2_cosgtos_z(i,j)
+      enddo
+    enddo
+
+  else
+
     dim1=100
 
     ! -- Dummy call to provide everything
@@ -117,8 +133,12 @@
     enddo
     !$OMP END PARALLEL DO
 
+  endif
+
 END_PROVIDER
 
+! ---
+
 BEGIN_PROVIDER [double precision, ao_kinetic_integrals, (ao_num,ao_num)]
   implicit none
   BEGIN_DOC

src/ao_one_e_ints/pot_ao_ints.irp.f

@@ -1,4 +1,8 @@
+
+! ---
+
 BEGIN_PROVIDER [ double precision, ao_integrals_n_e, (ao_num,ao_num)]
+
   BEGIN_DOC
   !  Nucleus-electron interaction, in the |AO| basis set.
   !
@@ -6,17 +10,30 @@ BEGIN_PROVIDER [ double precision, ao_integrals_n_e, (ao_num,ao_num)]
   !
   !  These integrals also contain the pseudopotential integrals.
   END_DOC
+
   implicit none
-  double precision               :: alpha, beta, gama, delta
+  integer          :: num_A, num_B, power_A(3), power_B(3)
-  integer                        :: num_A,num_B
+  integer          :: i, j, k, l, n_pt_in, m
+  double precision :: alpha, beta
   double precision :: A_center(3),B_center(3),C_center(3)
-  integer                        :: power_A(3),power_B(3)
-  integer                        :: i,j,k,l,n_pt_in,m
   double precision :: overlap_x,overlap_y,overlap_z,overlap,dx,NAI_pol_mult
 
   if (read_ao_integrals_n_e) then
+
     call ezfio_get_ao_one_e_ints_ao_integrals_n_e(ao_integrals_n_e)
     print *,  'AO N-e integrals read from disk'
+
+  else
+
+    if(use_cosgtos) then
+      !print *, " use_cosgtos for ao_integrals_n_e ?", use_cosgtos
+
+      do j = 1, ao_num
+        do i = 1, ao_num
+          ao_integrals_n_e(i,j) = ao_integrals_n_e_cosgtos(i,j)
+        enddo
+      enddo
+
     else
 
       ao_integrals_n_e = 0.d0
@@ -29,7 +46,7 @@ BEGIN_PROVIDER [ double precision, ao_integrals_n_e, (ao_num,ao_num)]
       !$OMP PARALLEL                                                   &
           !$OMP DEFAULT (NONE)                                         &
           !$OMP PRIVATE (i,j,k,l,m,alpha,beta,A_center,B_center,C_center,power_A,power_B,&
-        !$OMP          num_A,num_B,Z,c,n_pt_in)                      &
+          !$OMP          num_A,num_B,Z,c,c1,n_pt_in)                      &
           !$OMP SHARED (ao_num,ao_prim_num,ao_expo_ordered_transp,ao_power,ao_nucl,nucl_coord,ao_coef_normalized_ordered_transp,&
           !$OMP         n_pt_max_integrals,ao_integrals_n_e,nucl_num,nucl_charge)
 
@@ -54,7 +71,7 @@ BEGIN_PROVIDER [ double precision, ao_integrals_n_e, (ao_num,ao_num)]
             do m=1,ao_prim_num(i)
               beta = ao_expo_ordered_transp(m,i)
 
-            double precision               :: c
+              double precision               :: c, c1
               c = 0.d0
 
               do  k = 1, nucl_num
@@ -63,8 +80,16 @@ BEGIN_PROVIDER [ double precision, ao_integrals_n_e, (ao_num,ao_num)]
 
                 C_center(1:3) = nucl_coord(k,1:3)
 
-              c = c - Z * NAI_pol_mult(A_center,B_center,            &
+                !print *, ' '
-                  power_A,power_B,alpha,beta,C_center,n_pt_in)
+                !print *, A_center, B_center, C_center, power_A, power_B
+                !print *, alpha, beta
+
+                c1 = NAI_pol_mult( A_center, B_center, power_A, power_B &
+                                 , alpha, beta, C_center, n_pt_in )
+
+                !print *, ' c1 = ', c1
+
+                c = c - Z * c1
 
               enddo
               ao_integrals_n_e(i,j) = ao_integrals_n_e(i,j)  &
@@ -77,7 +102,11 @@ BEGIN_PROVIDER [ double precision, ao_integrals_n_e, (ao_num,ao_num)]
 
     !$OMP END DO
     !$OMP END PARALLEL
-    IF (DO_PSEUDO) THEN
+
+    endif
+
+
+    IF(DO_PSEUDO) THEN
        ao_integrals_n_e += ao_pseudo_integrals
     ENDIF
 
@@ -98,7 +127,7 @@ BEGIN_PROVIDER [ double precision, ao_integrals_n_e_imag, (ao_num,ao_num)]
   !  :math:`\langle \chi_i | -\sum_A \frac{1}{|r-R_A|} | \chi_j \rangle`
   END_DOC
   implicit none
-  double precision               :: alpha, beta, gama, delta
+  double precision               :: alpha, beta
   integer                        :: num_A,num_B
   double precision               :: A_center(3),B_center(3),C_center(3)
   integer                        :: power_A(3),power_B(3)
@@ -121,7 +150,7 @@ BEGIN_PROVIDER [ double precision, ao_integrals_n_e_per_atom, (ao_num,ao_num,nuc
 ! :math:`\langle \chi_i | -\frac{1}{|r-R_A|} | \chi_j \rangle`
   END_DOC
   implicit none
-  double precision               :: alpha, beta, gama, delta
+  double precision               :: alpha, beta
   integer                        :: i_c,num_A,num_B
   double precision               :: A_center(3),B_center(3),C_center(3)
   integer                        :: power_A(3),power_B(3)
@@ -259,11 +288,14 @@ double precision function NAI_pol_mult(A_center,B_center,power_A,power_B,alpha,b
   ! sum of integrals of type : int {t,[0,1]}  exp-(rho.(P-Q)^2 * t^2) * t^i
   do i =0 ,n_pt_out,2
     accu +=  d(i) * rint(i/2,const)
+
+!    print *, i/2, const, d(i), rint(shiftr(i, 1), const)
   enddo
   NAI_pol_mult = accu * coeff
 
 end
 
+! ---
 
 subroutine give_polynomial_mult_center_one_e(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out)
   implicit none
@@ -575,61 +607,3 @@ double precision function V_r(n,alpha)
 end
 
 
-double precision function V_phi(n,m)
-  implicit none
-  BEGIN_DOC
-  ! Computes the angular $\phi$ part of the nuclear attraction integral:
-  !
-  ! $\int_{0}^{2 \pi} \cos(\phi)^n \sin(\phi)^m d\phi$.
-  END_DOC
-  integer                        :: n,m, i
-  double precision               :: prod, Wallis
-  prod = 1.d0
-  do i = 0,shiftr(n,1)-1
-    prod = prod/ (1.d0 + dfloat(m+1)/dfloat(n-i-i-1))
-  enddo
-  V_phi = 4.d0 * prod * Wallis(m)
-end
-
-
-double precision function V_theta(n,m)
-  implicit none
-  BEGIN_DOC
-  ! Computes the angular $\theta$ part of the nuclear attraction integral:
-  !
-  ! $\int_{0}^{\pi} \cos(\theta)^n \sin(\theta)^m d\theta$
-  END_DOC
-  integer                        :: n,m,i
-  double precision               :: Wallis, prod
-  include 'utils/constants.include.F'
-  V_theta = 0.d0
-  prod = 1.d0
-  do i = 0,shiftr(n,1)-1
-    prod = prod / (1.d0 + dfloat(m+1)/dfloat(n-i-i-1))
-  enddo
-  V_theta = (prod+prod) * Wallis(m)
-end
-
-
-double precision function Wallis(n)
-  implicit none
-  BEGIN_DOC
-  ! Wallis integral:
-  !
-  ! $\int_{0}^{\pi} \cos(\theta)^n d\theta$.
-  END_DOC
-  double precision               :: fact
-  integer                        :: n,p
-  include 'utils/constants.include.F'
-  if(iand(n,1).eq.0)then
-    Wallis = fact(shiftr(n,1))
-    Wallis = pi * fact(n) / (dble(ibset(0_8,n)) * (Wallis+Wallis)*Wallis)
-  else
-    p = shiftr(n,1)
-    Wallis = fact(p)
-    Wallis = dble(ibset(0_8,p+p)) * Wallis*Wallis / fact(p+p+1)
-  endif
-
-end
-
-

src/ao_one_e_ints/pot_ao_pseudo_ints.irp.f

@@ -28,7 +28,6 @@ BEGIN_PROVIDER [ double precision, ao_pseudo_integrals, (ao_num,ao_num)]
 END_PROVIDER
 
 BEGIN_PROVIDER [ double precision, ao_pseudo_integrals_local, (ao_num,ao_num)]
-  use omp_lib
   implicit none
   BEGIN_DOC
   ! Local pseudo-potential
@@ -43,6 +42,7 @@ BEGIN_PROVIDER [ double precision, ao_pseudo_integrals_local, (ao_num,ao_num)]
 
   double precision               :: wall_1, wall_2, wall_0
   integer                        :: thread_num
+  integer                        :: omp_get_thread_num
   double precision               :: c
   double precision               :: Z
 
@@ -158,7 +158,6 @@ BEGIN_PROVIDER [ double precision, ao_pseudo_integrals_local, (ao_num,ao_num)]
 
 
  BEGIN_PROVIDER [ double precision, ao_pseudo_integrals_non_local, (ao_num,ao_num)]
-  use omp_lib
   implicit none
   BEGIN_DOC
   ! Non-local pseudo-potential
@@ -170,6 +169,7 @@ BEGIN_PROVIDER [ double precision, ao_pseudo_integrals_local, (ao_num,ao_num)]
   integer                        :: power_A(3),power_B(3)
   integer                        :: i,j,k,l,m
   double precision               :: Vloc, Vpseudo
+  integer                        :: omp_get_thread_num
 
   double precision               :: wall_1, wall_2, wall_0
   integer                        :: thread_num

src/ao_tc_eff_map/EZFIO.cfg

@@ -0,0 +1,12 @@
+
+[j1b_gauss_pen]
+type: double precision
+doc: exponents of the 1-body Jastrow
+interface: ezfio
+size: (nuclei.nucl_num)
+
+[j1b_gauss]
+type: integer
+doc: Use 1-body Gaussian Jastrow
+interface: ezfio, provider, ocaml
+default: 0

src/ao_tc_eff_map/NEED

@@ -0,0 +1,4 @@
+ao_two_e_erf_ints
+mo_one_e_ints
+ao_many_one_e_ints
+dft_utils_in_r

src/ao_tc_eff_map/README.rst

@@ -0,0 +1,12 @@
+ao_tc_eff_map
+=============
+
+This is a module to obtain the integrals on the AO basis of the SCALAR HERMITIAN 
+effective potential defined in Eq. 32 of JCP 154, 084119 (2021)
+It also contains the modification by a one-body Jastrow factor.  
+
+The main routine/providers are
+
++) ao_tc_sym_two_e_pot_map : map of the SCALAR PART of total effective two-electron on the AO basis in PHYSICIST notations. It might contain the two-electron term coming from the one-e correlation factor. 
++) get_ao_tc_sym_two_e_pot(i,j,k,l,ao_tc_sym_two_e_pot_map) : routine to get the integrals from ao_tc_sym_two_e_pot_map. 
++) ao_tc_sym_two_e_pot(i,j,k,l) : FUNCTION that returns the scalar part of TC-potential EXCLUDING the erf(mu r12)/r12. See two_e_ints_gauss.irp.f for more details. 

src/ao_tc_eff_map/compute_ints_eff_pot.irp.f

@@ -0,0 +1,75 @@
+subroutine compute_ao_tc_sym_two_e_pot_jl(j, l, n_integrals, buffer_i, buffer_value)
+
+  use map_module
+
+  BEGIN_DOC
+  !  Parallel client for AO integrals of the TC integrals involving purely hermitian operators 
+  END_DOC
+
+  implicit none
+
+  integer, intent(in)             :: j, l
+  integer,intent(out)             :: n_integrals
+  integer(key_kind),intent(out)   :: buffer_i(ao_num*ao_num)
+  real(integral_kind),intent(out) :: buffer_value(ao_num*ao_num)
+
+  integer                         :: i, k
+  integer                         :: kk, m, j1, i1
+  double precision                :: cpu_1, cpu_2, wall_1, wall_2
+  double precision                :: integral, wall_0, integral_pot, integral_erf
+  double precision                :: thr
+
+  logical, external               :: ao_two_e_integral_zero
+  double precision                :: ao_tc_sym_two_e_pot, ao_two_e_integral_erf
+  double precision                :: j1b_gauss_erf, j1b_gauss_coul
+  double precision                :: j1b_gauss_coul_debug
+  double precision                :: j1b_gauss_coul_modifdebug
+  double precision                :: j1b_gauss_coulerf
+
+
+  PROVIDE j1b_gauss
+
+  thr = ao_integrals_threshold
+
+  n_integrals = 0
+
+  j1 = j+ishft(l*l-l,-1)
+  do k = 1, ao_num           ! r1
+    i1 = ishft(k*k-k,-1)
+    if (i1 > j1) then
+      exit
+    endif
+    do i = 1, k
+      i1 += 1
+      if (i1 > j1) then
+        exit
+      endif
+
+      if (ao_two_e_integral_erf_schwartz(i,k)*ao_two_e_integral_erf_schwartz(j,l) < thr ) then
+        cycle
+      endif
+
+      !DIR$ FORCEINLINE
+      integral_pot = ao_tc_sym_two_e_pot  (i, k, j, l)  ! i,k : r1    j,l : r2
+      integral_erf = ao_two_e_integral_erf(i, k, j, l)
+      integral     = integral_erf + integral_pot
+
+      if( j1b_gauss .eq. 1 ) then
+        integral = integral                   & 
+                 + j1b_gauss_coulerf(i, k, j, l)
+      endif
+
+
+      if(abs(integral) < thr) then
+        cycle
+      endif
+
+      n_integrals += 1
+      !DIR$ FORCEINLINE
+      call two_e_integrals_index(i, j, k, l, buffer_i(n_integrals))
+      buffer_value(n_integrals) = integral
+    enddo
+  enddo
+
+end subroutine compute_ao_tc_sym_two_e_pot_jl
+

src/ao_tc_eff_map/integrals_eff_pot_in_map_slave.irp.f

@@ -0,0 +1,194 @@
+subroutine ao_tc_sym_two_e_pot_in_map_slave_tcp(i)
+  implicit none
+  integer, intent(in)            :: i
+  BEGIN_DOC
+! Computes a buffer of integrals. i is the ID of the current thread.
+  END_DOC
+  call ao_tc_sym_two_e_pot_in_map_slave(0,i)
+end
+
+
+subroutine ao_tc_sym_two_e_pot_in_map_slave_inproc(i)
+  implicit none
+  integer, intent(in)            :: i
+  BEGIN_DOC
+! Computes a buffer of integrals. i is the ID of the current thread.
+  END_DOC
+  call ao_tc_sym_two_e_pot_in_map_slave(1,i)
+end
+
+
+
+
+
+subroutine ao_tc_sym_two_e_pot_in_map_slave(thread,iproc)
+  use map_module
+  use f77_zmq
+  implicit none
+  BEGIN_DOC
+! Computes a buffer of integrals
+  END_DOC
+
+  integer, intent(in)            :: thread, iproc
+
+  integer                        :: j,l,n_integrals
+  integer                        :: rc
+  real(integral_kind), allocatable :: buffer_value(:)
+  integer(key_kind), allocatable :: buffer_i(:)
+
+  integer                        :: worker_id, task_id
+  character*(512)                :: task
+
+  integer(ZMQ_PTR),external      :: new_zmq_to_qp_run_socket
+  integer(ZMQ_PTR)               :: zmq_to_qp_run_socket
+
+  integer(ZMQ_PTR), external     :: new_zmq_push_socket
+  integer(ZMQ_PTR)               :: zmq_socket_push
+
+  character*(64)                 :: state
+
+  zmq_to_qp_run_socket = new_zmq_to_qp_run_socket()
+
+  integer, external :: connect_to_taskserver
+  if (connect_to_taskserver(zmq_to_qp_run_socket,worker_id,thread) == -1) then
+    call end_zmq_to_qp_run_socket(zmq_to_qp_run_socket)
+    return
+  endif
+
+  zmq_socket_push      = new_zmq_push_socket(thread)
+
+  allocate ( buffer_i(ao_num*ao_num), buffer_value(ao_num*ao_num) )
+
+
+  do
+    integer, external :: get_task_from_taskserver
+    if (get_task_from_taskserver(zmq_to_qp_run_socket,worker_id, task_id, task) == -1) then
+      exit
+    endif
+    if (task_id == 0) exit
+    read(task,*) j, l
+    integer, external :: task_done_to_taskserver
+    call compute_ao_tc_sym_two_e_pot_jl(j,l,n_integrals,buffer_i,buffer_value)
+    if (task_done_to_taskserver(zmq_to_qp_run_socket,worker_id,task_id) == -1) then
+        stop 'Unable to send task_done'
+    endif
+    call push_integrals(zmq_socket_push, n_integrals, buffer_i, buffer_value, task_id)
+  enddo
+
+  integer, external :: disconnect_from_taskserver
+  if (disconnect_from_taskserver(zmq_to_qp_run_socket,worker_id) == -1) then
+    continue
+  endif
+  deallocate( buffer_i, buffer_value )
+  call end_zmq_to_qp_run_socket(zmq_to_qp_run_socket)
+  call end_zmq_push_socket(zmq_socket_push,thread)
+
+end
+
+
+subroutine ao_tc_sym_two_e_pot_in_map_collector(zmq_socket_pull)
+  use map_module
+  use f77_zmq
+  implicit none
+  BEGIN_DOC
+! Collects results from the AO integral calculation
+  END_DOC
+
+  integer(ZMQ_PTR), intent(in)   :: zmq_socket_pull
+  integer                        :: j,l,n_integrals
+  integer                        :: rc
+
+  real(integral_kind), allocatable :: buffer_value(:)
+  integer(key_kind), allocatable :: buffer_i(:)
+
+  integer(ZMQ_PTR),external      :: new_zmq_to_qp_run_socket
+  integer(ZMQ_PTR)               :: zmq_to_qp_run_socket
+
+  integer(ZMQ_PTR), external     :: new_zmq_pull_socket
+
+  integer*8                      :: control, accu, sze
+  integer                        :: task_id, more
+
+  zmq_to_qp_run_socket = new_zmq_to_qp_run_socket()
+
+  sze = ao_num*ao_num
+  allocate ( buffer_i(sze), buffer_value(sze) )
+
+  accu = 0_8
+  more = 1
+  do while (more == 1)
+
+    rc = f77_zmq_recv( zmq_socket_pull, n_integrals, 4, 0)
+    if (rc == -1) then
+      n_integrals = 0
+      return
+    endif
+    if (rc /= 4) then
+      print *, irp_here,  ': f77_zmq_recv( zmq_socket_pull, n_integrals, 4, 0)'
+      stop 'error'
+    endif
+
+    if (n_integrals >= 0) then
+
+      if (n_integrals > sze) then
+        deallocate (buffer_value, buffer_i)
+        sze = n_integrals
+        allocate (buffer_value(sze), buffer_i(sze))
+      endif
+
+      rc = f77_zmq_recv( zmq_socket_pull, buffer_i, key_kind*n_integrals, 0)
+      if (rc /= key_kind*n_integrals) then
+        print *,  rc, key_kind, n_integrals
+        print *, irp_here,  ': f77_zmq_recv( zmq_socket_pull, buffer_i, key_kind*n_integrals, 0)'
+        stop 'error'
+      endif
+
+      rc = f77_zmq_recv( zmq_socket_pull, buffer_value, integral_kind*n_integrals, 0)
+      if (rc /= integral_kind*n_integrals) then
+        print *, irp_here,  ': f77_zmq_recv( zmq_socket_pull, buffer_value, integral_kind*n_integrals, 0)'
+        stop 'error'
+      endif
+
+      rc = f77_zmq_recv( zmq_socket_pull, task_id, 4, 0)
+
+IRP_IF ZMQ_PUSH
+IRP_ELSE
+      rc = f77_zmq_send( zmq_socket_pull, 0, 4, 0)
+      if (rc /= 4) then
+        print *,  irp_here, ' : f77_zmq_send (zmq_socket_pull,...'
+        stop 'error'
+      endif
+IRP_ENDIF
+
+
+      call insert_into_ao_tc_sym_two_e_pot_map(n_integrals,buffer_i,buffer_value)
+      accu += n_integrals
+      if (task_id /= 0) then
+        integer, external :: zmq_delete_task
+        if (zmq_delete_task(zmq_to_qp_run_socket,zmq_socket_pull,task_id,more) == -1) then
+          stop 'Unable to delete task'
+        endif
+      endif
+    endif
+
+  enddo
+
+  deallocate( buffer_i, buffer_value )
+
+  integer (map_size_kind) :: get_ao_tc_sym_two_e_pot_map_size
+  control = get_ao_tc_sym_two_e_pot_map_size(ao_tc_sym_two_e_pot_map)
+
+  if (control /= accu) then
+      print *, ''
+      print *, irp_here
+      print *, 'Control : ', control
+      print *, 'Accu    : ', accu
+      print *, 'Some integrals were lost during the parallel computation.'
+      print *, 'Try to reduce the number of threads.'
+      stop
+  endif
+
+  call end_zmq_to_qp_run_socket(zmq_to_qp_run_socket)
+
+end
+

src/ao_tc_eff_map/j1b_1eInteg.py

@@ -0,0 +1,299 @@
+import sys, os
+QP_PATH=os.environ["QP_EZFIO"]
+sys.path.insert(0,QP_PATH+"/Python/")
+from ezfio import ezfio
+from datetime import datetime
+import time
+from math import exp, sqrt, pi
+import numpy as np
+import subprocess
+from scipy.integrate import tplquad
+import multiprocessing
+from multiprocessing import Pool
+
+
+# _____________________________________________________________________________
+#
+def read_ao():
+
+    with open('ao_data') as f:
+        lines = f.readlines()
+
+    ao_prim_num = np.zeros((ao_num), dtype=int)
+    ao_nucl     = np.zeros((ao_num), dtype=int)
+    ao_power    = np.zeros((ao_num, 3))
+    nucl_coord  = np.zeros((ao_num, 3))
+    ao_expo     = np.zeros((ao_num, ao_num))
+    ao_coef     = np.zeros((ao_num, ao_num))
+
+    iline = 0
+    for j in range(ao_num):
+       
+        line   = lines[iline]
+        iline += 1
+        ao_nucl[j] = int(line) - 1
+
+        line   = lines[iline].split()
+        iline += 1
+        ao_power[j, 0] = float(line[0])
+        ao_power[j, 1] = float(line[1])
+        ao_power[j, 2] = float(line[2])
+
+        line   = lines[iline].split()
+        iline += 1
+        nucl_coord[ao_nucl[j], 0] = float(line[0])
+        nucl_coord[ao_nucl[j], 1] = float(line[1])
+        nucl_coord[ao_nucl[j], 2] = float(line[2])
+
+        line   = lines[iline]
+        iline += 1
+        ao_prim_num[j] = int(line)
+
+        for l in range(ao_prim_num[j]):
+
+            line   = lines[iline].split()
+            iline += 1
+            ao_expo[l, j] = float(line[0])
+            ao_coef[l, j] = float(line[1])
+
+    return( ao_prim_num
+          , ao_nucl
+          , ao_power
+          , nucl_coord 
+          , ao_expo 
+          , ao_coef )
+# _____________________________________________________________________________
+
+
+# _____________________________________________________________________________
+#
+def Gao(X, i_ao):
+
+    ii  = ao_nucl[i_ao]
+    C   = np.array([nucl_coord[ii,0], nucl_coord[ii,1], nucl_coord[ii,2]])
+    Y   = X - C
+    dis = np.dot(Y,Y)
+
+    ip  = np.array([ao_power[i_ao,0], ao_power[i_ao,1], ao_power[i_ao,2]])
+    pol = np.prod(Y**ip)
+
+    xi  = np.sum( ao_coef[:,i_ao] * np.exp(-dis*ao_expo[:,i_ao]) )
+
+    return(xi*pol)
+# _____________________________________________________________________________
+
+
+# _____________________________________________________________________________
+#
+def grad_Gao(X, i_ao):
+
+    ii = ao_nucl[i_ao]
+    C  = np.array([nucl_coord[ii,0], nucl_coord[ii,1], nucl_coord[ii,2]])
+
+    ix = ao_power[i_ao,0]
+    iy = ao_power[i_ao,1]
+    iz = ao_power[i_ao,2]
+
+    Y   = X - C
+    dis = np.dot(Y,Y)
+
+    xm = np.sum(                ao_coef[:,i_ao]*np.exp(-dis*ao_expo[:,i_ao]))
+    xp = np.sum(ao_expo[:,i_ao]*ao_coef[:,i_ao]*np.exp(-dis*ao_expo[:,i_ao]))
+
+    ip  = np.array([ix+1, iy, iz])
+    dx  = -2. * np.prod(Y**ip) * xp 
+    if(ix > 0):
+        ip  = np.array([ix-1, iy, iz])
+        dx += ix * np.prod(Y**ip) * xm
+
+    ip  = np.array([ix, iy+1, iz])
+    dy  = -2. * np.prod(Y**ip) * xp 
+    if(iy > 0):
+        ip  = np.array([ix, iy-1, iz])
+        dy += iy * np.prod(Y**ip) * xm
+
+    ip  = np.array([ix, iy, iz+1])
+    dz  = -2. * np.prod(Y**ip) * xp 
+    if(iz > 0):
+        ip  = np.array([ix, iy, iz-1])
+        dz += iz * np.prod(Y**ip) * xm
+
+    return(np.array([dx, dy, dz]))
+# _____________________________________________________________________________
+
+
+# _____________________________________________________________________________
+#
+#              3 x < XA |       exp[-gama r_C^2] | XB > 
+#            - 2 x < XA | r_A^2 exp[-gama r_C^2] | XB >
+#
+def integ_lap(z, y, x, i_ao, j_ao):
+
+    X = np.array([x, y, z])
+
+    Gi = Gao(X, i_ao)
+    Gj = Gao(X, j_ao)
+
+    c = 0.
+    for k in range(nucl_num):
+        gama = j1b_gauss_pen[k]
+        C    = nucl_coord[k,:]  
+        Y    = X - C
+        dis  = np.dot(Y, Y)
+        arg  = exp(-gama*dis)
+        arg  = exp(-gama*dis)
+        c += ( 3. - 2. * dis * gama ) * arg * gama * Gi * Gj 
+
+    return(c)
+# _____________________________________________________________________________
+
+
+# _____________________________________________________________________________
+#
+#
+def integ_grad2(z, y, x, i_ao, j_ao):
+
+    X = np.array([x, y, z])
+
+    Gi = Gao(X, i_ao)
+    Gj = Gao(X, j_ao)
+
+    c = np.zeros((3))
+    for k in range(nucl_num):
+        gama = j1b_gauss_pen[k]
+        C    = nucl_coord[k,:]  
+        Y    = X - C
+        c   += gama * exp(-gama*np.dot(Y, Y)) * Y
+
+    return(-2*np.dot(c,c)*Gi*Gj)
+# _____________________________________________________________________________
+
+
+# _____________________________________________________________________________
+#
+#
+def integ_nonh(z, y, x, i_ao, j_ao):
+
+    X = np.array([x, y, z])
+
+    Gi = Gao(X, i_ao)
+
+    c = 0.
+    for k in range(nucl_num):
+        gama = j1b_gauss_pen[k]
+        C    = nucl_coord[k,:]  
+        Y    = X - C
+        grad = grad_Gao(X, j_ao)
+        c   += gama * exp(-gama*np.dot(Y,Y)) * np.dot(Y,grad)
+
+    return(2*c*Gi)
+# _____________________________________________________________________________
+
+
+# _____________________________________________________________________________
+#
+def perform_integ( ind_ao ):
+
+    i_ao = ind_ao[0]
+    j_ao = ind_ao[1]
+
+    a      = -15. #-np.Inf
+    b      = +15. #+np.Inf
+    epsrel = 1e-5
+
+    res_lap, err_lap = tplquad( integ_lap
+                              , a, b
+                              , lambda x  : a, lambda x  : b
+                              , lambda x,y: a, lambda x,y: b
+                              , (i_ao, j_ao)
+                              , epsrel=epsrel )
+
+    res_grd, err_grd = tplquad( integ_grad2
+                              , a, b
+                              , lambda x  : a, lambda x  : b
+                              , lambda x,y: a, lambda x,y: b
+                              , (i_ao, j_ao)
+                              , epsrel=epsrel )
+
+    res_nnh, err_nnh = tplquad( integ_nonh
+                              , a, b
+                              , lambda x  : a, lambda x  : b
+                              , lambda x,y: a, lambda x,y: b
+                              , (i_ao, j_ao)
+                              , epsrel=epsrel )
+  
+    return( [ res_lap, err_lap
+            , res_grd, err_grd
+            , res_nnh, err_nnh ])
+# _____________________________________________________________________________
+
+
+# _____________________________________________________________________________
+#
+def integ_eval():
+
+    list_ind = []
+    for i_ao in range(ao_num):
+        for j_ao in range(ao_num):
+            list_ind.append( [i_ao, j_ao] )
+
+    nb_proc = multiprocessing.cpu_count()
+    print(" --- Excexution with {} processors ---\n".format(nb_proc))
+
+    p   = Pool(nb_proc)
+    res = np.array( p.map( perform_integ, list_ind ) )
+
+    ii = 0
+    for i_ao in range(ao_num):
+        for j_ao in range(ao_num):
+            print(" {} {}     {:+e} {:+e}     {:+e} {:+e}".format( i_ao, j_ao
+                 , res[ii][0], res[ii][1], res[ii][2], res[ii][3]) )
+            ii += 1
+
+    p.close()
+# _____________________________________________________________________________
+
+
+
+# _____________________________________________________________________________
+#
+if __name__=="__main__":
+  
+    t0 = time.time()
+
+    EZFIO_file = sys.argv[1]
+    ezfio.set_file(EZFIO_file)
+
+    print(" Today's date:", datetime.now() )
+    print(" EZFIO file = {}".format(EZFIO_file))
+
+    nucl_num      = ezfio.get_nuclei_nucl_num()
+    ao_num        = ezfio.get_ao_basis_ao_num()
+    j1b_gauss_pen = ezfio.get_ao_tc_eff_map_j1b_gauss_pen() 
+
+    ao_prim_num, ao_nucl, ao_power, nucl_coord, ao_expo, ao_coef = read_ao()
+
+    #integ_eval()
+
+    i_ao   = 0 
+    j_ao   = 0
+
+    a      = -5. 
+    b      = +5. 
+    epsrel = 1e-1
+    res_grd, err_grd = tplquad( integ_nonh
+                              , a, b
+                              , lambda x  : a, lambda x  : b
+                              , lambda x,y: a, lambda x,y: b
+                              , (i_ao, j_ao)
+                              , epsrel=epsrel )
+
+    print(res_grd, err_grd)
+ 
+
+    tf = time.time() - t0
+    print(' end after {} min'.format(tf/60.))
+# _____________________________________________________________________________
+
+
+

src/ao_tc_eff_map/j1b_pen.irp.f

@@ -0,0 +1,59 @@
+
+! ---
+
+BEGIN_PROVIDER [ double precision, j1b_gauss_pen, (nucl_num) ]
+
+  BEGIN_DOC
+  ! exponents of the 1-body Jastrow
+  END_DOC
+
+  implicit none
+  logical :: exists
+
+  PROVIDE ezfio_filename
+
+  if (mpi_master) then
+    call ezfio_has_ao_tc_eff_map_j1b_gauss_pen(exists)
+  endif
+
+  IRP_IF MPI_DEBUG
+    print *,  irp_here, mpi_rank
+    call MPI_BARRIER(MPI_COMM_WORLD, ierr)
+  IRP_ENDIF
+
+  IRP_IF MPI
+    include 'mpif.h'
+    integer :: ierr
+    call MPI_BCAST(j1b_gauss_pen, (nucl_num), MPI_DOUBLE_PRECISION, 0, MPI_COMM_WORLD, ierr)
+    if (ierr /= MPI_SUCCESS) then
+      stop 'Unable to read j1b_gauss_pen with MPI'
+    endif
+  IRP_ENDIF
+
+  if (exists) then
+
+    if (mpi_master) then
+      write(6,'(A)') '.. >>>>> [ IO READ: j1b_gauss_pen ] <<<<< ..'
+      call ezfio_get_ao_tc_eff_map_j1b_gauss_pen(j1b_gauss_pen)
+      IRP_IF MPI
+        call MPI_BCAST(j1b_gauss_pen, (nucl_num), MPI_DOUBLE_PRECISION, 0, MPI_COMM_WORLD, ierr)
+        if (ierr /= MPI_SUCCESS) then
+          stop 'Unable to read j1b_gauss_pen with MPI'
+        endif
+      IRP_ENDIF
+    endif
+
+  else
+ 
+    integer :: i
+    do i = 1, nucl_num
+      j1b_gauss_pen(i) = 1d5
+    enddo
+
+  endif
+
+END_PROVIDER
+
+! ---
+
+

src/ao_tc_eff_map/map_integrals_eff_pot.irp.f

@@ -0,0 +1,291 @@
+use map_module
+
+!! AO Map
+!! ======
+
+BEGIN_PROVIDER [ type(map_type), ao_tc_sym_two_e_pot_map ]
+  implicit none
+  BEGIN_DOC
+  ! |AO| integrals
+  END_DOC
+  integer(key_kind)              :: key_max
+  integer(map_size_kind)         :: sze
+  call two_e_integrals_index(ao_num,ao_num,ao_num,ao_num,key_max)
+  sze = key_max
+  call map_init(ao_tc_sym_two_e_pot_map,sze)
+  print*,  'ao_tc_sym_two_e_pot_map map initialized : ', sze
+END_PROVIDER
+
+ BEGIN_PROVIDER [ integer, ao_tc_sym_two_e_pot_cache_min ]
+&BEGIN_PROVIDER [ integer, ao_tc_sym_two_e_pot_cache_max ]
+ implicit none
+ BEGIN_DOC
+ ! Min and max values of the AOs for which the integrals are in the cache
+ END_DOC
+ ao_tc_sym_two_e_pot_cache_min = max(1,ao_num - 63)
+ ao_tc_sym_two_e_pot_cache_max = ao_num
+
+END_PROVIDER
+
+BEGIN_PROVIDER [ double precision, ao_tc_sym_two_e_pot_cache, (0:64*64*64*64) ]
+  use map_module
+ implicit none
+ BEGIN_DOC
+ ! Cache of |AO| integrals for fast access
+ END_DOC
+ PROVIDE ao_tc_sym_two_e_pot_in_map
+ integer                        :: i,j,k,l,ii
+ integer(key_kind)              :: idx
+ real(integral_kind)            :: integral
+ !$OMP PARALLEL DO PRIVATE (i,j,k,l,idx,ii,integral)
+ do l=ao_tc_sym_two_e_pot_cache_min,ao_tc_sym_two_e_pot_cache_max
+   do k=ao_tc_sym_two_e_pot_cache_min,ao_tc_sym_two_e_pot_cache_max
+     do j=ao_tc_sym_two_e_pot_cache_min,ao_tc_sym_two_e_pot_cache_max
+       do i=ao_tc_sym_two_e_pot_cache_min,ao_tc_sym_two_e_pot_cache_max
+         !DIR$ FORCEINLINE
+         call two_e_integrals_index(i,j,k,l,idx)
+         !DIR$ FORCEINLINE
+         call map_get(ao_tc_sym_two_e_pot_map,idx,integral)
+         ii = l-ao_tc_sym_two_e_pot_cache_min
+         ii = ior( ishft(ii,6), k-ao_tc_sym_two_e_pot_cache_min)
+         ii = ior( ishft(ii,6), j-ao_tc_sym_two_e_pot_cache_min)
+         ii = ior( ishft(ii,6), i-ao_tc_sym_two_e_pot_cache_min)
+         ao_tc_sym_two_e_pot_cache(ii) = integral
+       enddo
+     enddo
+   enddo
+ enddo
+ !$OMP END PARALLEL DO
+
+END_PROVIDER
+
+
+subroutine insert_into_ao_tc_sym_two_e_pot_map(n_integrals,buffer_i, buffer_values)
+  use map_module
+  implicit none
+  BEGIN_DOC
+  ! Create new entry into |AO| map
+  END_DOC
+
+  integer, intent(in)                :: n_integrals
+  integer(key_kind), intent(inout)   :: buffer_i(n_integrals)
+  real(integral_kind), intent(inout) :: buffer_values(n_integrals)
+
+  call map_append(ao_tc_sym_two_e_pot_map, buffer_i, buffer_values, n_integrals)
+end
+
+double precision function get_ao_tc_sym_two_e_pot(i,j,k,l,map) result(result)
+  use map_module
+  implicit none
+  BEGIN_DOC
+  ! Gets one |AO| two-electron integral from the |AO| map in PHYSICIST NOTATION
+  END_DOC
+  integer, intent(in)            :: i,j,k,l
+  integer(key_kind)              :: idx
+  type(map_type), intent(inout)  :: map
+  integer                        :: ii
+  real(integral_kind)            :: tmp
+  logical, external              :: ao_two_e_integral_zero
+  PROVIDE ao_tc_sym_two_e_pot_in_map ao_tc_sym_two_e_pot_cache ao_tc_sym_two_e_pot_cache_min
+  !DIR$ FORCEINLINE
+!  if (ao_two_e_integral_zero(i,j,k,l)) then
+  if (.False.) then
+    tmp = 0.d0
+  !else if (ao_two_e_integral_erf_schwartz(i,k)*ao_two_e_integral_erf_schwartz(j,l) < ao_integrals_threshold) then
+  !  tmp = 0.d0
+  else
+    ii = l-ao_tc_sym_two_e_pot_cache_min
+    ii = ior(ii, k-ao_tc_sym_two_e_pot_cache_min)
+    ii = ior(ii, j-ao_tc_sym_two_e_pot_cache_min)
+    ii = ior(ii, i-ao_tc_sym_two_e_pot_cache_min)
+    if (iand(ii, -64) /= 0) then
+      !DIR$ FORCEINLINE
+      call two_e_integrals_index(i,j,k,l,idx)
+      !DIR$ FORCEINLINE
+      call map_get(map,idx,tmp)
+      tmp = tmp
+    else
+      ii = l-ao_tc_sym_two_e_pot_cache_min
+      ii = ior( ishft(ii,6), k-ao_tc_sym_two_e_pot_cache_min)
+      ii = ior( ishft(ii,6), j-ao_tc_sym_two_e_pot_cache_min)
+      ii = ior( ishft(ii,6), i-ao_tc_sym_two_e_pot_cache_min)
+      tmp = ao_tc_sym_two_e_pot_cache(ii)
+    endif
+  endif
+  result = tmp
+end
+
+
+subroutine get_many_ao_tc_sym_two_e_pot(j,k,l,sze,out_val)
+  use map_module
+  BEGIN_DOC
+  ! Gets multiple |AO| two-electron integral from the |AO| map .
+  ! All i are retrieved for j,k,l fixed.
+  END_DOC
+  implicit none
+  integer, intent(in)            :: j,k,l, sze
+  real(integral_kind), intent(out) :: out_val(sze)
+
+  integer                        :: i
+  integer(key_kind)              :: hash
+  double precision               :: thresh
+! logical, external              :: ao_one_e_integral_zero
+  PROVIDE ao_tc_sym_two_e_pot_in_map ao_tc_sym_two_e_pot_map
+  thresh = ao_integrals_threshold
+
+! if (ao_one_e_integral_zero(j,l)) then
+  if (.False.) then
+    out_val = 0.d0
+    return
+  endif
+
+  double precision :: get_ao_tc_sym_two_e_pot
+  do i=1,sze
+    out_val(i) = get_ao_tc_sym_two_e_pot(i,j,k,l,ao_tc_sym_two_e_pot_map)
+  enddo
+
+end
+
+subroutine get_many_ao_tc_sym_two_e_pot_non_zero(j,k,l,sze,out_val,out_val_index,non_zero_int)
+  use map_module
+  implicit none
+  BEGIN_DOC
+  ! Gets multiple |AO| two-electron integrals from the |AO| map .
+  ! All non-zero i are retrieved for j,k,l fixed.
+  END_DOC
+  integer, intent(in)            :: j,k,l, sze
+  real(integral_kind), intent(out) :: out_val(sze)
+  integer, intent(out)           :: out_val_index(sze),non_zero_int
+
+  integer                        :: i
+  integer(key_kind)              :: hash
+  double precision               :: thresh,tmp
+! logical, external              :: ao_one_e_integral_zero
+  PROVIDE ao_tc_sym_two_e_pot_in_map
+  thresh = ao_integrals_threshold
+
+  non_zero_int = 0
+! if (ao_one_e_integral_zero(j,l)) then
+  if (.False.) then
+    out_val = 0.d0
+    return
+  endif
+
+  non_zero_int = 0
+  do i=1,sze
+    integer, external :: ao_l4
+    double precision, external :: ao_two_e_integral_eff_pot
+    !DIR$ FORCEINLINE
+    !if (ao_two_e_integral_erf_schwartz(i,k)*ao_two_e_integral_erf_schwartz(j,l) < thresh) then
+    !  cycle
+    !endif
+    call two_e_integrals_index(i,j,k,l,hash)
+    call map_get(ao_tc_sym_two_e_pot_map, hash,tmp)
+    if (dabs(tmp) < thresh ) cycle
+    non_zero_int = non_zero_int+1
+    out_val_index(non_zero_int) = i
+    out_val(non_zero_int) = tmp
+  enddo
+
+end
+
+
+function get_ao_tc_sym_two_e_pot_map_size()
+  implicit none
+  integer (map_size_kind) :: get_ao_tc_sym_two_e_pot_map_size
+  BEGIN_DOC
+  ! Returns the number of elements in the |AO| map
+  END_DOC
+  get_ao_tc_sym_two_e_pot_map_size = ao_tc_sym_two_e_pot_map % n_elements
+end
+
+subroutine clear_ao_tc_sym_two_e_pot_map
+  implicit none
+  BEGIN_DOC
+  ! Frees the memory of the |AO| map
+  END_DOC
+  call map_deinit(ao_tc_sym_two_e_pot_map)
+  FREE ao_tc_sym_two_e_pot_map
+end
+
+
+
+subroutine dump_ao_tc_sym_two_e_pot(filename)
+  use map_module
+  implicit none
+  BEGIN_DOC
+  ! Save to disk the |AO| eff_pot integrals
+  END_DOC
+  character*(*), intent(in)      :: filename
+  integer(cache_key_kind), pointer :: key(:)
+  real(integral_kind), pointer   :: val(:)
+  integer*8                      :: i,j, n
+  call ezfio_set_work_empty(.False.)
+  open(unit=66,file=filename,FORM='unformatted')
+  write(66) integral_kind, key_kind
+  write(66) ao_tc_sym_two_e_pot_map%sorted, ao_tc_sym_two_e_pot_map%map_size,    &
+      ao_tc_sym_two_e_pot_map%n_elements
+  do i=0_8,ao_tc_sym_two_e_pot_map%map_size
+    write(66) ao_tc_sym_two_e_pot_map%map(i)%sorted, ao_tc_sym_two_e_pot_map%map(i)%map_size,&
+        ao_tc_sym_two_e_pot_map%map(i)%n_elements
+  enddo
+  do i=0_8,ao_tc_sym_two_e_pot_map%map_size
+    key => ao_tc_sym_two_e_pot_map%map(i)%key
+    val => ao_tc_sym_two_e_pot_map%map(i)%value
+    n = ao_tc_sym_two_e_pot_map%map(i)%n_elements
+    write(66) (key(j), j=1,n), (val(j), j=1,n)
+  enddo
+  close(66)
+
+end
+
+
+
+integer function load_ao_tc_sym_two_e_pot(filename)
+  implicit none
+  BEGIN_DOC
+  ! Read from disk the |AO| eff_pot integrals
+  END_DOC
+  character*(*), intent(in)      :: filename
+  integer*8                      :: i
+  integer(cache_key_kind), pointer :: key(:)
+  real(integral_kind), pointer   :: val(:)
+  integer                        :: iknd, kknd
+  integer*8                      :: n, j
+  load_ao_tc_sym_two_e_pot = 1
+  open(unit=66,file=filename,FORM='unformatted',STATUS='UNKNOWN')
+  read(66,err=98,end=98) iknd, kknd
+  if (iknd /= integral_kind) then
+    print *,  'Wrong integrals kind in file :', iknd
+    stop 1
+  endif
+  if (kknd /= key_kind) then
+    print *,  'Wrong key kind in file :', kknd
+    stop 1
+  endif
+  read(66,err=98,end=98) ao_tc_sym_two_e_pot_map%sorted, ao_tc_sym_two_e_pot_map%map_size,&
+      ao_tc_sym_two_e_pot_map%n_elements
+  do i=0_8, ao_tc_sym_two_e_pot_map%map_size
+    read(66,err=99,end=99) ao_tc_sym_two_e_pot_map%map(i)%sorted,          &
+        ao_tc_sym_two_e_pot_map%map(i)%map_size, ao_tc_sym_two_e_pot_map%map(i)%n_elements
+    call cache_map_reallocate(ao_tc_sym_two_e_pot_map%map(i),ao_tc_sym_two_e_pot_map%map(i)%map_size)
+  enddo
+  do i=0_8, ao_tc_sym_two_e_pot_map%map_size
+    key => ao_tc_sym_two_e_pot_map%map(i)%key
+    val => ao_tc_sym_two_e_pot_map%map(i)%value
+    n = ao_tc_sym_two_e_pot_map%map(i)%n_elements
+    read(66,err=99,end=99) (key(j), j=1,n), (val(j), j=1,n)
+  enddo
+  call map_sort(ao_tc_sym_two_e_pot_map)
+  load_ao_tc_sym_two_e_pot = 0
+  return
+  99 continue
+  call map_deinit(ao_tc_sym_two_e_pot_map)
+  98 continue
+  stop 'Problem reading ao_tc_sym_two_e_pot_map file in work/'
+
+end
+
+
+
+

src/ao_tc_eff_map/one_e_1bgauss_hermit.irp.f

@@ -0,0 +1,519 @@
+
+BEGIN_PROVIDER [ double precision, j1b_gauss_hermII, (ao_num,ao_num)]
+
+  BEGIN_DOC
+  !
+  ! Hermitian part of 1-body Jastrow factow in the |AO| basis set.
+  !
+  !  :math:`\langle \chi_A | -0.5 \grad \tau_{1b} \cdot \grad \tau_{1b} | \chi_B \rangle` 
+  !
+  END_DOC
+
+  implicit none
+
+  integer          :: num_A, num_B
+  integer          :: power_A(3), power_B(3)
+  integer          :: i, j, k1, k2, l, m
+  double precision :: alpha, beta, gama1, gama2
+  double precision :: A_center(3), B_center(3), C_center1(3), C_center2(3)
+  double precision :: c1, c
+
+  integer          :: dim1
+  double precision :: overlap_y, d_a_2, overlap_z, overlap
+
+  double precision :: int_gauss_4G
+
+  PROVIDE j1b_gauss_pen
+
+  ! --------------------------------------------------------------------------------
+  ! -- Dummy call to provide everything
+  dim1        = 100
+  A_center(:) = 0.d0
+  B_center(:) = 1.d0
+  alpha       = 1.d0
+  beta        = 0.1d0
+  power_A(:)  = 1
+  power_B(:)  = 0
+  call overlap_gaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
+                           , overlap_y, d_a_2, overlap_z, overlap, dim1 )
+  ! --------------------------------------------------------------------------------
+  
+
+  j1b_gauss_hermII(1:ao_num,1:ao_num) = 0.d0
+
+ !$OMP PARALLEL                                                 &
+ !$OMP DEFAULT (NONE)                                           &
+ !$OMP PRIVATE (i, j, k1, k2, l, m, alpha, beta, gama1, gama2,  &
+ !$OMP          A_center, B_center, C_center1, C_center2,       &
+ !$OMP          power_A, power_B, num_A, num_B, c1, c)          &
+ !$OMP SHARED (ao_num, ao_prim_num, ao_expo_ordered_transp,     & 
+ !$OMP         ao_power, ao_nucl, nucl_coord,                   &
+ !$OMP         ao_coef_normalized_ordered_transp,               &
+ !$OMP         nucl_num, j1b_gauss_pen, j1b_gauss_hermII)
+
+ !$OMP DO SCHEDULE (dynamic)
+
+  do j = 1, ao_num
+
+    num_A         = ao_nucl(j)
+    power_A(1:3)  = ao_power(j,1:3)
+    A_center(1:3) = nucl_coord(num_A,1:3)
+
+    do i = 1, ao_num
+
+      num_B         = ao_nucl(i)
+      power_B(1:3)  = ao_power(i,1:3)
+      B_center(1:3) = nucl_coord(num_B,1:3)
+
+      do l = 1, ao_prim_num(j)
+        alpha = ao_expo_ordered_transp(l,j)
+
+        do m = 1, ao_prim_num(i)
+          beta = ao_expo_ordered_transp(m,i)
+
+          c = 0.d0
+          do k1 = 1, nucl_num
+            gama1          = j1b_gauss_pen(k1)
+            C_center1(1:3) = nucl_coord(k1,1:3)
+
+            do k2 = 1, nucl_num
+              gama2          = j1b_gauss_pen(k2)
+              C_center2(1:3) = nucl_coord(k2,1:3)
+
+              ! < XA | exp[-gama1 r_C1^2 -gama2 r_C2^2] r_C1 \cdot r_C2 | XB >
+              c1 = int_gauss_4G( A_center, B_center, C_center1, C_center2     &
+                               , power_A, power_B, alpha, beta, gama1, gama2  )
+
+              c = c - 2.d0 * gama1 * gama2 * c1
+            enddo
+          enddo
+
+          j1b_gauss_hermII(i,j) = j1b_gauss_hermII(i,j)      & 
+                    + ao_coef_normalized_ordered_transp(l,j) &
+                    * ao_coef_normalized_ordered_transp(m,i) * c
+
+        enddo
+      enddo
+    enddo
+  enddo
+
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+END_PROVIDER
+
+
+
+
+
+!_____________________________________________________________________________________________________________
+!
+!               < XA | exp[-gama1 r_C1^2 -gama2 r_C2^2] r_C1 \cdot r_C2 | XB >
+!
+double precision function int_gauss_4G( A_center, B_center, C_center1, C_center2, power_A, power_B &
+                                      , alpha, beta, gama1, gama2 )
+
+  ! for max_dim
+  include 'constants.include.F'
+
+  implicit none
+
+  integer         , intent(in) :: power_A(3), power_B(3)
+  double precision, intent(in) :: A_center(3), B_center(3), C_center1(3), C_center2(3)
+  double precision, intent(in) :: alpha, beta, gama1, gama2
+
+  integer                      :: i, dim1, power_C
+  integer                      :: iorder(3)
+  double precision             :: AB_expo, fact_AB, AB_center(3), P_AB(0:max_dim,3)
+  double precision             :: gama, fact_C, C_center(3)
+  double precision             :: cx0, cy0, cz0, c_tmp1, c_tmp2, cx, cy, cz
+  double precision             :: int_tmp
+
+  double precision             :: overlap_gaussian_x
+
+  dim1 = 100
+
+  ! P_AB(0:max_dim,3) polynomial
+  ! AB_center(3)      new center
+  ! AB_expo           new exponent
+  ! fact_AB           constant factor
+  ! iorder(3)         i_order(i) = order of the polynomials
+  call give_explicit_poly_and_gaussian( P_AB, AB_center, AB_expo, fact_AB &
+                                      , iorder, alpha, beta, power_A, power_B, A_center, B_center, dim1)
+
+  call gaussian_product(gama1, C_center1, gama2, C_center2, fact_C, gama, C_center)
+
+  ! <<<
+  ! to avoid multi-evaluation
+  power_C = 0
+
+  cx0 = 0.d0
+  do i = 0, iorder(1)
+    cx0 = cx0 + P_AB(i,1) * overlap_gaussian_x( AB_center(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+  enddo
+  cy0 = 0.d0
+  do i = 0, iorder(2)
+    cy0 = cy0 + P_AB(i,2) * overlap_gaussian_x( AB_center(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+  enddo
+  cz0 = 0.d0
+  do i = 0, iorder(3)
+    cz0 = cz0 + P_AB(i,3) * overlap_gaussian_x( AB_center(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+  enddo
+  ! >>>
+
+  int_tmp = 0.d0
+
+  ! -----------------------------------------------------------------------------------------------
+  !
+  ! x term:
+  !          < XA | exp[-gama1 r_C1^2 -gama2 r_C2^2] (x - x_C1) (x - x_C2) | XB > 
+  !
+
+  c_tmp1 = 2.d0 * C_center(1) - C_center1(1) - C_center2(1)
+  c_tmp2 = ( C_center(1) - C_center1(1) ) * ( C_center(1) - C_center2(1) ) 
+
+  cx = 0.d0
+  do i = 0, iorder(1)
+    
+    ! < XA | exp[-gama r_C^2] (x - x_C)^2 | XB >
+    power_C = 2
+    cx      = cx + P_AB(i,1) &
+            * overlap_gaussian_x( AB_center(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+
+    ! < XA | exp[-gama r_C^2] (x - x_C) | XB >
+    power_C = 1
+    cx      = cx + P_AB(i,1) * c_tmp1 &
+            * overlap_gaussian_x( AB_center(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+
+    ! < XA | exp[-gama r_C^2] | XB >
+    power_C = 0
+    cx      = cx + P_AB(i,1) * c_tmp2 &
+            * overlap_gaussian_x( AB_center(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+
+  enddo
+
+  int_tmp += cx * cy0 * cz0
+
+  ! -----------------------------------------------------------------------------------------------
+
+
+  ! -----------------------------------------------------------------------------------------------
+  !
+  ! y term:
+  !          < XA | exp[-gama1 r_C1^2 -gama2 r_C2^2] (y - y_C1) (y - y_C2) | XB > 
+  !
+
+  c_tmp1 = 2.d0 * C_center(2) - C_center1(2) - C_center2(2)
+  c_tmp2 = ( C_center(2) - C_center1(2) ) * ( C_center(2) - C_center2(2) ) 
+
+  cy = 0.d0
+  do i = 0, iorder(2)
+    
+    ! < XA | exp[-gama r_C^2] (y - y_C)^2 | XB >
+    power_C = 2
+    cy      = cy + P_AB(i,2) &
+            * overlap_gaussian_x( AB_center(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+
+    ! < XA | exp[-gama r_C^2] (y - y_C) | XB >
+    power_C = 1
+    cy      = cy + P_AB(i,2) * c_tmp1 &
+            * overlap_gaussian_x( AB_center(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+
+    ! < XA | exp[-gama r_C^2] | XB >
+    power_C = 0
+    cy      = cy + P_AB(i,2) * c_tmp2 &
+            * overlap_gaussian_x( AB_center(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+
+  enddo
+
+  int_tmp += cx0 * cy * cz0
+
+  ! -----------------------------------------------------------------------------------------------
+
+
+  ! -----------------------------------------------------------------------------------------------
+  !
+  ! z term:
+  !          < XA | exp[-gama1 r_C1^2 -gama2 r_C2^2] (z - z_C1) (z - z_C2) | XB > 
+  !
+
+  c_tmp1 = 2.d0 * C_center(3) - C_center1(3) - C_center2(3)
+  c_tmp2 = ( C_center(3) - C_center1(3) ) * ( C_center(3) - C_center2(3) ) 
+
+  cz = 0.d0
+  do i = 0, iorder(3)
+    
+    ! < XA | exp[-gama r_C^2] (z - z_C)^2 | XB >
+    power_C = 2
+    cz      = cz + P_AB(i,3) &
+            * overlap_gaussian_x( AB_center(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+
+    ! < XA | exp[-gama r_C^2] (z - z_C) | XB >
+    power_C = 1
+    cz      = cz + P_AB(i,3) * c_tmp1 &
+            * overlap_gaussian_x( AB_center(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+
+    ! < XA | exp[-gama r_C^2] | XB >
+    power_C = 0
+    cz      = cz + P_AB(i,3) * c_tmp2 &
+            * overlap_gaussian_x( AB_center(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+
+  enddo
+
+  int_tmp += cx0 * cy0 * cz
+
+  ! -----------------------------------------------------------------------------------------------
+
+  int_gauss_4G = fact_AB * fact_C * int_tmp
+
+  return
+end function int_gauss_4G
+!_____________________________________________________________________________________________________________
+!_____________________________________________________________________________________________________________
+
+BEGIN_PROVIDER [ double precision, j1b_gauss_hermI, (ao_num,ao_num)]
+
+  BEGIN_DOC
+  !
+  ! Hermitian part of 1-body Jastrow factow in the |AO| basis set.
+  !
+  !  :math:`\langle \chi_A | -0.5 \Delta \tau_{1b} | \chi_B \rangle` 
+  !
+  END_DOC
+
+  implicit none
+
+  integer          :: num_A, num_B
+  integer          :: power_A(3), power_B(3)
+  integer          :: i, j, k, l, m
+  double precision :: alpha, beta, gama
+  double precision :: A_center(3), B_center(3), C_center(3)
+  double precision :: c1, c2, c
+
+  integer          :: dim1
+  double precision :: overlap_y, d_a_2, overlap_z, overlap
+
+  double precision :: int_gauss_r0, int_gauss_r2
+
+  PROVIDE j1b_gauss_pen
+
+  ! --------------------------------------------------------------------------------
+  ! -- Dummy call to provide everything
+  dim1        = 100
+  A_center(:) = 0.d0
+  B_center(:) = 1.d0
+  alpha       = 1.d0
+  beta        = 0.1d0
+  power_A(:)  = 1
+  power_B(:)  = 0
+  call overlap_gaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
+                           , overlap_y, d_a_2, overlap_z, overlap, dim1 )
+  ! --------------------------------------------------------------------------------
+  
+  j1b_gauss_hermI(1:ao_num,1:ao_num) = 0.d0
+
+ !$OMP PARALLEL                                                 &
+ !$OMP DEFAULT (NONE)                                           &
+ !$OMP PRIVATE (i, j, k, l, m, alpha, beta, gama,               &
+ !$OMP          A_center, B_center, C_center, power_A, power_B, &
+ !$OMP          num_A, num_B, c1, c2, c)                        &
+ !$OMP SHARED (ao_num, ao_prim_num, ao_expo_ordered_transp,     & 
+ !$OMP         ao_power, ao_nucl, nucl_coord,                   &
+ !$OMP         ao_coef_normalized_ordered_transp,               &
+ !$OMP         nucl_num, j1b_gauss_pen, j1b_gauss_hermI)
+
+ !$OMP DO SCHEDULE (dynamic)
+
+  do j = 1, ao_num
+
+    num_A         = ao_nucl(j)
+    power_A(1:3)  = ao_power(j,1:3)
+    A_center(1:3) = nucl_coord(num_A,1:3)
+
+    do i = 1, ao_num
+
+      num_B         = ao_nucl(i)
+      power_B(1:3)  = ao_power(i,1:3)
+      B_center(1:3) = nucl_coord(num_B,1:3)
+
+      do l = 1, ao_prim_num(j)
+        alpha = ao_expo_ordered_transp(l,j)
+
+        do m = 1, ao_prim_num(i)
+          beta = ao_expo_ordered_transp(m,i)
+
+          c = 0.d0
+          do k = 1, nucl_num
+
+            gama          = j1b_gauss_pen(k)
+            C_center(1:3) = nucl_coord(k,1:3)
+
+            ! < XA | exp[-gama r_C^2] | XB >
+            c1 = int_gauss_r0( A_center, B_center, C_center        &
+                             , power_A, power_B, alpha, beta, gama )
+
+            ! < XA | r_A^2 exp[-gama r_C^2] | XB >
+            c2 = int_gauss_r2( A_center, B_center, C_center        &
+                             , power_A, power_B, alpha, beta, gama )
+
+            c = c + 3.d0 * gama * c1 - 2.d0 * gama * gama * c2
+          enddo
+
+          j1b_gauss_hermI(i,j) = j1b_gauss_hermI(i,j)      & 
+                  + ao_coef_normalized_ordered_transp(l,j) &
+                  * ao_coef_normalized_ordered_transp(m,i) * c
+
+        enddo
+      enddo
+    enddo
+  enddo
+
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+END_PROVIDER
+
+
+!_____________________________________________________________________________________________________________
+!
+!                             < XA | exp[-gama r_C^2] | XB >
+!
+double precision function int_gauss_r0(A_center, B_center, C_center, power_A, power_B, alpha, beta, gama)
+
+  ! for max_dim
+  include 'constants.include.F'
+
+  implicit none
+
+  integer         , intent(in) :: power_A(3), power_B(3)
+  double precision, intent(in) :: A_center(3), B_center(3), C_center(3)
+  double precision, intent(in) :: alpha, beta, gama 
+
+  integer                      :: i, power_C, dim1
+  integer                      :: iorder(3)
+  integer                      :: nmax
+  double precision             :: AB_expo, fact_AB, AB_center(3), P_AB(0:max_dim,3)
+  double precision             :: cx, cy, cz 
+
+  double precision             :: overlap_gaussian_x 
+
+  dim1 = 100
+
+  ! P_AB(0:max_dim,3) polynomial
+  ! AB_center(3)      new center
+  ! AB_expo           new exponent
+  ! fact_AB           constant factor
+  ! iorder(3)         i_order(i) = order of the polynomials
+  call give_explicit_poly_and_gaussian( P_AB, AB_center, AB_expo, fact_AB &
+                                      , iorder, alpha, beta, power_A, power_B, A_center, B_center, dim1)
+
+  if( fact_AB .lt. 1d-20 ) then
+    int_gauss_r0 = 0.d0
+    return
+  endif
+
+  power_C = 0
+  cx = 0.d0
+  do i = 0, iorder(1)
+    cx = cx + P_AB(i,1) * overlap_gaussian_x(AB_center(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+  enddo
+  cy = 0.d0
+  do i = 0, iorder(2)
+    cy = cy + P_AB(i,2) * overlap_gaussian_x(AB_center(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+  enddo
+  cz = 0.d0
+  do i = 0, iorder(3)
+    cz = cz + P_AB(i,3) * overlap_gaussian_x(AB_center(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+  enddo
+
+  int_gauss_r0 = fact_AB * cx * cy * cz
+
+  return
+end function int_gauss_r0 
+!_____________________________________________________________________________________________________________
+!_____________________________________________________________________________________________________________
+
+
+
+!_____________________________________________________________________________________________________________
+!
+!                             < XA | r_C^2 exp[-gama r_C^2] | XB >
+!
+double precision function int_gauss_r2(A_center, B_center, C_center, power_A, power_B, alpha, beta, gama)
+
+  ! for max_dim
+  include 'constants.include.F'
+
+  implicit none
+
+  integer,          intent(in) :: power_A(3), power_B(3)
+  double precision, intent(in) :: A_center(3), B_center(3), C_center(3)
+  double precision, intent(in) :: alpha, beta, gama 
+
+  integer                      :: i, power_C, dim1
+  integer                      :: iorder(3)
+  double precision             :: AB_expo, fact_AB, AB_center(3), P_AB(0:max_dim,3)
+  double precision             :: cx0, cy0, cz0, cx, cy, cz
+  double precision             :: int_tmp
+
+  double precision             :: overlap_gaussian_x
+
+  dim1 = 100
+
+  ! P_AB(0:max_dim,3) polynomial centered on AB_center
+  ! AB_center(3)      new center
+  ! AB_expo           new exponent
+  ! fact_AB           constant factor
+  ! iorder(3)         i_order(i) = order of the polynomials
+  call give_explicit_poly_and_gaussian( P_AB, AB_center, AB_expo, fact_AB &
+                                      , iorder, alpha, beta, power_A, power_B, A_center, B_center, dim1)
+
+  ! <<<
+  ! to avoid multi-evaluation
+  power_C = 0
+
+  cx0 = 0.d0
+  do i = 0, iorder(1)
+    cx0 = cx0 + P_AB(i,1) * overlap_gaussian_x(AB_center(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+  enddo
+  cy0 = 0.d0
+  do i = 0, iorder(2)
+    cy0 = cy0 + P_AB(i,2) * overlap_gaussian_x(AB_center(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+  enddo
+  cz0 = 0.d0
+  do i = 0, iorder(3)
+    cz0 = cz0 + P_AB(i,3) * overlap_gaussian_x(AB_center(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+  enddo
+  ! >>>
+
+  int_tmp = 0.d0
+
+  power_C = 2
+
+  ! ( x - XC)^2
+  cx = 0.d0
+  do i = 0, iorder(1)
+    cx = cx + P_AB(i,1) * overlap_gaussian_x(AB_center(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+  enddo
+  int_tmp += cx * cy0 * cz0
+
+  ! ( y - YC)^2
+  cy = 0.d0
+  do i = 0, iorder(2)
+    cy = cy + P_AB(i,2) * overlap_gaussian_x(AB_center(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+  enddo
+  int_tmp += cx0 * cy * cz0
+
+  ! ( z - ZC)^2
+  cz = 0.d0
+  do i = 0, iorder(3)
+    cz = cz + P_AB(i,3) * overlap_gaussian_x(AB_center(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+  enddo
+  int_tmp += cx0 * cy0 * cz
+
+  int_gauss_r2 = fact_AB * int_tmp
+
+  return
+end function int_gauss_r2
+!_____________________________________________________________________________________________________________
+!_____________________________________________________________________________________________________________

src/ao_tc_eff_map/one_e_1bgauss_nonherm.irp.f

@@ -0,0 +1,319 @@
+BEGIN_PROVIDER [ double precision, j1b_gauss_nonherm, (ao_num,ao_num)]
+
+  BEGIN_DOC
+  !
+  ! Hermitian part of 1-body Jastrow factow in the |AO| basis set.
+  !
+  !              \langle \chi_i | - grad \tau_{1b} \cdot grad | \chi_j \rangle  = 
+  !  2 \sum_A aA \langle \chi_i | exp[-aA riA^2] (ri-rA) \cdot grad | \chi_j \rangle
+  !
+  END_DOC
+
+  implicit none
+
+  integer          :: num_A, num_B
+  integer          :: power_A(3), power_B(3)
+  integer          :: i, j, k, l, m
+  double precision :: alpha, beta, gama
+  double precision :: A_center(3), B_center(3), C_center(3)
+  double precision :: c1, c
+
+  integer          :: dim1
+  double precision :: overlap_y, d_a_2, overlap_z, overlap
+
+  double precision :: int_gauss_deriv
+
+  PROVIDE j1b_gauss_pen
+
+  ! --------------------------------------------------------------------------------
+  ! -- Dummy call to provide everything
+  dim1        = 100
+  A_center(:) = 0.d0
+  B_center(:) = 1.d0
+  alpha       = 1.d0
+  beta        = 0.1d0
+  power_A(:)  = 1
+  power_B(:)  = 0
+  call overlap_gaussian_xyz( A_center, B_center, alpha, beta, power_A, power_B &
+                           , overlap_y, d_a_2, overlap_z, overlap, dim1 )
+  ! --------------------------------------------------------------------------------
+  
+
+  j1b_gauss_nonherm(1:ao_num,1:ao_num) = 0.d0
+
+ !$OMP PARALLEL                                                 &
+ !$OMP DEFAULT (NONE)                                           &
+ !$OMP PRIVATE (i, j, k, l, m, alpha, beta, gama,               &
+ !$OMP          A_center, B_center, C_center, power_A, power_B, &
+ !$OMP          num_A, num_B, c1, c)                            &
+ !$OMP SHARED (ao_num, ao_prim_num, ao_expo_ordered_transp,     & 
+ !$OMP         ao_power, ao_nucl, nucl_coord,                   &
+ !$OMP         ao_coef_normalized_ordered_transp,               &
+ !$OMP         nucl_num, j1b_gauss_pen, j1b_gauss_nonherm)
+
+ !$OMP DO SCHEDULE (dynamic)
+
+  do j = 1, ao_num
+
+    num_A         = ao_nucl(j)
+    power_A(1:3)  = ao_power(j,1:3)
+    A_center(1:3) = nucl_coord(num_A,1:3)
+
+    do i = 1, ao_num
+
+      num_B         = ao_nucl(i)
+      power_B(1:3)  = ao_power(i,1:3)
+      B_center(1:3) = nucl_coord(num_B,1:3)
+
+      do l = 1, ao_prim_num(j)
+        alpha = ao_expo_ordered_transp(l,j)
+
+        do m = 1, ao_prim_num(i)
+          beta = ao_expo_ordered_transp(m,i)
+
+          c = 0.d0
+          do k = 1, nucl_num
+
+            gama          = j1b_gauss_pen(k)
+            C_center(1:3) = nucl_coord(k,1:3)
+
+            !  \langle \chi_A | exp[-gama r_C^2] r_C \cdot grad | \chi_B \rangle
+            c1 = int_gauss_deriv( A_center, B_center, C_center        &
+                                , power_A, power_B, alpha, beta, gama )
+
+            c = c + 2.d0 * gama * c1 
+          enddo
+
+          j1b_gauss_nonherm(i,j) =  j1b_gauss_nonherm(i,j) & 
+                  + ao_coef_normalized_ordered_transp(l,j) &
+                  * ao_coef_normalized_ordered_transp(m,i) * c
+
+        enddo
+      enddo
+    enddo
+  enddo
+
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+END_PROVIDER
+
+
+
+
+
+!_____________________________________________________________________________________________________________
+!
+!                            < XA | exp[-gama r_C^2] r_C \cdot grad | XB >
+!
+double precision function int_gauss_deriv(A_center, B_center, C_center, power_A, power_B, alpha, beta, gama)
+
+  ! for max_dim
+  include 'constants.include.F'
+
+  implicit none
+
+  double precision, intent(in) :: A_center(3), B_center(3), C_center(3)
+  integer         , intent(in) :: power_A(3), power_B(3)
+  double precision, intent(in) :: alpha, beta, gama 
+
+  integer                      :: i, power_C, dim1
+  integer                      :: iorder(3), power_D(3)
+  double precision             :: AB_expo
+  double precision             :: fact_AB, center_AB(3), pol_AB(0:max_dim,3)
+  double precision             :: cx, cy, cz
+
+  double precision             :: overlap_gaussian_x
+
+  dim1 = 100
+
+  int_gauss_deriv = 0.d0
+
+  ! ===============
+  ! term I:
+  !     \partial_x
+  ! ===============
+
+  if( power_B(1) .ge. 1 ) then
+
+    power_D(1) = power_B(1) - 1
+    power_D(2) = power_B(2)
+    power_D(3) = power_B(3)
+
+    call give_explicit_poly_and_gaussian( pol_AB, center_AB, AB_expo, fact_AB &
+                                        , iorder, alpha, beta, power_A, power_D, A_center, B_center, dim1)
+    power_C = 1
+    cx = 0.d0
+    do i = 0, iorder(1)
+      cx = cx + pol_AB(i,1) * overlap_gaussian_x( center_AB(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+    enddo
+    power_C = 0
+    cy = 0.d0
+    do i = 0, iorder(2)
+      cy = cy + pol_AB(i,2) * overlap_gaussian_x( center_AB(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+    enddo
+    power_C = 0
+    cz = 0.d0
+    do i = 0, iorder(3)
+      cz = cz + pol_AB(i,3) * overlap_gaussian_x( center_AB(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+    enddo
+
+    int_gauss_deriv = int_gauss_deriv + fact_AB * dble(power_B(1)) * cx * cy * cz
+  endif
+
+  ! ===============
+
+  power_D(1) = power_B(1) + 1
+  power_D(2) = power_B(2)
+  power_D(3) = power_B(3)
+
+  call give_explicit_poly_and_gaussian( pol_AB, center_AB, AB_expo, fact_AB &
+                                      , iorder, alpha, beta, power_A, power_D, A_center, B_center, dim1)
+  power_C = 1
+  cx = 0.d0
+  do i = 0, iorder(1)
+    cx = cx + pol_AB(i,1) * overlap_gaussian_x( center_AB(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+  enddo
+  power_C = 0
+  cy = 0.d0
+  do i = 0, iorder(2)
+    cy = cy + pol_AB(i,2) * overlap_gaussian_x( center_AB(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+  enddo
+  power_C = 0
+  cz = 0.d0
+  do i = 0, iorder(3)
+    cz = cz + pol_AB(i,3) * overlap_gaussian_x( center_AB(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+  enddo
+
+  int_gauss_deriv = int_gauss_deriv - 2.d0 * beta * fact_AB * cx * cy * cz
+
+  ! ===============
+  ! ===============
+
+
+  ! ===============
+  ! term II:
+  !     \partial_y
+  ! ===============
+
+  if( power_B(2) .ge. 1 ) then
+
+    power_D(1) = power_B(1) 
+    power_D(2) = power_B(2) - 1
+    power_D(3) = power_B(3)
+
+    call give_explicit_poly_and_gaussian( pol_AB, center_AB, AB_expo, fact_AB &
+                                        , iorder, alpha, beta, power_A, power_D, A_center, B_center, dim1)
+    power_C = 0
+    cx = 0.d0
+    do i = 0, iorder(1)
+      cx = cx + pol_AB(i,1) * overlap_gaussian_x( center_AB(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+    enddo
+    power_C = 1
+    cy = 0.d0
+    do i = 0, iorder(2)
+      cy = cy + pol_AB(i,2) * overlap_gaussian_x( center_AB(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+    enddo
+    power_C = 0
+    cz = 0.d0
+    do i = 0, iorder(3)
+      cz = cz + pol_AB(i,3) * overlap_gaussian_x( center_AB(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+    enddo
+
+    int_gauss_deriv = int_gauss_deriv + fact_AB * dble(power_B(2)) * cx * cy * cz
+  endif
+
+  ! ===============
+
+  power_D(1) = power_B(1) 
+  power_D(2) = power_B(2) + 1
+  power_D(3) = power_B(3)
+
+  call give_explicit_poly_and_gaussian( pol_AB, center_AB, AB_expo, fact_AB &
+                                      , iorder, alpha, beta, power_A, power_D, A_center, B_center, dim1)
+  power_C = 0
+  cx = 0.d0
+  do i = 0, iorder(1)
+    cx = cx + pol_AB(i,1) * overlap_gaussian_x( center_AB(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+  enddo
+  power_C = 1
+  cy = 0.d0
+  do i = 0, iorder(2)
+    cy = cy + pol_AB(i,2) * overlap_gaussian_x( center_AB(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+  enddo
+  power_C = 0
+  cz = 0.d0
+  do i = 0, iorder(3)
+    cz = cz + pol_AB(i,3) * overlap_gaussian_x( center_AB(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+  enddo
+
+  int_gauss_deriv = int_gauss_deriv - 2.d0 * beta * fact_AB * cx * cy * cz
+
+  ! ===============
+  ! ===============
+
+  ! ===============
+  ! term III:
+  !     \partial_z
+  ! ===============
+
+  if( power_B(3) .ge. 1 ) then
+
+    power_D(1) = power_B(1) 
+    power_D(2) = power_B(2) 
+    power_D(3) = power_B(3) - 1
+
+    call give_explicit_poly_and_gaussian( pol_AB, center_AB, AB_expo, fact_AB &
+                                        , iorder, alpha, beta, power_A, power_D, A_center, B_center, dim1)
+    power_C = 0
+    cx = 0.d0
+    do i = 0, iorder(1)
+      cx = cx + pol_AB(i,1) * overlap_gaussian_x( center_AB(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+    enddo
+    power_C = 0
+    cy = 0.d0
+    do i = 0, iorder(2)
+      cy = cy + pol_AB(i,2) * overlap_gaussian_x( center_AB(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+    enddo
+    power_C = 1
+    cz = 0.d0
+    do i = 0, iorder(3)
+      cz = cz + pol_AB(i,3) * overlap_gaussian_x( center_AB(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+    enddo
+
+    int_gauss_deriv = int_gauss_deriv + fact_AB * dble(power_B(3)) * cx * cy * cz
+  endif
+
+  ! ===============
+
+  power_D(1) = power_B(1) 
+  power_D(2) = power_B(2)
+  power_D(3) = power_B(3) + 1
+
+  call give_explicit_poly_and_gaussian( pol_AB, center_AB, AB_expo, fact_AB &
+                                      , iorder, alpha, beta, power_A, power_D, A_center, B_center, dim1)
+  power_C = 0
+  cx = 0.d0
+  do i = 0, iorder(1)
+    cx = cx + pol_AB(i,1) * overlap_gaussian_x( center_AB(1), C_center(1), AB_expo, gama, i, power_C, dim1)
+  enddo
+  power_C = 0
+  cy = 0.d0
+  do i = 0, iorder(2)
+    cy = cy + pol_AB(i,2) * overlap_gaussian_x( center_AB(2), C_center(2), AB_expo, gama, i, power_C, dim1)
+  enddo
+  power_C = 1
+  cz = 0.d0
+  do i = 0, iorder(3)
+    cz = cz + pol_AB(i,3) * overlap_gaussian_x( center_AB(3), C_center(3), AB_expo, gama, i, power_C, dim1)
+  enddo
+
+  int_gauss_deriv = int_gauss_deriv - 2.d0 * beta * fact_AB * cx * cy * cz
+
+  ! ===============
+  ! ===============
+
+  return
+end function int_gauss_deriv
+!_____________________________________________________________________________________________________________
+!_____________________________________________________________________________________________________________

src/ao_tc_eff_map/potential.irp.f

@@ -0,0 +1,203 @@
+BEGIN_PROVIDER [integer, n_gauss_eff_pot]
+ implicit none
+ BEGIN_DOC
+! number of gaussians to represent the effective potential :
+!
+! V(mu,r12) = -0.25 * (1 - erf(mu*r12))^2 + 1/(\sqrt(pi)mu) * exp(-(mu*r12)^2)
+!
+! Here (1 - erf(mu*r12))^2 is expanded in Gaussians as Eqs A11-A20 in JCP 154, 084119 (2021)
+ END_DOC
+ n_gauss_eff_pot = n_max_fit_slat + 1
+END_PROVIDER 
+
+BEGIN_PROVIDER [integer, n_gauss_eff_pot_deriv]
+ implicit none
+ BEGIN_DOC
+! V(r12) = -(1 - erf(mu*r12))^2 is expanded in Gaussians as Eqs A11-A20 in JCP 154, 084119 (2021)
+ END_DOC
+ n_gauss_eff_pot_deriv = n_max_fit_slat 
+END_PROVIDER 
+
+ BEGIN_PROVIDER [double precision, expo_gauss_eff_pot, (n_gauss_eff_pot)]
+&BEGIN_PROVIDER [double precision, coef_gauss_eff_pot, (n_gauss_eff_pot)]
+ implicit none
+ BEGIN_DOC
+! Coefficients and exponents of the Fit on Gaussians of V(X) = -(1 - erf(mu*X))^2 + 1/(\sqrt(pi)mu) * exp(-(mu*X)^2)
+!
+! V(X) = \sum_{i=1,n_gauss_eff_pot} coef_gauss_eff_pot(i) * exp(-expo_gauss_eff_pot(i) * X^2)
+!
+! Relies on the fit proposed in Eqs A11-A20 in JCP 154, 084119 (2021)
+ END_DOC
+ include 'constants.include.F'
+
+ integer :: i
+ ! fit of the -0.25 * (1 - erf(mu*x))^2 with n_max_fit_slat gaussians 
+ do i = 1, n_max_fit_slat
+  expo_gauss_eff_pot(i) = expo_gauss_1_erf_x_2(i) 
+  coef_gauss_eff_pot(i) = -0.25d0 * coef_gauss_1_erf_x_2(i) ! -1/4 * (1 - erf(mu*x))^2
+ enddo
+ ! Analytical Gaussian part of the potential: + 1/(\sqrt(pi)mu) * exp(-(mu*x)^2) 
+ expo_gauss_eff_pot(n_max_fit_slat+1) = mu_erf * mu_erf
+ coef_gauss_eff_pot(n_max_fit_slat+1) =  1.d0 * mu_erf * inv_sq_pi
+
+END_PROVIDER 
+
+
+double precision function eff_pot_gauss(x,mu)
+ implicit none
+ BEGIN_DOC
+ ! V(mu,r12) = -0.25 * (1 - erf(mu*r12))^2 + 1/(\sqrt(pi)mu) * exp(-(mu*r12)^2)
+ END_DOC
+ double precision, intent(in) :: x,mu
+ eff_pot_gauss =  mu/dsqrt(dacos(-1.d0)) * dexp(-mu*mu*x*x) - 0.25d0 * (1.d0 - derf(mu*x))**2.d0
+end
+
+
+
+! -------------------------------------------------------------------------------------------------
+! ---
+
+double precision function eff_pot_fit_gauss(x)
+ implicit none
+ BEGIN_DOC
+ ! V(mu,r12) = -0.25 * (1 - erf(mu*r12))^2 + 1/(\sqrt(pi)mu) * exp(-(mu*r12)^2) 
+ ! 
+ ! but fitted with gaussians 
+ END_DOC
+ double precision, intent(in) :: x
+ integer :: i
+ double precision :: alpha
+ eff_pot_fit_gauss = derf(mu_erf*x)/x
+ do i = 1, n_gauss_eff_pot
+  alpha = expo_gauss_eff_pot(i)
+  eff_pot_fit_gauss += coef_gauss_eff_pot(i) * dexp(-alpha*x*x)
+ enddo
+end
+
+BEGIN_PROVIDER [integer, n_fit_1_erf_x]
+ implicit none
+ BEGIN_DOC
+! 
+ END_DOC
+ n_fit_1_erf_x = 2
+
+END_PROVIDER 
+
+BEGIN_PROVIDER [double precision, expos_slat_gauss_1_erf_x, (n_fit_1_erf_x)]
+ implicit none
+ BEGIN_DOC
+! 1 - erf(mu*x) is fitted with a Slater and gaussian as in Eq.A15 of  JCP 154, 084119 (2021)
+!
+! 1 - erf(mu*x) = e^{-expos_slat_gauss_1_erf_x(1) * mu *x} * e^{-expos_slat_gauss_1_erf_x(2) * mu^2 * x^2}
+ END_DOC
+ expos_slat_gauss_1_erf_x(1) = 1.09529d0
+ expos_slat_gauss_1_erf_x(2) = 0.756023d0
+END_PROVIDER 
+
+ BEGIN_PROVIDER [double precision, expo_gauss_1_erf_x, (n_max_fit_slat)]
+&BEGIN_PROVIDER [double precision, coef_gauss_1_erf_x, (n_max_fit_slat)]
+ implicit none
+ BEGIN_DOC
+! (1 - erf(mu*x)) = \sum_i coef_gauss_1_erf_x(i) * exp(-expo_gauss_1_erf_x(i) * x^2)
+!
+! This is based on a fit of (1 - erf(mu*x)) by exp(-alpha * x) exp(-beta*mu^2x^2) 
+!
+! and the slater function exp(-alpha * x) is fitted with n_max_fit_slat gaussians 
+!
+! See Appendix 2 of JCP 154, 084119 (2021)
+ END_DOC
+ integer :: i
+ double precision :: expos(n_max_fit_slat),alpha,beta
+ alpha = expos_slat_gauss_1_erf_x(1) * mu_erf
+ call expo_fit_slater_gam(alpha,expos)
+ beta = expos_slat_gauss_1_erf_x(2) * mu_erf**2.d0
+ 
+ do i = 1, n_max_fit_slat
+  expo_gauss_1_erf_x(i) = expos(i) + beta
+  coef_gauss_1_erf_x(i) = coef_fit_slat_gauss(i)
+ enddo
+END_PROVIDER 
+
+double precision function fit_1_erf_x(x)
+ implicit none
+ double precision, intent(in) :: x
+ BEGIN_DOC
+! fit_1_erf_x(x) = \sum_i c_i exp (-alpha_i x^2) \approx (1 - erf(mu*x))
+ END_DOC
+ integer :: i
+ fit_1_erf_x = 0.d0
+ do i = 1, n_max_fit_slat
+  fit_1_erf_x += dexp(-expo_gauss_1_erf_x(i) *x*x) * coef_gauss_1_erf_x(i)
+ enddo
+
+end
+
+ BEGIN_PROVIDER [double precision, expo_gauss_1_erf_x_2, (n_max_fit_slat)]
+&BEGIN_PROVIDER [double precision, coef_gauss_1_erf_x_2, (n_max_fit_slat)]
+ implicit none
+ BEGIN_DOC
+! (1 - erf(mu*x))^2 = \sum_i coef_gauss_1_erf_x_2(i) * exp(-expo_gauss_1_erf_x_2(i) * x^2)
+!
+! This is based on a fit of (1 - erf(mu*x)) by exp(-alpha * x) exp(-beta*mu^2x^2)
+!
+! and the slater function exp(-alpha * x) is fitted with n_max_fit_slat gaussians 
+ END_DOC
+ integer :: i
+ double precision :: expos(n_max_fit_slat),alpha,beta
+ alpha = 2.d0 * expos_slat_gauss_1_erf_x(1) * mu_erf
+ call expo_fit_slater_gam(alpha,expos)
+ beta = 2.d0 * expos_slat_gauss_1_erf_x(2) * mu_erf**2.d0
+ do i = 1, n_max_fit_slat
+  expo_gauss_1_erf_x_2(i) = expos(i) + beta
+  coef_gauss_1_erf_x_2(i) = coef_fit_slat_gauss(i)
+ enddo
+END_PROVIDER 
+
+double precision function fit_1_erf_x_2(x)
+ implicit none
+ double precision, intent(in) :: x
+ BEGIN_DOC
+! fit_1_erf_x_2(x) = \sum_i c_i exp (-alpha_i x^2) \approx (1 - erf(mu*x))^2
+ END_DOC
+ integer :: i
+ fit_1_erf_x_2 = 0.d0
+ do i = 1, n_max_fit_slat
+  fit_1_erf_x_2 += dexp(-expo_gauss_1_erf_x_2(i) *x*x) * coef_gauss_1_erf_x_2(i)
+ enddo
+
+end
+
+subroutine inv_r_times_poly(r, dist_r, dist_vec, poly)
+ implicit none
+ BEGIN_DOC
+! returns 
+!
+! poly(1) = x / sqrt(x^2+y^2+z^2), poly(2) = y / sqrt(x^2+y^2+z^2), poly(3) = z / sqrt(x^2+y^2+z^2)
+!
+! with the arguments  
+!
+! r(1)  = x, r(2) = y, r(3) = z, dist_r = sqrt(x^2+y^2+z^2)
+!
+! dist_vec(1) = sqrt(y^2+z^2), dist_vec(2) = sqrt(x^2+z^2), dist_vec(3) = sqrt(x^2+y^2)
+ END_DOC
+ double precision, intent(in) :: r(3), dist_r, dist_vec(3)
+ double precision, intent(out):: poly(3)
+ double precision :: inv_dist
+ integer :: i
+ if (dist_r.gt. 1.d-8)then
+  inv_dist = 1.d0/dist_r
+  do i = 1, 3
+   poly(i) = r(i) * inv_dist 
+  enddo
+ else
+  do i = 1, 3
+   if(dabs(r(i)).lt.dist_vec(i))then
+    inv_dist = 1.d0/dist_r
+    poly(i) = r(i) * inv_dist 
+   else !if(dabs(r(i)))then
+    poly(i) = 1.d0 
+!    poly(i) = 0.d0 
+   endif
+  enddo
+ endif
+end                      

src/ao_tc_eff_map/providers_ao_eff_pot.irp.f

@@ -0,0 +1,86 @@
+
+BEGIN_PROVIDER [ logical, ao_tc_sym_two_e_pot_in_map ]
+  implicit none
+  use f77_zmq
+  use map_module
+  BEGIN_DOC
+  !  Map of Atomic integrals
+  !     i(r1) j(r2) 1/r12 k(r1) l(r2)
+  END_DOC
+
+  integer                        :: i,j,k,l
+  double precision               :: ao_tc_sym_two_e_pot,cpu_1,cpu_2, wall_1, wall_2
+  double precision               :: integral, wall_0
+  include 'utils/constants.include.F'
+
+  ! For integrals file
+  integer(key_kind),allocatable  :: buffer_i(:)
+  integer,parameter              :: size_buffer = 1024*64
+  real(integral_kind),allocatable :: buffer_value(:)
+
+  integer                        :: n_integrals, rc
+  integer                        :: kk, m, j1, i1, lmax
+  character*(64)                 :: fmt
+
+  !double precision               :: j1b_gauss_coul_debug
+  !integral = j1b_gauss_coul_debug(1,1,1,1)
+
+  integral = ao_tc_sym_two_e_pot(1,1,1,1)
+
+  double precision               :: map_mb
+
+  print*, 'Providing the ao_tc_sym_two_e_pot_map integrals'
+  call wall_time(wall_0)
+  call wall_time(wall_1)
+  call cpu_time(cpu_1)
+
+  integer(ZMQ_PTR) :: zmq_to_qp_run_socket, zmq_socket_pull
+  call new_parallel_job(zmq_to_qp_run_socket,zmq_socket_pull,'ao_tc_sym_two_e_pot')
+
+  character(len=:), allocatable :: task
+  allocate(character(len=ao_num*12) :: task)
+  write(fmt,*) '(', ao_num, '(I5,X,I5,''|''))'
+  do l=1,ao_num
+    write(task,fmt) (i,l, i=1,l)
+    integer, external :: add_task_to_taskserver
+    if (add_task_to_taskserver(zmq_to_qp_run_socket,trim(task)) == -1) then
+      stop 'Unable to add task to server'
+    endif
+  enddo
+  deallocate(task)
+
+  integer, external :: zmq_set_running
+  if (zmq_set_running(zmq_to_qp_run_socket) == -1) then
+    print *,  irp_here, ': Failed in zmq_set_running'
+  endif
+
+  PROVIDE nproc
+  !$OMP PARALLEL DEFAULT(shared) private(i) num_threads(nproc+1)
+      i = omp_get_thread_num()
+      if (i==0) then
+        call ao_tc_sym_two_e_pot_in_map_collector(zmq_socket_pull)
+      else
+        call ao_tc_sym_two_e_pot_in_map_slave_inproc(i)
+      endif
+  !$OMP END PARALLEL
+
+  call end_parallel_job(zmq_to_qp_run_socket, zmq_socket_pull, 'ao_tc_sym_two_e_pot')
+
+
+  print*, 'Sorting the map'
+  call map_sort(ao_tc_sym_two_e_pot_map)
+  call cpu_time(cpu_2)
+  call wall_time(wall_2)
+  integer(map_size_kind)         :: get_ao_tc_sym_two_e_pot_map_size, ao_eff_pot_map_size
+  ao_eff_pot_map_size = get_ao_tc_sym_two_e_pot_map_size()
+
+  print*, 'AO eff_pot integrals provided:'
+  print*, ' Size of AO eff_pot map :         ', map_mb(ao_tc_sym_two_e_pot_map) ,'MB'
+  print*, ' Number of AO eff_pot integrals :', ao_eff_pot_map_size
+  print*, ' cpu  time :',cpu_2 - cpu_1, 's'
+  print*, ' wall time :',wall_2 - wall_1, 's  ( x ', (cpu_2-cpu_1)/(wall_2-wall_1+tiny(1.d0)), ' )'
+
+  ao_tc_sym_two_e_pot_in_map = .True.
+
+
+END_PROVIDER

src/ao_tc_eff_map/two_e_1bgauss_coul.irp.f

@@ -0,0 +1,800 @@
+double precision function j1b_gauss_coul(i, j, k, l)
+
+  BEGIN_DOC
+  ! 
+  !  integral in the AO basis:
+  !     i(r1) j(r1) f(r12) k(r2) l(r2)
+  !
+  !  with:
+  !     f(r12) = - [ 0.5 / r12 ] (r1-r2) \cdot \sum_A (-2 a_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
+  !            = [ 1 / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !                                     + (r2-RA)^2 exp(-aA r2A^2) 
+  !                                     - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) 
+  !                                     - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  END_DOC
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer, intent(in) :: i, j, k, l
+
+  integer             :: p, q, r, s, ii
+  integer             :: num_i, num_j, num_k, num_l, num_ii 
+  integer             :: I_power(3), J_power(3), K_power(3), L_power(3)
+  integer             :: iorder_p(3), iorder_q(3)
+  integer             :: shift_P(3), shift_Q(3)
+  integer             :: dim1
+
+  double precision    :: coef1, coef2, coef3, coef4
+  double precision    :: expo1, expo2, expo3, expo4
+  double precision    :: p_inv, q_inv
+  double precision    :: P_new_tmp(0:max_dim,3), P_center_tmp(3), fact_p_tmp, pp_tmp
+  double precision    :: Q_new_tmp(0:max_dim,3), Q_center_tmp(3), fact_q_tmp, qq_tmp
+  double precision    :: P_new(0:max_dim,3), P_center(3), fact_p, pp
+  double precision    :: Q_new(0:max_dim,3), Q_center(3), fact_q, qq
+  double precision    :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision    :: expoii, factii, Centerii(3)
+  double precision    :: ff, gg, cx, cy, cz
+
+  double precision    :: general_primitive_integral_coul_shifted
+  
+  PROVIDE j1b_gauss_pen
+
+  dim1 = n_pt_max_integrals
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+
+  do p = 1, 3
+    I_power(p)  = ao_power(i,p)
+    J_power(p)  = ao_power(j,p)
+    K_power(p)  = ao_power(k,p)
+    L_power(p)  = ao_power(l,p)
+    I_center(p) = nucl_coord(num_i,p)
+    J_center(p) = nucl_coord(num_j,p)
+    K_center(p) = nucl_coord(num_k,p)
+    L_center(p) = nucl_coord(num_l,p)
+  enddo
+
+  j1b_gauss_coul = 0.d0
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                               [ 1 / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  shift_Q = (/ 0, 0, 0 /)
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new_tmp, P_center_tmp, pp_tmp, fact_p_tmp, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1                          )
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new, Q_center, qq, fact_q, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1          )
+          q_inv = 1.d0 / qq
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp_tmp, P_center_tmp, expoii, Centerii, factii, pp, P_center)
+
+            fact_p = fact_p_tmp * factii
+            p_inv  = 1.d0 / pp
+
+            ! pol centerd on P_center_tmp ==> centerd on P_center
+            call pol_modif_center( P_center_tmp, P_center, iorder_p, P_new_tmp, P_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            ff = P_center(1) - Centerii(1) 
+
+            shift_P = (/ 2, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 1, 0, 0 /)
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_P = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! y term:
+
+            ff = P_center(2) - Centerii(2) 
+
+            shift_P = (/ 0, 2, 0 /)
+            cy = cy + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 0, 1, 0 /)
+            cy = cy + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_P = (/ 0, 0, 0 /)
+            cy = cy + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! z term:
+
+            ff = P_center(3) - Centerii(3) 
+
+            shift_P = (/ 0, 0, 2 /)
+            cz = cz + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 0, 0, 1 /)
+            cz = cz + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_P = (/ 0, 0, 0 /)
+            cz = cz + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul = j1b_gauss_coul + coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                               [ 1 / r12 ] \sum_A a_A [ (r2-RA)^2 exp(-aA r2A^2)
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  shift_P = (/ 0, 0, 0 /)
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new, P_center, pp, fact_p, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1          )
+      p_inv = 1.d0 / pp
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new_tmp, Q_center_tmp, qq_tmp, fact_q_tmp, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1                          )
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(qq_tmp, Q_center_tmp, expoii, Centerii, factii, qq, Q_center)
+
+            fact_q = fact_q_tmp * factii
+            q_inv  = 1.d0 / qq
+
+            ! pol centerd on Q_center_tmp ==> centerd on Q_center
+            call pol_modif_center( Q_center_tmp, Q_center, iorder_q, Q_new_tmp, Q_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            ff = Q_center(1) - Centerii(1) 
+
+            shift_Q = (/ 2, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! y term:
+
+            ff = Q_center(2) - Centerii(2) 
+
+            shift_Q = (/ 0, 2, 0 /)
+            cy = cy + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! z term:
+
+            ff = Q_center(3) - Centerii(3) 
+
+            shift_Q = (/ 0, 0, 2 /)
+            cz = cz + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul = j1b_gauss_coul + coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                          - [ 1 / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) ]
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new_tmp, P_center_tmp, pp_tmp, fact_p_tmp, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1                          )
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new, Q_center, qq, fact_q, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1          )
+          q_inv = 1.d0 / qq
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp_tmp, P_center_tmp, expoii, Centerii, factii, pp, P_center)
+
+            fact_p = fact_p_tmp * factii
+            p_inv  = 1.d0 / pp
+
+            ! pol centerd on P_center_tmp ==> centerd on P_center
+            call pol_modif_center( P_center_tmp, P_center, iorder_p, P_new_tmp, P_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            ff = P_center(1) - Centerii(1) 
+            gg = Q_center(1) - Centerii(1) 
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! y term:
+
+            ff = P_center(2) - Centerii(2) 
+            gg = Q_center(2) - Centerii(2) 
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy + expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy + expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy + expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! z term:
+
+            ff = P_center(3) - Centerii(3) 
+            gg = Q_center(3) - Centerii(3) 
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz + expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz + expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz + expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul = j1b_gauss_coul - coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                          - [ 1 / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new, P_center, pp, fact_p, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1          )
+      p_inv = 1.d0 / pp
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new_tmp, Q_center_tmp, qq_tmp, fact_q_tmp, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1                          )
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(qq_tmp, Q_center_tmp, expoii, Centerii, factii, qq, Q_center)
+
+            fact_q = fact_q_tmp * factii
+            q_inv  = 1.d0 / qq
+
+            ! pol centerd on Q_center_tmp ==> centerd on Q_center
+            call pol_modif_center( Q_center_tmp, Q_center, iorder_q, Q_new_tmp, Q_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            ff = P_center(1) - Centerii(1) 
+            gg = Q_center(1) - Centerii(1) 
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! y term:
+
+            ff = P_center(2) - Centerii(2) 
+            gg = Q_center(2) - Centerii(2) 
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+ 
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy + expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy + expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy + expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! z term:
+
+            ff = P_center(3) - Centerii(3) 
+            gg = Q_center(3) - Centerii(3) 
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz + expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz + expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz + expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul = j1b_gauss_coul - coef4 * ( cx + cy + cz )
+
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  return
+end function j1b_gauss_coul
+
+
+
+
+!______________________________________________________________________________________________________________________
+!______________________________________________________________________________________________________________________
+
+double precision function general_primitive_integral_coul_shifted( dim                                                  &
+                                                                 , P_new, P_center, fact_p, p, p_inv, iorder_p, shift_P &
+                                                                 , Q_new, Q_center, fact_q, q, q_inv, iorder_q, shift_Q )
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer,          intent(in) :: dim
+  integer,          intent(in) :: iorder_p(3), shift_P(3)
+  integer,          intent(in) :: iorder_q(3), shift_Q(3)
+  double precision, intent(in) :: P_new(0:max_dim,3), P_center(3), fact_p, p, p_inv
+  double precision, intent(in) :: Q_new(0:max_dim,3), Q_center(3), fact_q, q, q_inv
+
+  integer                      :: n_Ix, n_Iy, n_Iz, nx, ny, nz
+  integer                      :: ix, iy, iz, jx, jy, jz, i
+  integer                      :: n_pt_tmp, n_pt_out, iorder
+  integer                      :: ii, jj
+  double precision             :: rho, dist
+  double precision             :: dx(0:max_dim), Ix_pol(0:max_dim)
+  double precision             :: dy(0:max_dim), Iy_pol(0:max_dim)
+  double precision             :: dz(0:max_dim), Iz_pol(0:max_dim)
+  double precision             :: a, b, c, d, e, f, accu, pq, const
+  double precision             :: pq_inv, p10_1, p10_2, p01_1, p01_2, pq_inv_2
+  double precision             :: d1(0:max_dim), d_poly(0:max_dim)
+  double precision             :: p_plus_q
+
+  double precision             :: rint_sum
+
+  general_primitive_integral_coul_shifted = 0.d0
+
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: dx, Ix_pol, dy, Iy_pol, dz, Iz_pol
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: d1, d_poly
+
+  ! Gaussian Product
+  ! ----------------
+  p_plus_q = (p+q) 
+  pq       = p_inv * 0.5d0 * q_inv
+  pq_inv   = 0.5d0 / p_plus_q
+  p10_1    = q * pq             ! 1/(2p)
+  p01_1    = p * pq             ! 1/(2q)
+  pq_inv_2 = pq_inv + pq_inv
+  p10_2    = pq_inv_2 * p10_1 * q ! 0.5d0 * q / (pq + p*p)
+  p01_2    = pq_inv_2 * p01_1 * p ! 0.5d0 * p / (q*q + pq)
+
+  accu = 0.d0
+
+  iorder = iorder_p(1) + iorder_q(1) + iorder_p(1) + iorder_q(1)
+  iorder = iorder + shift_P(1) + shift_Q(1)
+  iorder = iorder + shift_P(1) + shift_Q(1)
+  !DIR$ VECTOR ALIGNED
+  do ix = 0, iorder
+    Ix_pol(ix) = 0.d0
+  enddo
+  n_Ix = 0
+  do ix = 0, iorder_p(1)
+
+    ii = ix + shift_P(1)
+    a  = P_new(ix,1)
+    if(abs(a) < thresh) cycle
+
+    do jx = 0, iorder_q(1)
+
+      jj = jx + shift_Q(1)
+      d  = a * Q_new(jx,1)
+      if(abs(d) < thresh) cycle
+
+      !DEC$ FORCEINLINE
+      call give_polynom_mult_center_x( P_center(1), Q_center(1), ii, jj &
+                                     , p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dx, nx )
+      !DEC$ FORCEINLINE
+      call add_poly_multiply(dx, nx, d, Ix_pol, n_Ix)
+    enddo
+  enddo
+  if(n_Ix == -1) then
+    return
+  endif
+
+  iorder = iorder_p(2) + iorder_q(2) + iorder_p(2) + iorder_q(2)
+  iorder = iorder + shift_P(2) + shift_Q(2)
+  iorder = iorder + shift_P(2) + shift_Q(2)
+  !DIR$ VECTOR ALIGNED
+  do ix = 0, iorder
+    Iy_pol(ix) = 0.d0
+  enddo
+  n_Iy = 0
+  do iy = 0, iorder_p(2)
+
+    if(abs(P_new(iy,2)) > thresh) then
+
+      ii = iy + shift_P(2)
+      b  = P_new(iy,2)
+
+      do jy = 0, iorder_q(2)
+
+        jj = jy + shift_Q(2)
+        e  = b * Q_new(jy,2)
+        if(abs(e) < thresh) cycle
+
+        !DEC$ FORCEINLINE
+        call give_polynom_mult_center_x( P_center(2), Q_center(2), ii, jj &
+                                       , p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dy, ny )
+        !DEC$ FORCEINLINE
+        call add_poly_multiply(dy, ny, e, Iy_pol, n_Iy)
+      enddo
+    endif
+  enddo
+  if(n_Iy == -1) then
+    return
+  endif
+
+  iorder = iorder_p(3) + iorder_q(3) + iorder_p(3) + iorder_q(3)
+  iorder = iorder + shift_P(3) + shift_Q(3)
+  iorder = iorder + shift_P(3) + shift_Q(3)
+  do ix = 0, iorder
+    Iz_pol(ix) = 0.d0
+  enddo
+  n_Iz = 0
+  do iz = 0, iorder_p(3)
+
+    if( abs(P_new(iz,3)) > thresh ) then
+
+      ii = iz + shift_P(3)
+      c  = P_new(iz,3)
+
+      do jz = 0, iorder_q(3)
+
+        jj = jz + shift_Q(3)
+        f  = c * Q_new(jz,3)
+        if(abs(f) < thresh) cycle
+
+        !DEC$ FORCEINLINE
+        call give_polynom_mult_center_x( P_center(3), Q_center(3), ii, jj &
+                                       , p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dz, nz )
+        !DEC$ FORCEINLINE
+        call add_poly_multiply(dz, nz, f, Iz_pol, n_Iz)
+      enddo
+    endif
+  enddo
+  if(n_Iz == -1) then
+    return
+  endif
+
+  rho = p * q * pq_inv_2
+  dist = (P_center(1) - Q_center(1)) * (P_center(1) - Q_center(1)) &
+       + (P_center(2) - Q_center(2)) * (P_center(2) - Q_center(2)) &
+       + (P_center(3) - Q_center(3)) * (P_center(3) - Q_center(3))
+  const = dist*rho
+
+  n_pt_tmp = n_Ix + n_Iy
+  do i = 0, n_pt_tmp
+    d_poly(i) = 0.d0
+  enddo
+
+  !DEC$ FORCEINLINE
+  call multiply_poly(Ix_pol, n_Ix, Iy_pol, n_Iy, d_poly, n_pt_tmp)
+  if(n_pt_tmp == -1) then
+    return
+  endif
+  n_pt_out = n_pt_tmp + n_Iz
+  do i = 0, n_pt_out
+    d1(i) = 0.d0
+  enddo
+
+  !DEC$ FORCEINLINE
+  call multiply_poly(d_poly, n_pt_tmp, Iz_pol, n_Iz, d1, n_pt_out)
+  accu = accu + rint_sum(n_pt_out, const, d1)
+
+  general_primitive_integral_coul_shifted = fact_p * fact_q * accu * pi_5_2 * p_inv * q_inv / dsqrt(p_plus_q)
+
+  return
+end function general_primitive_integral_coul_shifted
+!______________________________________________________________________________________________________________________
+!______________________________________________________________________________________________________________________

src/ao_tc_eff_map/two_e_1bgauss_coul_acc.irp.f

@@ -0,0 +1,433 @@
+double precision function j1b_gauss_coul_acc(i, j, k, l)
+
+  BEGIN_DOC
+  ! 
+  !  integral in the AO basis:
+  !     i(r1) j(r1) f(r12) k(r2) l(r2)
+  !
+  !  with:
+  !     f(r12) = - [ 0.5 / r12 ] (r1-r2) \cdot \sum_A (-2 a_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
+  !            = [ 1 / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !                                     + (r2-RA)^2 exp(-aA r2A^2) 
+  !                                     - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) 
+  !                                     - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  END_DOC
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer, intent(in) :: i, j, k, l
+
+  integer             :: p, q, r, s, ii
+  integer             :: num_i, num_j, num_k, num_l, num_ii 
+  integer             :: I_power(3), J_power(3), K_power(3), L_power(3)
+  integer             :: iorder_p(3), iorder_q(3)
+  integer             :: shift_P(3), shift_Q(3)
+  integer             :: dim1
+
+  double precision    :: coef1, coef2, coef3, coef4
+  double precision    :: expo1, expo2, expo3, expo4
+  double precision    :: p1_inv, q1_inv, p2_inv, q2_inv
+  double precision    :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1
+  double precision    :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2
+  double precision    :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1
+  double precision    :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2
+  double precision    :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision    :: expoii, factii, Centerii(3)
+  double precision    :: ff, gg, cx, cy, cz
+
+  double precision    :: general_primitive_integral_coul_shifted
+  !double precision    :: j1b_gauss_coul_schwartz_accel
+  
+  PROVIDE j1b_gauss_pen
+
+  dim1 = n_pt_max_integrals
+
+  ! TODO
+  !if( ao_prim_num(i) * ao_prim_num(j) * ao_prim_num(k) * ao_prim_num(l) > 1024 ) then
+  !  j1b_gauss_coul_schwartz_accel = j1b_gauss_coul_schwartz_accel(i, j, k, l)
+  !  return
+  !endif
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+
+  do p = 1, 3
+    I_power(p)  = ao_power(i,p)
+    J_power(p)  = ao_power(j,p)
+    K_power(p)  = ao_power(k,p)
+    L_power(p)  = ao_power(l,p)
+    I_center(p) = nucl_coord(num_i,p)
+    J_center(p) = nucl_coord(num_j,p)
+    K_center(p) = nucl_coord(num_k,p)
+    L_center(p) = nucl_coord(num_l,p)
+  enddo
+
+  j1b_gauss_coul_acc = 0.d0
+
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P1_new, P1_center, pp1, fact_p1, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1 )
+      p1_inv = 1.d0 / pp1
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1 )
+          q1_inv = 1.d0 / qq1
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp1, P1_center, expoii, Centerii, factii, pp2, P2_center)
+            fact_p2 = fact_p1 * factii
+            p2_inv  = 1.d0 / pp2
+            call pol_modif_center( P1_center, P2_center, iorder_p, P1_new, P2_new)
+
+            call gaussian_product(qq1, Q1_center, expoii, Centerii, factii, qq2, Q2_center)
+            fact_q2 = fact_q1 * factii
+            q2_inv  = 1.d0 / qq2
+            call pol_modif_center( Q1_center, Q2_center, iorder_q, Q1_new, Q2_new)
+
+
+            ! ----------------------------------------------------------------------------------------------------
+            !                         [ 1 / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+            ! ----------------------------------------------------------------------------------------------------
+
+            shift_Q = (/ 0, 0, 0 /)
+
+            ! x term:
+            ff = P2_center(1) - Centerii(1) 
+
+            shift_P = (/ 2, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 1, 0, 0 /)
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P        &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q        )
+
+            shift_P = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+
+            ! y term:
+            ff = P2_center(2) - Centerii(2) 
+
+            shift_P = (/ 0, 2, 0 /)
+            cy = cy + expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 0, 1, 0 /)
+            cy = cy + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P        &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q        )
+
+            shift_P = (/ 0, 0, 0 /)
+            cy = cy + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+
+            ! z term:
+            ff = P2_center(3) - Centerii(3) 
+
+            shift_P = (/ 0, 0, 2 /)
+            cz = cz + expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 0, 0, 1 /)
+            cz = cz + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P        &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q        )
+
+            shift_P = (/ 0, 0, 0 /)
+            cz = cz + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+
+
+            ! ----------------------------------------------------------------------------------------------------
+            !                         [ 1 / r12 ] \sum_A a_A [ (r2-RA)^2 exp(-aA r2A^2)
+            ! ----------------------------------------------------------------------------------------------------
+
+            shift_P = (/ 0, 0, 0 /)
+
+            ! x term:
+            ff = Q2_center(1) - Centerii(1) 
+
+            shift_Q = (/ 2, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P        &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q        )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+
+            ! y term:
+            ff = Q2_center(2) - Centerii(2) 
+
+            shift_Q = (/ 0, 2, 0 /)
+            cy = cy + expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P        &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q        )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+
+            ! z term:
+            ff = Q2_center(3) - Centerii(3) 
+
+            shift_Q = (/ 0, 0, 2 /)
+            cz = cz + expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P        &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q        )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+
+
+            ! ----------------------------------------------------------------------------------------------------
+            !                 - [ 1 / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) ]
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! x term:
+            ff = P2_center(1) - Centerii(1) 
+            gg = Q1_center(1) - Centerii(1) 
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx - expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+
+            ! y term:
+            ff = P2_center(2) - Centerii(2) 
+            gg = Q1_center(2) - Centerii(2) 
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy - expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+
+            ! z term:
+            ff = P2_center(3) - Centerii(3) 
+            gg = Q1_center(3) - Centerii(3) 
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz - expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+
+
+            ! ----------------------------------------------------------------------------------------------------
+            !                 - [ 1 / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! x term:
+            ff = P1_center(1) - Centerii(1) 
+            gg = Q2_center(1) - Centerii(1) 
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx - expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+
+            ! y term:
+            ff = P1_center(2) - Centerii(2) 
+            gg = Q2_center(2) - Centerii(2) 
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy - expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+
+            ! z term:
+            ff = P1_center(3) - Centerii(3) 
+            gg = Q2_center(3) - Centerii(3) 
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz - expoii * general_primitive_integral_coul_shifted( dim1      &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul_acc = j1b_gauss_coul_acc + coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  return
+end function j1b_gauss_coul_acc

src/ao_tc_eff_map/two_e_1bgauss_coul_debug.irp.f

@@ -0,0 +1,397 @@
+double precision function j1b_gauss_coul_debug(i, j, k, l)
+
+  BEGIN_DOC
+  ! 
+  !  integral in the AO basis:
+  !     i(r1) j(r1) f(r12) k(r2) l(r2)
+  !
+  !  with:
+  !     f(r12) = - [ 0.5 / r12 ] (r1-r2) \cdot \sum_A (-2 a_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
+  !            = [ 1 / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !                                     + (r2-RA)^2 exp(-aA r2A^2) 
+  !                                     - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) 
+  !                                     - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  END_DOC
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer, intent(in) :: i, j, k, l
+
+  integer             :: p, q, r, s, ii
+  integer             :: num_i, num_j, num_k, num_l, num_ii 
+  integer             :: I_power(3), J_power(3), K_power(3), L_power(3)
+  integer             :: iorder_p(3), iorder_q(3)
+  integer             :: shift_P(3), shift_Q(3)
+  integer             :: dim1
+
+  double precision    :: coef1, coef2, coef3, coef4
+  double precision    :: expo1, expo2, expo3, expo4
+  double precision    :: p_inv, q_inv
+  double precision    :: P_new_tmp(0:max_dim,3), P_center_tmp(3), fact_p_tmp, pp_tmp
+  double precision    :: Q_new_tmp(0:max_dim,3), Q_center_tmp(3), fact_q_tmp, qq_tmp
+  double precision    :: P_new(0:max_dim,3), P_center(3), fact_p, pp
+  double precision    :: Q_new(0:max_dim,3), Q_center(3), fact_q, qq
+  double precision    :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision    :: expoii, factii, Centerii(3)
+  double precision    :: ff, gg, cx, cy, cz
+
+  double precision    :: general_primitive_integral_coul_shifted
+  
+  PROVIDE j1b_gauss_pen
+
+  dim1 = n_pt_max_integrals
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+
+  do p = 1, 3
+    I_power(p)  = ao_power(i,p)
+    J_power(p)  = ao_power(j,p)
+    K_power(p)  = ao_power(k,p)
+    L_power(p)  = ao_power(l,p)
+    I_center(p) = nucl_coord(num_i,p)
+    J_center(p) = nucl_coord(num_j,p)
+    K_center(p) = nucl_coord(num_k,p)
+    L_center(p) = nucl_coord(num_l,p)
+  enddo
+
+  j1b_gauss_coul_debug = 0.d0
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                               [ 1 / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  shift_Q = (/ 0, 0, 0 /)
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new_tmp, P_center_tmp, pp_tmp, fact_p_tmp, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1                          )
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new, Q_center, qq, fact_q, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1          )
+          q_inv = 1.d0 / qq
+
+          cx = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp_tmp, P_center_tmp, expoii, Centerii, factii, pp, P_center)
+
+            fact_p = fact_p_tmp * factii
+            p_inv  = 1.d0 / pp
+
+            ! pol centerd on P_center_tmp ==> centerd on P_center
+            call pol_modif_center( P_center_tmp, P_center, iorder_p, P_new_tmp, P_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            ff = P_center(1) - Centerii(1) 
+
+            shift_P = (/ 2, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 1, 0, 0 /)
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_P = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul_debug = j1b_gauss_coul_debug + coef4 * cx 
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+!  ! -------------------------------------------------------------------------------------------------------------------
+!  !
+!  !                               [ 1 / r12 ] \sum_A a_A [ (r2-RA)^2 exp(-aA r2A^2)
+!  !
+!  ! -------------------------------------------------------------------------------------------------------------------
+!
+!  shift_P = (/ 0, 0, 0 /)
+! 
+!  do p = 1, ao_prim_num(i)
+!    coef1 = ao_coef_normalized_ordered_transp(p, i)
+!    expo1 = ao_expo_ordered_transp(p, i)
+!
+!    do q = 1, ao_prim_num(j)
+!      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+!      expo2 = ao_expo_ordered_transp(q, j)
+!
+!      call give_explicit_poly_and_gaussian( P_new, P_center, pp, fact_p, iorder_p, expo1, expo2 &
+!                                          , I_power, J_power, I_center, J_center, dim1          )
+!      p_inv = 1.d0 / pp
+!
+!      do r = 1, ao_prim_num(k)
+!        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+!        expo3 = ao_expo_ordered_transp(r, k)
+!
+!        do s = 1, ao_prim_num(l)
+!          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+!          expo4 = ao_expo_ordered_transp(s, l)
+! 
+!          call give_explicit_poly_and_gaussian( Q_new_tmp, Q_center_tmp, qq_tmp, fact_q_tmp, iorder_q, expo3, expo4 &
+!                                              , K_power, L_power, K_center, L_center, dim1                          )
+!
+!          cx = 0.d0
+!          do ii = 1, nucl_num
+!            expoii        = j1b_gauss_pen(ii)
+!            Centerii(1:3) = nucl_coord(ii, 1:3)
+!
+!            call gaussian_product(qq_tmp, Q_center_tmp, expoii, Centerii, factii, qq, Q_center)
+!
+!            fact_q = fact_q_tmp * factii
+!            q_inv  = 1.d0 / qq
+!
+!            ! pol centerd on Q_center_tmp ==> centerd on Q_center
+!            call pol_modif_center( Q_center_tmp, Q_center, iorder_q, Q_new_tmp, Q_new)
+!
+!            ! ----------------------------------------------------------------------------------------------------
+!            ! x term:
+!
+!            ff = Q_center(1) - Centerii(1) 
+!
+!            shift_Q = (/ 2, 0, 0 /)
+!            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+!                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+!                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+!
+!            shift_Q = (/ 1, 0, 0 /)
+!            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+!                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+!                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+!
+!            shift_Q = (/ 0, 0, 0 /)
+!            cx = cx + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+!                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+!                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+!
+!            ! ----------------------------------------------------------------------------------------------------
+!
+!          enddo
+!
+!          j1b_gauss_coul_debug = j1b_gauss_coul_debug + coef4 * cx
+!        enddo ! s
+!      enddo  ! r
+!    enddo   ! q
+!  enddo    ! p
+!
+!  ! -------------------------------------------------------------------------------------------------------------------
+!  ! -------------------------------------------------------------------------------------------------------------------
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                          - [ 1 / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) ]
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new_tmp, P_center_tmp, pp_tmp, fact_p_tmp, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1                          )
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new, Q_center, qq, fact_q, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1          )
+          q_inv = 1.d0 / qq
+
+          cx = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp_tmp, P_center_tmp, expoii, Centerii, factii, pp, P_center)
+
+            fact_p = fact_p_tmp * factii
+            p_inv  = 1.d0 / pp
+
+            ! pol centerd on P_center_tmp ==> centerd on P_center
+            call pol_modif_center( P_center_tmp, P_center, iorder_p, P_new_tmp, P_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            ff = P_center(1) - Centerii(1) 
+            gg = Q_center(1) - Centerii(1) 
+
+            shift_P = (/ 1, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 1, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P = (/ 0, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul_debug = j1b_gauss_coul_debug - coef4 * cx
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+
+!  ! -------------------------------------------------------------------------------------------------------------------
+!  !
+!  !                          - [ 1 / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+!  !
+!  ! -------------------------------------------------------------------------------------------------------------------
+! 
+!  do p = 1, ao_prim_num(i)
+!    coef1 = ao_coef_normalized_ordered_transp(p, i)
+!    expo1 = ao_expo_ordered_transp(p, i)
+!
+!    do q = 1, ao_prim_num(j)
+!      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+!      expo2 = ao_expo_ordered_transp(q, j)
+!
+!      call give_explicit_poly_and_gaussian( P_new, P_center, pp, fact_p, iorder_p, expo1, expo2 &
+!                                          , I_power, J_power, I_center, J_center, dim1          )
+!      p_inv = 1.d0 / pp
+!
+!      do r = 1, ao_prim_num(k)
+!        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+!        expo3 = ao_expo_ordered_transp(r, k)
+!
+!        do s = 1, ao_prim_num(l)
+!          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+!          expo4 = ao_expo_ordered_transp(s, l)
+! 
+!          call give_explicit_poly_and_gaussian( Q_new_tmp, Q_center_tmp, qq_tmp, fact_q_tmp, iorder_q, expo3, expo4 &
+!                                              , K_power, L_power, K_center, L_center, dim1                          )
+!
+!          cx = 0.d0
+!          do ii = 1, nucl_num
+!            expoii        = j1b_gauss_pen(ii)
+!            Centerii(1:3) = nucl_coord(ii, 1:3)
+!
+!            call gaussian_product(qq_tmp, Q_center_tmp, expoii, Centerii, factii, qq, Q_center)
+!
+!            fact_q = fact_q_tmp * factii
+!            q_inv  = 1.d0 / qq
+!
+!            ! pol centerd on Q_center_tmp ==> centerd on Q_center
+!            call pol_modif_center( Q_center_tmp, Q_center, iorder_q, Q_new_tmp, Q_new)
+!
+!            ! ----------------------------------------------------------------------------------------------------
+!            ! x term:
+!
+!            ff = P_center(1) - Centerii(1) 
+!            gg = Q_center(1) - Centerii(1) 
+!
+!            shift_P = (/ 1, 0, 0 /)
+!            shift_Q = (/ 1, 0, 0 /)
+!            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+!                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+!                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+!
+!            shift_P = (/ 1, 0, 0 /)
+!            shift_Q = (/ 0, 0, 0 /)
+!            cx = cx + expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+!                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+!                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+!
+!            shift_P = (/ 0, 0, 0 /)
+!            shift_Q = (/ 1, 0, 0 /)
+!            cx = cx + expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+!                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+!                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+!
+!            shift_P = (/ 0, 0, 0 /)
+!            shift_Q = (/ 0, 0, 0 /)
+!            cx = cx + expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+!                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+!                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+!
+!            ! ----------------------------------------------------------------------------------------------------
+!
+!          enddo
+!
+!          j1b_gauss_coul_debug = j1b_gauss_coul_debug - coef4 * cx
+!
+!        enddo ! s
+!      enddo  ! r
+!    enddo   ! q
+!  enddo    ! p
+!
+!  ! -------------------------------------------------------------------------------------------------------------------
+!  ! -------------------------------------------------------------------------------------------------------------------
+
+  return
+end function j1b_gauss_coul_debug
+

src/ao_tc_eff_map/two_e_1bgauss_coul_modifdebug.irp.f

@@ -0,0 +1,324 @@
+double precision function j1b_gauss_coul_modifdebug(i, j, k, l)
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer, intent(in) :: i, j, k, l
+
+  integer             :: p, q, r, s, ii
+  integer             :: num_i, num_j, num_k, num_l, num_ii 
+  integer             :: I_power(3), J_power(3), K_power(3), L_power(3)
+  integer             :: iorder_p(3), iorder_q(3)
+  integer             :: shift_P(3), shift_Q(3)
+  integer             :: dim1
+
+  double precision    :: coef1, coef2, coef3, coef4
+  double precision    :: expo1, expo2, expo3, expo4
+  double precision    :: p_inv, q_inv
+  double precision    :: P_new_tmp(0:max_dim,3), P_center_tmp(3), fact_p_tmp, pp_tmp
+  double precision    :: Q_new_tmp(0:max_dim,3), Q_center_tmp(3), fact_q_tmp, qq_tmp
+  double precision    :: P_new(0:max_dim,3), P_center(3), fact_p, pp
+  double precision    :: Q_new(0:max_dim,3), Q_center(3), fact_q, qq
+  double precision    :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision    :: expoii, factii, Centerii(3)
+  double precision    :: ff, gg, cx, cy, cz
+
+  double precision    :: general_primitive_integral_coul
+  double precision    :: general_primitive_integral_coul_shifted
+  double precision    :: ao_two_e_integral
+  
+  PROVIDE j1b_gauss_pen
+
+  dim1 = n_pt_max_integrals
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+
+  do p = 1, 3
+    I_power(p)  = ao_power(i,p)
+    J_power(p)  = ao_power(j,p)
+    K_power(p)  = ao_power(k,p)
+    L_power(p)  = ao_power(l,p)
+    I_center(p) = nucl_coord(num_i,p)
+    J_center(p) = nucl_coord(num_j,p)
+    K_center(p) = nucl_coord(num_k,p)
+    L_center(p) = nucl_coord(num_l,p)
+  enddo
+
+  j1b_gauss_coul_modifdebug = 0.d0
+
+!  do ii = 1, nucl_num
+!    expoii = j1b_gauss_pen(ii)
+!    j1b_gauss_coul_modifdebug += expoii * ao_two_e_integral(i, j, k, l)
+!  enddo
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                               [ 1 / r12 ] \sum_A a_A exp(-aA r1A^2)
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  shift_P = (/ 0, 0, 0 /)
+  shift_Q = (/ 0, 0, 0 /)
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new_tmp, P_center_tmp, pp_tmp, fact_p_tmp, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1                          )
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new, Q_center, qq, fact_q, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1          )
+          q_inv = 1.d0 / qq
+
+          cx = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp_tmp, P_center_tmp, expoii, Centerii, factii, pp, P_center)
+            fact_p = fact_p_tmp * factii
+            p_inv  = 1.d0 / pp
+            P_new(:,:) = 0.d0
+            call pol_modif_center( P_center_tmp, P_center, iorder_p, P_new_tmp, P_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul_modifdebug = j1b_gauss_coul_modifdebug + coef4 * cx 
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                               [ 1 / r12 ] \sum_A a_A exp(-aA r2A^2)
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  shift_P = (/ 0, 0, 0 /)
+  shift_Q = (/ 0, 0, 0 /)
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new, P_center, pp, fact_p, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1 )
+      p_inv  = 1.d0 / pp
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new_tmp, Q_center_tmp, qq_tmp, fact_q_tmp, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1 )
+
+          cx = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(qq_tmp, Q_center_tmp, expoii, Centerii, factii, qq, Q_center)
+            fact_q = fact_q_tmp * factii
+            Q_inv  = 1.d0 / qq
+            call pol_modif_center( Q_center_tmp, Q_center, iorder_q, Q_new_tmp, Q_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            cx = cx + expoii * general_primitive_integral_coul_shifted( dim1 &
+                     , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                     , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_coul_modifdebug = j1b_gauss_coul_modifdebug + coef4 * cx 
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  return
+end function j1b_gauss_coul_modifdebug
+
+
+
+
+double precision function general_primitive_integral_coul(dim,            &
+      P_new,P_center,fact_p,p,p_inv,iorder_p,                        &
+      Q_new,Q_center,fact_q,q,q_inv,iorder_q)
+  implicit none
+  BEGIN_DOC
+  ! Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
+  END_DOC
+  integer,intent(in)             :: dim
+  include 'utils/constants.include.F'
+  double precision, intent(in)   :: P_new(0:max_dim,3),P_center(3),fact_p,p,p_inv
+  double precision, intent(in)   :: Q_new(0:max_dim,3),Q_center(3),fact_q,q,q_inv
+  integer, intent(in)            :: iorder_p(3)
+  integer, intent(in)            :: iorder_q(3)
+
+  double precision               :: r_cut,gama_r_cut,rho,dist
+  double precision               :: dx(0:max_dim),Ix_pol(0:max_dim),dy(0:max_dim),Iy_pol(0:max_dim),dz(0:max_dim),Iz_pol(0:max_dim)
+  integer                        :: n_Ix,n_Iy,n_Iz,nx,ny,nz
+  double precision               :: bla
+  integer                        :: ix,iy,iz,jx,jy,jz,i
+  double precision               :: a,b,c,d,e,f,accu,pq,const
+  double precision               :: pq_inv, p10_1, p10_2, p01_1, p01_2,pq_inv_2
+  integer                        :: n_pt_tmp,n_pt_out, iorder
+  double precision               :: d1(0:max_dim),d_poly(0:max_dim),rint,d1_screened(0:max_dim)
+
+  general_primitive_integral_coul = 0.d0
+
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: dx,Ix_pol,dy,Iy_pol,dz,Iz_pol
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: d1, d_poly
+
+  ! Gaussian Product
+  ! ----------------
+
+  pq = p_inv*0.5d0*q_inv
+  pq_inv = 0.5d0/(p+q)
+  p10_1 = q*pq  ! 1/(2p)
+  p01_1 = p*pq  ! 1/(2q)
+  pq_inv_2 = pq_inv+pq_inv
+  p10_2 = pq_inv_2 * p10_1*q !0.5d0*q/(pq + p*p)
+  p01_2 = pq_inv_2 * p01_1*p !0.5d0*p/(q*q + pq)
+
+
+  accu = 0.d0
+  iorder = iorder_p(1)+iorder_q(1)+iorder_p(1)+iorder_q(1)
+  do ix=0,iorder
+    Ix_pol(ix) = 0.d0
+  enddo
+  n_Ix = 0
+  do ix = 0, iorder_p(1)
+    if (abs(P_new(ix,1)) < thresh) cycle
+    a = P_new(ix,1)
+    do jx = 0, iorder_q(1)
+      d = a*Q_new(jx,1)
+      if (abs(d) < thresh) cycle
+      !DIR$ FORCEINLINE
+      call give_polynom_mult_center_x(P_center(1),Q_center(1),ix,jx,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dx,nx)
+      !DIR$ FORCEINLINE
+      call add_poly_multiply(dx,nx,d,Ix_pol,n_Ix)
+    enddo
+  enddo
+  if (n_Ix == -1) then
+    return
+  endif
+  iorder = iorder_p(2)+iorder_q(2)+iorder_p(2)+iorder_q(2)
+  do ix=0, iorder
+    Iy_pol(ix) = 0.d0
+  enddo
+  n_Iy = 0
+  do iy = 0, iorder_p(2)
+    if (abs(P_new(iy,2)) > thresh) then
+      b = P_new(iy,2)
+      do jy = 0, iorder_q(2)
+        e = b*Q_new(jy,2)
+        if (abs(e) < thresh) cycle
+        !DIR$ FORCEINLINE
+        call   give_polynom_mult_center_x(P_center(2),Q_center(2),iy,jy,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dy,ny)
+        !DIR$ FORCEINLINE
+        call add_poly_multiply(dy,ny,e,Iy_pol,n_Iy)
+      enddo
+    endif
+  enddo
+  if (n_Iy == -1) then
+    return
+  endif
+
+  iorder = iorder_p(3)+iorder_q(3)+iorder_p(3)+iorder_q(3)
+  do ix=0,iorder
+    Iz_pol(ix) = 0.d0
+  enddo
+  n_Iz = 0
+  do iz = 0, iorder_p(3)
+    if (abs(P_new(iz,3)) > thresh) then
+      c = P_new(iz,3)
+      do jz = 0, iorder_q(3)
+        f = c*Q_new(jz,3)
+        if (abs(f) < thresh) cycle
+        !DIR$ FORCEINLINE
+        call   give_polynom_mult_center_x(P_center(3),Q_center(3),iz,jz,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dz,nz)
+        !DIR$ FORCEINLINE
+        call add_poly_multiply(dz,nz,f,Iz_pol,n_Iz)
+      enddo
+    endif
+  enddo
+  if (n_Iz == -1) then
+    return
+  endif
+
+  rho = p*q *pq_inv_2
+  dist =  (P_center(1) - Q_center(1))*(P_center(1) - Q_center(1)) +  &
+      (P_center(2) - Q_center(2))*(P_center(2) - Q_center(2)) +      &
+      (P_center(3) - Q_center(3))*(P_center(3) - Q_center(3))
+  const = dist*rho
+
+  n_pt_tmp = n_Ix+n_Iy
+  do i=0,n_pt_tmp
+    d_poly(i)=0.d0
+  enddo
+
+  !DIR$ FORCEINLINE
+  call multiply_poly(Ix_pol,n_Ix,Iy_pol,n_Iy,d_poly,n_pt_tmp)
+  if (n_pt_tmp == -1) then
+    return
+  endif
+  n_pt_out = n_pt_tmp+n_Iz
+  do i=0,n_pt_out
+    d1(i)=0.d0
+  enddo
+
+  !DIR$ FORCEINLINE
+  call multiply_poly(d_poly ,n_pt_tmp ,Iz_pol,n_Iz,d1,n_pt_out)
+  double precision               :: rint_sum
+  accu = accu + rint_sum(n_pt_out,const,d1)
+
+  general_primitive_integral_coul = fact_p * fact_q * accu *pi_5_2*p_inv*q_inv/dsqrt(p+q)
+end function general_primitive_integral_coul

src/ao_tc_eff_map/two_e_1bgauss_coulerf.irp.f

@@ -0,0 +1,102 @@
+double precision function j1b_gauss_coulerf(i, j, k, l)
+
+  BEGIN_DOC
+  ! 
+  !  integral in the AO basis:
+  !     i(r1) j(r1) f(r12) k(r2) l(r2)
+  !
+  !  with:
+  !     f(r12) = - [ (0.5 - 0.5 erf(mu r12)) / r12 ] (r1-r2) \cdot \sum_A (-2 a_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
+  !            = [ (1 - erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !                                                    + (r2-RA)^2 exp(-aA r2A^2) 
+  !                                                    - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2)
+  !                                                    - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  END_DOC
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer, intent(in) :: i, j, k, l
+
+  integer             :: p, q, r, s
+  integer             :: num_i, num_j, num_k, num_l, num_ii 
+  integer             :: I_power(3), J_power(3), K_power(3), L_power(3)
+  integer             :: iorder_p(3), iorder_q(3)
+  integer             :: shift_P(3), shift_Q(3)
+  integer             :: dim1
+
+  double precision    :: coef1, coef2, coef3, coef4
+  double precision    :: expo1, expo2, expo3, expo4
+  double precision    :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
+  double precision    :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
+  double precision    :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision    :: ff, gg, cx, cy, cz
+
+  double precision    :: j1b_gauss_coulerf_schwartz
+  
+  PROVIDE j1b_gauss_pen
+
+  dim1 = n_pt_max_integrals
+
+  if( ao_prim_num(i) * ao_prim_num(j) * ao_prim_num(k) * ao_prim_num(l) > 1024 ) then
+    j1b_gauss_coulerf = j1b_gauss_coulerf_schwartz(i, j, k, l)
+    return
+  endif
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+
+  do p = 1, 3
+    I_power(p)  = ao_power(i,p)
+    J_power(p)  = ao_power(j,p)
+    K_power(p)  = ao_power(k,p)
+    L_power(p)  = ao_power(l,p)
+    I_center(p) = nucl_coord(num_i,p)
+    J_center(p) = nucl_coord(num_j,p)
+    K_center(p) = nucl_coord(num_k,p)
+    L_center(p) = nucl_coord(num_l,p)
+  enddo
+
+  j1b_gauss_coulerf = 0.d0
+
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P1_new, P1_center, pp1, fact_p1, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1 )
+      p1_inv = 1.d0 / pp1
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1 )
+          q1_inv = 1.d0 / qq1
+
+          call get_cxcycz( dim1, cx, cy, cz                                  &
+                         , P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p &
+                         , Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q )
+
+          j1b_gauss_coulerf = j1b_gauss_coulerf + coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  return
+end function j1b_gauss_coulerf
+

src/ao_tc_eff_map/two_e_1bgauss_coulerf_schwartz.irp.f

@@ -0,0 +1,624 @@
+double precision function j1b_gauss_coulerf_schwartz(i, j, k, l)
+
+  BEGIN_DOC
+  ! 
+  !  integral in the AO basis:
+  !     i(r1) j(r1) f(r12) k(r2) l(r2)
+  !
+  !  with:
+  !     f(r12) = - [ (0.5 - 0.5 erf(mu r12)) / r12 ] (r1-r2) \cdot \sum_A (-2 a_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
+  !            = [ (1 - erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !                                                    + (r2-RA)^2 exp(-aA r2A^2) 
+  !                                                    - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2)
+  !                                                    - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  END_DOC
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer, intent(in)           :: i, j, k, l
+
+  integer                       :: p, q, r, s
+  integer                       :: num_i, num_j, num_k, num_l, num_ii 
+  integer                       :: I_power(3), J_power(3), K_power(3), L_power(3)
+  integer                       :: iorder_p(3), iorder_q(3)
+  integer                       :: dim1
+
+  double precision              :: coef1, coef2, coef3, coef4
+  double precision              :: expo1, expo2, expo3, expo4
+  double precision              :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
+  double precision              :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
+  double precision              :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision              :: cx, cy, cz
+  double precision              :: schwartz_ij, thr
+  double precision, allocatable :: schwartz_kl(:,:) 
+
+  PROVIDE j1b_gauss_pen
+
+  dim1 = n_pt_max_integrals
+  thr  = ao_integrals_threshold * ao_integrals_threshold
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+
+  do p = 1, 3
+    I_power(p)  = ao_power(i,p)
+    J_power(p)  = ao_power(j,p)
+    K_power(p)  = ao_power(k,p)
+    L_power(p)  = ao_power(l,p)
+    I_center(p) = nucl_coord(num_i,p)
+    J_center(p) = nucl_coord(num_j,p)
+    K_center(p) = nucl_coord(num_k,p)
+    L_center(p) = nucl_coord(num_l,p)
+  enddo
+
+
+  allocate( schwartz_kl(0:ao_prim_num(l) , 0:ao_prim_num(k)) )
+
+  schwartz_kl(0,0) = 0.d0
+  do r = 1, ao_prim_num(k)
+    expo3 = ao_expo_ordered_transp(r,k)
+    coef3 = ao_coef_normalized_ordered_transp(r,k) * ao_coef_normalized_ordered_transp(r,k)
+
+    schwartz_kl(0,r) = 0.d0
+    do s = 1, ao_prim_num(l)
+      expo4 = ao_expo_ordered_transp(s,l)
+      coef4 = coef3 * ao_coef_normalized_ordered_transp(s,l) * ao_coef_normalized_ordered_transp(s,l)
+
+      call give_explicit_poly_and_gaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q, expo3, expo4 &
+                                          , K_power, L_power, K_center, L_center, dim1 )
+      q1_inv = 1.d0 / qq1
+
+      call get_cxcycz( dim1, cx, cy, cz                                  &
+                     , Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q &
+                     , Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q )
+
+      schwartz_kl(s,r) = coef4 * dabs( cx + cy + cz )
+      schwartz_kl(0,r) = max( schwartz_kl(0,r) , schwartz_kl(s,r) )
+    enddo
+
+    schwartz_kl(0,0) = max( schwartz_kl(0,r) , schwartz_kl(0,0) )
+  enddo
+
+
+  j1b_gauss_coulerf_schwartz = 0.d0
+
+  do p = 1, ao_prim_num(i)
+    expo1 = ao_expo_ordered_transp(p, i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      expo2 = ao_expo_ordered_transp(q, j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P1_new, P1_center, pp1, fact_p1, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1 )
+      p1_inv = 1.d0 / pp1
+
+      call get_cxcycz( dim1, cx, cy, cz                                  &
+                     , P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p &
+                     , P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p )
+
+      schwartz_ij = coef2 * coef2 * dabs( cx + cy + cz )
+      if( schwartz_kl(0,0) * schwartz_ij < thr ) cycle
+
+      do r = 1, ao_prim_num(k)
+        if( schwartz_kl(0,r) * schwartz_ij < thr ) cycle
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          if( schwartz_kl(s,r) * schwartz_ij < thr ) cycle
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1 )
+          q1_inv = 1.d0 / qq1
+
+          call get_cxcycz( dim1, cx, cy, cz                                  &
+                         , P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p &
+                         , Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q )
+
+          j1b_gauss_coulerf_schwartz = j1b_gauss_coulerf_schwartz + coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  deallocate( schwartz_kl )
+
+  return
+end function j1b_gauss_coulerf_schwartz
+
+
+
+
+
+subroutine get_cxcycz( dim1, cx, cy, cz                                  &
+                     , P1_center, P1_new, pp1, fact_p1, p1_inv, iorder_p &
+                     , Q1_center, Q1_new, qq1, fact_q1, q1_inv, iorder_q )
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer,          intent(in)  :: dim1
+  integer,          intent(in)  :: iorder_p(3), iorder_q(3)
+  double precision, intent(in)  :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1, p1_inv
+  double precision, intent(in)  :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1, q1_inv
+  double precision, intent(out) :: cx, cy, cz
+
+  integer                       :: ii
+  integer                       :: shift_P(3), shift_Q(3)
+  double precision              :: expoii, factii, Centerii(3)
+  double precision              :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2, p2_inv
+  double precision              :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2, q2_inv
+  double precision              :: ff, gg
+
+  double precision              :: general_primitive_integral_erf_shifted
+  double precision              :: general_primitive_integral_coul_shifted
+
+  cx = 0.d0
+  cy = 0.d0
+  cz = 0.d0
+  do ii = 1, nucl_num
+
+    expoii        = j1b_gauss_pen(ii)
+    Centerii(1:3) = nucl_coord(ii, 1:3)
+
+    call gaussian_product(pp1, P1_center, expoii, Centerii, factii, pp2, P2_center)
+    fact_p2 = fact_p1 * factii
+    p2_inv  = 1.d0 / pp2
+    call pol_modif_center( P1_center, P2_center, iorder_p, P1_new, P2_new )
+
+    call gaussian_product(qq1, Q1_center, expoii, Centerii, factii, qq2, Q2_center)
+    fact_q2 = fact_q1 * factii
+    q2_inv  = 1.d0 / qq2
+    call pol_modif_center( Q1_center, Q2_center, iorder_q, Q1_new, Q2_new )
+
+
+    ! ----------------------------------------------------------------------------------------------------
+    !                     [ (1-erf(mu r12)) / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+    ! ----------------------------------------------------------------------------------------------------
+
+    shift_Q = (/ 0, 0, 0 /)
+
+    ! x term:
+    ff = P2_center(1) - Centerii(1) 
+
+    shift_P = (/ 2, 0, 0 /)
+    cx = cx + expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cx = cx - expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_P = (/ 1, 0, 0 /)
+    cx = cx + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P        &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q        )
+    cx = cx - expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P       &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q       )
+
+    shift_P = (/ 0, 0, 0 /)
+    cx = cx + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+    cx = cx - expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+    ! y term:
+    ff = P2_center(2) - Centerii(2) 
+
+    shift_P = (/ 0, 2, 0 /)
+    cy = cy + expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cy = cy - expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_P = (/ 0, 1, 0 /)
+    cy = cy + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P        &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q        )
+    cy = cy - expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P       &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q       )
+
+    shift_P = (/ 0, 0, 0 /)
+    cy = cy + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+    cy = cy - expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+    ! z term:
+    ff = P2_center(3) - Centerii(3) 
+
+    shift_P = (/ 0, 0, 2 /)
+    cz = cz + expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cz = cz - expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_P = (/ 0, 0, 1 /)
+    cz = cz + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P        &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q        )
+    cz = cz - expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P       &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q       )
+
+    shift_P = (/ 0, 0, 0 /)
+    cz = cz + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+    cz = cz - expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+    ! ----------------------------------------------------------------------------------------------------
+
+
+
+    ! ----------------------------------------------------------------------------------------------------
+    !                     [ (1-erf(mu r12)) / r12 ] \sum_A a_A [ (r2-RA)^2 exp(-aA r2A^2)
+    ! ----------------------------------------------------------------------------------------------------
+
+    shift_P = (/ 0, 0, 0 /)
+
+    ! x term:
+    ff = Q2_center(1) - Centerii(1) 
+
+    shift_Q = (/ 2, 0, 0 /)
+    cx = cx + expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cx = cx - expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_Q = (/ 1, 0, 0 /)
+    cx = cx + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P        &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q        )
+    cx = cx - expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P       &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q       )
+
+    shift_Q = (/ 0, 0, 0 /)
+    cx = cx + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+    cx = cx - expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+    ! y term:
+    ff = Q2_center(2) - Centerii(2) 
+
+    shift_Q = (/ 0, 2, 0 /)
+    cy = cy + expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cy = cy - expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_Q = (/ 0, 1, 0 /)
+    cy = cy + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P        &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q        )
+    cy = cy - expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P       &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q       )
+
+    shift_Q = (/ 0, 0, 0 /)
+    cy = cy + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+    cy = cy - expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+    ! z term:
+    ff = Q2_center(3) - Centerii(3) 
+
+    shift_Q = (/ 0, 0, 2 /)
+    cz = cz + expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cz = cz - expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_Q = (/ 0, 0, 1 /)
+    cz = cz + expoii * 2.d0 * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P        &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q        )
+    cz = cz - expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P       &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q       )
+
+    shift_Q = (/ 0, 0, 0 /)
+    cz = cz + expoii * ff * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+    cz = cz - expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+    ! ----------------------------------------------------------------------------------------------------
+
+
+
+    ! ----------------------------------------------------------------------------------------------------
+    !              - [ (1-erf(mu r12)) / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) ]
+    ! ----------------------------------------------------------------------------------------------------
+
+    ! x term:
+    ff = P2_center(1) - Centerii(1) 
+    gg = Q1_center(1) - Centerii(1) 
+
+    shift_p = (/ 1, 0, 0 /)
+    shift_Q = (/ 1, 0, 0 /)
+    cx = cx - expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cx = cx + expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 1, 0, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cx = cx - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cx = cx + expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 1, 0, 0 /)
+    cx = cx - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cx = cx + expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cx = cx - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+    cx = cx + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+    ! y term:
+    ff = P2_center(2) - Centerii(2) 
+    gg = Q1_center(2) - Centerii(2) 
+
+    shift_p = (/ 0, 1, 0 /)
+    shift_Q = (/ 0, 1, 0 /)
+    cy = cy - expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cy = cy + expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 1, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cy = cy - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cy = cy + expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 1, 0 /)
+    cy = cy - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cy = cy + expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cy = cy - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+    cy = cy + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+    ! z term:
+    ff = P2_center(3) - Centerii(3) 
+    gg = Q1_center(3) - Centerii(3) 
+
+    shift_p = (/ 0, 0, 1 /)
+    shift_Q = (/ 0, 0, 1 /)
+    cz = cz - expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cz = cz + expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 1 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cz = cz - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cz = cz + expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 0, 1 /)
+    cz = cz - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+    cz = cz + expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cz = cz - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P      &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q      )
+    cz = cz + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+             , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+             , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+    ! ----------------------------------------------------------------------------------------------------
+
+
+
+    ! ----------------------------------------------------------------------------------------------------
+    !              - [ (1-erf(mu r12)) / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+    ! ----------------------------------------------------------------------------------------------------
+
+    ! x term:
+    ff = P1_center(1) - Centerii(1) 
+    gg = Q2_center(1) - Centerii(1) 
+
+    shift_p = (/ 1, 0, 0 /)
+    shift_Q = (/ 1, 0, 0 /)
+    cx = cx - expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cx = cx + expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 1, 0, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cx = cx - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cx = cx + expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 1, 0, 0 /)
+    cx = cx - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cx = cx + expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cx = cx - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+    cx = cx + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+    ! y term:
+    ff = P1_center(2) - Centerii(2) 
+    gg = Q2_center(2) - Centerii(2) 
+
+    shift_p = (/ 0, 1, 0 /)
+    shift_Q = (/ 0, 1, 0 /)
+    cy = cy - expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cy = cy + expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 1, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cy = cy - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cy = cy + expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 1, 0 /)
+    cy = cy - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cy = cy + expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cy = cy - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+    cy = cy + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+    ! z term:
+    ff = P1_center(3) - Centerii(3) 
+    gg = Q2_center(3) - Centerii(3) 
+
+    shift_p = (/ 0, 0, 1 /)
+    shift_Q = (/ 0, 0, 1 /)
+    cz = cz - expoii * general_primitive_integral_coul_shifted( dim1      &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cz = cz + expoii * general_primitive_integral_erf_shifted( dim1       &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 1 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cz = cz - expoii * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cz = cz + expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 0, 1 /)
+    cz = cz - expoii * ff * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+    cz = cz + expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+    shift_p = (/ 0, 0, 0 /)
+    shift_Q = (/ 0, 0, 0 /)
+    cz = cz - expoii * ff * gg * general_primitive_integral_coul_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P      &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q      )
+    cz = cz + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+             , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+             , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+    ! ----------------------------------------------------------------------------------------------------
+
+  enddo
+
+  return
+end subroutine get_cxcycz
+

src/ao_tc_eff_map/two_e_1bgauss_erf.irp.f

@@ -0,0 +1,854 @@
+double precision function j1b_gauss_erf(i, j, k, l)
+
+  BEGIN_DOC
+  ! 
+  !  integral in the AO basis:
+  !     i(r1) j(r1) f(r12) k(r2) l(r2)
+  !
+  !  with:
+  !     f(r12) = - [ -0.5 erf(mu r12) / r12 ] (r1-r2) \cdot \sum_A (-2 a_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
+  !            = - [ erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !                                                 + (r2-RA)^2 exp(-aA r2A^2) 
+  !                                                 - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2)
+  !                                                 - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  END_DOC
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer, intent(in) :: i, j, k, l
+
+  integer             :: p, q, r, s, ii
+  integer             :: num_i, num_j, num_k, num_l, num_ii 
+  integer             :: I_power(3), J_power(3), K_power(3), L_power(3)
+  integer             :: iorder_p(3), iorder_q(3)
+  integer             :: shift_P(3), shift_Q(3)
+  integer             :: dim1
+
+  double precision    :: coef1, coef2, coef3, coef4
+  double precision    :: expo1, expo2, expo3, expo4
+  double precision    :: p_inv, q_inv
+  double precision    :: P_new_tmp(0:max_dim,3), P_center_tmp(3), fact_p_tmp, pp_tmp
+  double precision    :: Q_new_tmp(0:max_dim,3), Q_center_tmp(3), fact_q_tmp, qq_tmp
+  double precision    :: P_new(0:max_dim,3), P_center(3), fact_p, pp
+  double precision    :: Q_new(0:max_dim,3), Q_center(3), fact_q, qq
+  double precision    :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision    :: expoii, factii, Centerii(3)
+  double precision    :: ff, gg, cx, cy, cz
+
+  double precision    :: general_primitive_integral_erf_shifted
+  
+  PROVIDE mu_erf
+  PROVIDE j1b_gauss_pen
+
+  dim1 = n_pt_max_integrals
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+
+  do p = 1, 3
+    I_power(p)  = ao_power(i,p)
+    J_power(p)  = ao_power(j,p)
+    K_power(p)  = ao_power(k,p)
+    L_power(p)  = ao_power(l,p)
+    I_center(p) = nucl_coord(num_i,p)
+    J_center(p) = nucl_coord(num_j,p)
+    K_center(p) = nucl_coord(num_k,p)
+    L_center(p) = nucl_coord(num_l,p)
+  enddo
+
+  j1b_gauss_erf = 0.d0
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !               - [ erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  shift_Q(1) = 0
+  shift_Q(2) = 0
+  shift_Q(3) = 0
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new_tmp, P_center_tmp, pp_tmp, fact_p_tmp, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1                          )
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new, Q_center, qq, fact_q, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1          )
+          q_inv = 1.d0 / qq
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp_tmp, P_center_tmp, expoii, Centerii, factii, pp, P_center)
+
+            fact_p = fact_p_tmp * factii
+            p_inv  = 1.d0 / pp
+
+            ! pol centerd on P_center_tmp ==> centerd on P_center
+            call pol_modif_center( P_center_tmp, P_center, iorder_p, P_new_tmp, P_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            shift_P(2) = 0
+            shift_P(3) = 0
+
+            ff = P_center(1) - Centerii(1) 
+
+            shift_P(1) = 2
+            cx = cx + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(1) = 1
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_P(1) = 0
+            cx = cx + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! y term:
+
+            shift_P(1) = 0
+            shift_P(3) = 0
+
+            ff = P_center(2) - Centerii(2) 
+
+            shift_P(2) = 2
+            cy = cy + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(2) = 1
+            cy = cy + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_P(2) = 0
+            cy = cy + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! z term:
+
+            shift_P(1) = 0
+            shift_P(2) = 0
+
+            ff = P_center(3) - Centerii(3) 
+
+            shift_P(3) = 2
+            cz = cz + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(3) = 1
+            cz = cz + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_P(3) = 0
+            cz = cz + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_erf = j1b_gauss_erf - coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !               - [ erf(mu r12) / r12 ] \sum_A a_A [ (r2-RA)^2 exp(-aA r2A^2)
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+
+  shift_P(1) = 0
+  shift_P(2) = 0
+  shift_P(3) = 0
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new, P_center, pp, fact_p, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1          )
+      p_inv = 1.d0 / pp
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new_tmp, Q_center_tmp, qq_tmp, fact_q_tmp, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1                          )
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(qq_tmp, Q_center_tmp, expoii, Centerii, factii, qq, Q_center)
+
+            fact_q = fact_q_tmp * factii
+            q_inv  = 1.d0 / qq
+
+            ! pol centerd on Q_center_tmp ==> centerd on Q_center
+            call pol_modif_center( Q_center_tmp, Q_center, iorder_q, Q_new_tmp, Q_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            shift_Q(2) = 0
+            shift_Q(3) = 0
+
+            ff = Q_center(1) - Centerii(1) 
+
+            shift_Q(1) = 2
+            cx = cx + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_Q(1) = 1
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_Q(1) = 0
+            cx = cx + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! y term:
+
+            shift_Q(1) = 0
+            shift_Q(3) = 0
+
+            ff = Q_center(2) - Centerii(2) 
+
+            shift_Q(2) = 2
+            cy = cy + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_Q(2) = 1
+            cy = cy + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_Q(2) = 0
+            cy = cy + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! z term:
+
+            shift_Q(1) = 0
+            shift_Q(2) = 0
+
+            ff = Q_center(3) - Centerii(3) 
+
+            shift_Q(3) = 2
+            cz = cz + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_Q(3) = 1
+            cz = cz + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P             &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q             )
+
+            shift_Q(3) = 0
+            cz = cz + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_erf = j1b_gauss_erf - coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                  [ erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) ]
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new_tmp, P_center_tmp, pp_tmp, fact_p_tmp, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1                          )
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new, Q_center, qq, fact_q, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1          )
+          q_inv = 1.d0 / qq
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp_tmp, P_center_tmp, expoii, Centerii, factii, pp, P_center)
+
+            fact_p = fact_p_tmp * factii
+            p_inv  = 1.d0 / pp
+
+            ! pol centerd on P_center_tmp ==> centerd on P_center
+            call pol_modif_center( P_center_tmp, P_center, iorder_p, P_new_tmp, P_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            shift_P(2) = 0
+            shift_P(3) = 0
+            shift_Q(2) = 0
+            shift_Q(3) = 0
+
+            ff = P_center(1) - Centerii(1) 
+            gg = Q_center(1) - Centerii(1) 
+
+            shift_P(1) = 1
+            shift_Q(1) = 1
+            cx = cx + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(1) = 1
+            shift_Q(1) = 0
+            cx = cx + expoii * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(1) = 0
+            shift_Q(1) = 1
+            cx = cx + expoii * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(1) = 0
+            shift_Q(1) = 0
+            cx = cx + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! y term:
+
+            shift_P(1) = 0
+            shift_P(3) = 0
+            shift_Q(1) = 0
+            shift_Q(3) = 0
+
+            ff = P_center(2) - Centerii(2) 
+            gg = Q_center(2) - Centerii(2) 
+
+            shift_P(2) = 1
+            shift_Q(2) = 1
+            cy = cy + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(2) = 1
+            shift_Q(2) = 0
+            cy = cy + expoii * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(2) = 0
+            shift_Q(2) = 1
+            cy = cy + expoii * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(2) = 0
+            shift_Q(2) = 0
+            cy = cy + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! z term:
+
+            shift_P(1) = 0
+            shift_P(2) = 0
+            shift_Q(1) = 0
+            shift_Q(2) = 0
+
+            ff = P_center(3) - Centerii(3) 
+            gg = Q_center(3) - Centerii(3) 
+
+            shift_P(3) = 1
+            shift_Q(3) = 1
+            cz = cz + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(3) = 1
+            shift_Q(3) = 0
+            cz = cz + expoii * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(3) = 0
+            shift_Q(3) = 1
+            cz = cz + expoii * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(3) = 0
+            shift_Q(3) = 0
+            cz = cz + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_erf = j1b_gauss_erf + coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  !
+  !                  [ erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  ! -------------------------------------------------------------------------------------------------------------------
+ 
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P_new, P_center, pp, fact_p, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1          )
+      p_inv = 1.d0 / pp
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q_new_tmp, Q_center_tmp, qq_tmp, fact_q_tmp, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1                          )
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(qq_tmp, Q_center_tmp, expoii, Centerii, factii, qq, Q_center)
+
+            fact_q = fact_q_tmp * factii
+            q_inv  = 1.d0 / qq
+
+            ! pol centerd on Q_center_tmp ==> centerd on Q_center
+            call pol_modif_center( Q_center_tmp, Q_center, iorder_q, Q_new_tmp, Q_new)
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! x term:
+
+            shift_P(2) = 0
+            shift_P(3) = 0
+            shift_Q(2) = 0
+            shift_Q(3) = 0
+
+            ff = P_center(1) - Centerii(1) 
+            gg = Q_center(1) - Centerii(1) 
+
+            shift_P(1) = 1
+            shift_Q(1) = 1
+            cx = cx + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(1) = 1
+            shift_Q(1) = 0
+            cx = cx + expoii * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(1) = 0
+            shift_Q(1) = 1
+            cx = cx + expoii * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(1) = 0
+            shift_Q(1) = 0
+            cx = cx + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! y term:
+
+            shift_P(1) = 0
+            shift_P(3) = 0
+            shift_Q(1) = 0
+            shift_Q(3) = 0
+
+            ff = P_center(2) - Centerii(2) 
+            gg = Q_center(2) - Centerii(2) 
+
+            shift_P(2) = 1
+            shift_Q(2) = 1
+            cy = cy + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(2) = 1
+            shift_Q(2) = 0
+            cy = cy + expoii * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(2) = 0
+            shift_Q(2) = 1
+            cy = cy + expoii * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(2) = 0
+            shift_Q(2) = 0
+            cy = cy + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! ----------------------------------------------------------------------------------------------------
+            ! z term:
+
+            shift_P(1) = 0
+            shift_P(2) = 0
+            shift_Q(1) = 0
+            shift_Q(2) = 0
+
+            ff = P_center(3) - Centerii(3) 
+            gg = Q_center(3) - Centerii(3) 
+
+            shift_P(3) = 1
+            shift_Q(3) = 1
+            cz = cz + expoii * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q )
+
+            shift_P(3) = 1
+            shift_Q(3) = 0
+            cz = cz + expoii * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(3) = 0
+            shift_Q(3) = 1
+            cz = cz + expoii * ff * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P      &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q      )
+
+            shift_P(3) = 0
+            shift_Q(3) = 0
+            cz = cz + expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                    , P_new, P_center, fact_p, pp, p_inv, iorder_p, shift_P           &
+                    , Q_new, Q_center, fact_q, qq, q_inv, iorder_q, shift_Q           )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_erf = j1b_gauss_erf + coef4 * ( cx + cy + cz )
+
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  ! -------------------------------------------------------------------------------------------------------------------
+  ! -------------------------------------------------------------------------------------------------------------------
+
+
+  return
+end function j1b_gauss_erf
+
+
+
+
+!______________________________________________________________________________________________________________________
+!______________________________________________________________________________________________________________________
+
+double precision function general_primitive_integral_erf_shifted( dim                                                  &
+                                                                , P_new, P_center, fact_p, p, p_inv, iorder_p, shift_P &
+                                                                , Q_new, Q_center, fact_q, q, q_inv, iorder_q, shift_Q )
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer,          intent(in) :: dim
+  integer,          intent(in) :: iorder_p(3), shift_P(3)
+  integer,          intent(in) :: iorder_q(3), shift_Q(3)
+  double precision, intent(in) :: P_new(0:max_dim,3), P_center(3), fact_p, p, p_inv
+  double precision, intent(in) :: Q_new(0:max_dim,3), Q_center(3), fact_q, q, q_inv
+
+  integer                      :: n_Ix, n_Iy, n_Iz, nx, ny, nz
+  integer                      :: ix, iy, iz, jx, jy, jz, i
+  integer                      :: n_pt_tmp, n_pt_out, iorder
+  integer                      :: ii, jj
+  double precision             :: rho, dist
+  double precision             :: dx(0:max_dim), Ix_pol(0:max_dim)
+  double precision             :: dy(0:max_dim), Iy_pol(0:max_dim)
+  double precision             :: dz(0:max_dim), Iz_pol(0:max_dim)
+  double precision             :: a, b, c, d, e, f, accu, pq, const
+  double precision             :: pq_inv, p10_1, p10_2, p01_1, p01_2, pq_inv_2
+  double precision             :: d1(0:max_dim), d_poly(0:max_dim)
+  double precision             :: p_plus_q
+
+  double precision             :: rint_sum
+
+  general_primitive_integral_erf_shifted = 0.d0
+
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: dx, Ix_pol, dy, Iy_pol, dz, Iz_pol
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: d1, d_poly
+
+  ! Gaussian Product
+  ! ----------------
+  p_plus_q = (p+q) * ( (p*q)/(p+q) + mu_erf*mu_erf ) / (mu_erf*mu_erf)
+  pq       = p_inv * 0.5d0 * q_inv
+  pq_inv   = 0.5d0 / p_plus_q
+  p10_1    = q * pq             ! 1/(2p)
+  p01_1    = p * pq             ! 1/(2q)
+  pq_inv_2 = pq_inv + pq_inv
+  p10_2    = pq_inv_2 * p10_1 * q ! 0.5d0 * q / (pq + p*p)
+  p01_2    = pq_inv_2 * p01_1 * p ! 0.5d0 * p / (q*q + pq)
+
+  accu = 0.d0
+
+  iorder = iorder_p(1) + iorder_q(1) + iorder_p(1) + iorder_q(1)
+  iorder = iorder + shift_P(1) + shift_Q(1)
+  iorder = iorder + shift_P(1) + shift_Q(1)
+  !DIR$ VECTOR ALIGNED
+  do ix = 0, iorder
+    Ix_pol(ix) = 0.d0
+  enddo
+  n_Ix = 0
+  do ix = 0, iorder_p(1)
+
+    ii = ix + shift_P(1)
+    a  = P_new(ix,1)
+    if(abs(a) < thresh) cycle
+
+    do jx = 0, iorder_q(1)
+
+      jj = jx + shift_Q(1)
+      d  = a * Q_new(jx,1)
+      if(abs(d) < thresh) cycle
+
+      !DEC$ FORCEINLINE
+      call give_polynom_mult_center_x( P_center(1), Q_center(1), ii, jj &
+                                     , p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dx, nx )
+      !DEC$ FORCEINLINE
+      call add_poly_multiply(dx, nx, d, Ix_pol, n_Ix)
+    enddo
+  enddo
+  if(n_Ix == -1) then
+    return
+  endif
+
+  iorder = iorder_p(2) + iorder_q(2) + iorder_p(2) + iorder_q(2)
+  iorder = iorder + shift_P(2) + shift_Q(2)
+  iorder = iorder + shift_P(2) + shift_Q(2)
+  !DIR$ VECTOR ALIGNED
+  do ix = 0, iorder
+    Iy_pol(ix) = 0.d0
+  enddo
+  n_Iy = 0
+  do iy = 0, iorder_p(2)
+
+    if(abs(P_new(iy,2)) > thresh) then
+
+      ii = iy + shift_P(2)
+      b  = P_new(iy,2)
+
+      do jy = 0, iorder_q(2)
+
+        jj = jy + shift_Q(2)
+        e  = b * Q_new(jy,2)
+        if(abs(e) < thresh) cycle
+
+        !DEC$ FORCEINLINE
+        call give_polynom_mult_center_x( P_center(2), Q_center(2), ii, jj &
+                                       , p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dy, ny )
+        !DEC$ FORCEINLINE
+        call add_poly_multiply(dy, ny, e, Iy_pol, n_Iy)
+      enddo
+    endif
+  enddo
+  if(n_Iy == -1) then
+    return
+  endif
+
+  iorder = iorder_p(3) + iorder_q(3) + iorder_p(3) + iorder_q(3)
+  iorder = iorder + shift_P(3) + shift_Q(3)
+  iorder = iorder + shift_P(3) + shift_Q(3)
+  do ix = 0, iorder
+    Iz_pol(ix) = 0.d0
+  enddo
+  n_Iz = 0
+  do iz = 0, iorder_p(3)
+
+    if( abs(P_new(iz,3)) > thresh ) then
+
+      ii = iz + shift_P(3)
+      c  = P_new(iz,3)
+
+      do jz = 0, iorder_q(3)
+
+        jj = jz + shift_Q(3)
+        f  = c * Q_new(jz,3)
+        if(abs(f) < thresh) cycle
+
+        !DEC$ FORCEINLINE
+        call give_polynom_mult_center_x( P_center(3), Q_center(3), ii, jj &
+                                       , p, q, iorder, pq_inv, pq_inv_2, p10_1, p01_1, p10_2, p01_2, dz, nz )
+        !DEC$ FORCEINLINE
+        call add_poly_multiply(dz, nz, f, Iz_pol, n_Iz)
+      enddo
+    endif
+  enddo
+  if(n_Iz == -1) then
+    return
+  endif
+
+  rho = p * q * pq_inv_2
+  dist = (P_center(1) - Q_center(1)) * (P_center(1) - Q_center(1)) &
+       + (P_center(2) - Q_center(2)) * (P_center(2) - Q_center(2)) &
+       + (P_center(3) - Q_center(3)) * (P_center(3) - Q_center(3))
+  const = dist*rho
+
+  n_pt_tmp = n_Ix + n_Iy
+  do i = 0, n_pt_tmp
+    d_poly(i) = 0.d0
+  enddo
+
+  !DEC$ FORCEINLINE
+  call multiply_poly(Ix_pol, n_Ix, Iy_pol, n_Iy, d_poly, n_pt_tmp)
+  if(n_pt_tmp == -1) then
+    return
+  endif
+  n_pt_out = n_pt_tmp + n_Iz
+  do i = 0, n_pt_out
+    d1(i) = 0.d0
+  enddo
+
+  !DEC$ FORCEINLINE
+  call multiply_poly(d_poly, n_pt_tmp, Iz_pol, n_Iz, d1, n_pt_out)
+  accu = accu + rint_sum(n_pt_out, const, d1)
+
+  general_primitive_integral_erf_shifted = fact_p * fact_q * accu * pi_5_2 * p_inv * q_inv / dsqrt(p_plus_q)
+
+  return
+end function general_primitive_integral_erf_shifted
+!______________________________________________________________________________________________________________________
+!______________________________________________________________________________________________________________________

src/ao_tc_eff_map/two_e_1bgauss_erf_acc.irp.f

@@ -0,0 +1,433 @@
+double precision function j1b_gauss_erf_acc(i, j, k, l)
+
+  BEGIN_DOC
+  ! 
+  !  integral in the AO basis:
+  !     i(r1) j(r1) f(r12) k(r2) l(r2)
+  !
+  !  with:
+  !     f(r12) = - [ -0.5 erf(mu r12) / r12 ] (r1-r2) \cdot \sum_A (-2 a_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
+  !            = - [ erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+  !                                                 + (r2-RA)^2 exp(-aA r2A^2) 
+  !                                                 - (r1-RA) \cdot (r2-RA) exp(-aA r1A^2)
+  !                                                 - (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+  !
+  END_DOC
+
+  include 'utils/constants.include.F'
+
+  implicit none
+
+  integer, intent(in) :: i, j, k, l
+
+  integer             :: p, q, r, s, ii
+  integer             :: num_i, num_j, num_k, num_l, num_ii 
+  integer             :: I_power(3), J_power(3), K_power(3), L_power(3)
+  integer             :: iorder_p(3), iorder_q(3)
+  integer             :: shift_P(3), shift_Q(3)
+  integer             :: dim1
+
+  double precision    :: coef1, coef2, coef3, coef4
+  double precision    :: expo1, expo2, expo3, expo4
+  double precision    :: p1_inv, q1_inv, p2_inv, q2_inv
+  double precision    :: P1_new(0:max_dim,3), P1_center(3), fact_p1, pp1
+  double precision    :: P2_new(0:max_dim,3), P2_center(3), fact_p2, pp2
+  double precision    :: Q1_new(0:max_dim,3), Q1_center(3), fact_q1, qq1
+  double precision    :: Q2_new(0:max_dim,3), Q2_center(3), fact_q2, qq2
+  double precision    :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision    :: expoii, factii, Centerii(3)
+  double precision    :: ff, gg, cx, cy, cz
+
+  double precision    :: general_primitive_integral_erf_shifted
+  !double precision    :: j1b_gauss_erf_schwartz_accel
+  
+  PROVIDE j1b_gauss_pen
+
+  dim1 = n_pt_max_integrals
+
+  ! TODO
+  !if( ao_prim_num(i) * ao_prim_num(j) * ao_prim_num(k) * ao_prim_num(l) > 1024 ) then
+  !  j1b_gauss_erf_schwartz_accel = j1b_gauss_erf_schwartz_accel(i, j, k, l)
+  !  return
+  !endif
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+
+  do p = 1, 3
+    I_power(p)  = ao_power(i,p)
+    J_power(p)  = ao_power(j,p)
+    K_power(p)  = ao_power(k,p)
+    L_power(p)  = ao_power(l,p)
+    I_center(p) = nucl_coord(num_i,p)
+    J_center(p) = nucl_coord(num_j,p)
+    K_center(p) = nucl_coord(num_k,p)
+    L_center(p) = nucl_coord(num_l,p)
+  enddo
+
+  j1b_gauss_erf_acc = 0.d0
+
+  do p = 1, ao_prim_num(i)
+    coef1 = ao_coef_normalized_ordered_transp(p, i)
+    expo1 = ao_expo_ordered_transp(p, i)
+
+    do q = 1, ao_prim_num(j)
+      coef2 = coef1 * ao_coef_normalized_ordered_transp(q, j)
+      expo2 = ao_expo_ordered_transp(q, j)
+
+      call give_explicit_poly_and_gaussian( P1_new, P1_center, pp1, fact_p1, iorder_p, expo1, expo2 &
+                                          , I_power, J_power, I_center, J_center, dim1 )
+      p1_inv = 1.d0 / pp1
+
+      do r = 1, ao_prim_num(k)
+        coef3 = coef2 * ao_coef_normalized_ordered_transp(r, k)
+        expo3 = ao_expo_ordered_transp(r, k)
+
+        do s = 1, ao_prim_num(l)
+          coef4 = coef3 * ao_coef_normalized_ordered_transp(s, l)
+          expo4 = ao_expo_ordered_transp(s, l)
+ 
+          call give_explicit_poly_and_gaussian( Q1_new, Q1_center, qq1, fact_q1, iorder_q, expo3, expo4 &
+                                              , K_power, L_power, K_center, L_center, dim1 )
+          q1_inv = 1.d0 / qq1
+
+          cx = 0.d0
+          cy = 0.d0
+          cz = 0.d0
+          do ii = 1, nucl_num
+            expoii        = j1b_gauss_pen(ii)
+            Centerii(1:3) = nucl_coord(ii, 1:3)
+
+            call gaussian_product(pp1, P1_center, expoii, Centerii, factii, pp2, P2_center)
+            fact_p2 = fact_p1 * factii
+            p2_inv  = 1.d0 / pp2
+            call pol_modif_center( P1_center, P2_center, iorder_p, P1_new, P2_new)
+
+            call gaussian_product(qq1, Q1_center, expoii, Centerii, factii, qq2, Q2_center)
+            fact_q2 = fact_q1 * factii
+            q2_inv  = 1.d0 / qq2
+            call pol_modif_center( Q1_center, Q2_center, iorder_q, Q1_new, Q2_new)
+
+
+            ! ----------------------------------------------------------------------------------------------------
+            !                         [ erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA)^2 exp(-aA r1A^2)
+            ! ----------------------------------------------------------------------------------------------------
+
+            shift_Q = (/ 0, 0, 0 /)
+
+            ! x term:
+            ff = P2_center(1) - Centerii(1) 
+
+            shift_P = (/ 2, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 1, 0, 0 /)
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P       &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q       )
+
+            shift_P = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+            ! y term:
+            ff = P2_center(2) - Centerii(2) 
+
+            shift_P = (/ 0, 2, 0 /)
+            cy = cy + expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 0, 1, 0 /)
+            cy = cy + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P       &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q       )
+
+            shift_P = (/ 0, 0, 0 /)
+            cy = cy + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+            ! z term:
+            ff = P2_center(3) - Centerii(3) 
+
+            shift_P = (/ 0, 0, 2 /)
+            cz = cz + expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_P = (/ 0, 0, 1 /)
+            cz = cz + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P       &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q       )
+
+            shift_P = (/ 0, 0, 0 /)
+            cz = cz + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+
+
+            ! ----------------------------------------------------------------------------------------------------
+            !                         [ erf(mu r12) / r12 ] \sum_A a_A [ (r2-RA)^2 exp(-aA r2A^2)
+            ! ----------------------------------------------------------------------------------------------------
+
+            shift_P = (/ 0, 0, 0 /)
+
+            ! x term:
+            ff = Q2_center(1) - Centerii(1) 
+
+            shift_Q = (/ 2, 0, 0 /)
+            cx = cx + expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P       &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q       )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+            ! y term:
+            ff = Q2_center(2) - Centerii(2) 
+
+            shift_Q = (/ 0, 2, 0 /)
+            cy = cy + expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P       &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q       )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+            ! z term:
+            ff = Q2_center(3) - Centerii(3) 
+
+            shift_Q = (/ 0, 0, 2 /)
+            cz = cz + expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz + expoii * 2.d0 * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P       &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q       )
+
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz + expoii * ff * ff * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+
+
+            ! ----------------------------------------------------------------------------------------------------
+            !                 - [ erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r1A^2) ]
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! x term:
+            ff = P2_center(1) - Centerii(1) 
+            gg = Q1_center(1) - Centerii(1) 
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx - expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx - expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx - expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx - expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+            ! y term:
+            ff = P2_center(2) - Centerii(2) 
+            gg = Q1_center(2) - Centerii(2) 
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy - expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy - expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy - expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy - expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+            ! z term:
+            ff = P2_center(3) - Centerii(3) 
+            gg = Q1_center(3) - Centerii(3) 
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz - expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz - expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz - expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz - expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                     , P2_new, P2_center, fact_p2, pp2, p2_inv, iorder_p, shift_P     &
+                     , Q1_new, Q1_center, fact_q1, qq1, q1_inv, iorder_q, shift_Q     )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+
+
+            ! ----------------------------------------------------------------------------------------------------
+            !                 - [ erf(mu r12) / r12 ] \sum_A a_A [ (r1-RA) \cdot (r2-RA) exp(-aA r2A^2) ]
+            ! ----------------------------------------------------------------------------------------------------
+
+            ! x term:
+            ff = P1_center(1) - Centerii(1) 
+            gg = Q2_center(1) - Centerii(1) 
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx - expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 1, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx - expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 1, 0, 0 /)
+            cx = cx - expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cx = cx - expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+            ! y term:
+            ff = P1_center(2) - Centerii(2) 
+            gg = Q2_center(2) - Centerii(2) 
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy - expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 1, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy - expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 1, 0 /)
+            cy = cy - expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cy = cy - expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+            ! z term:
+            ff = P1_center(3) - Centerii(3) 
+            gg = Q2_center(3) - Centerii(3) 
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz - expoii * general_primitive_integral_erf_shifted( dim1       &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 1 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz - expoii * gg * general_primitive_integral_erf_shifted( dim1  &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 1 /)
+            cz = cz - expoii * ff * general_primitive_integral_erf_shifted( dim1  &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q )
+
+            shift_p = (/ 0, 0, 0 /)
+            shift_Q = (/ 0, 0, 0 /)
+            cz = cz - expoii * ff * gg * general_primitive_integral_erf_shifted( dim1 &
+                     , P1_new, P1_center, fact_p1, pp1, p1_inv, iorder_p, shift_P     &
+                     , Q2_new, Q2_center, fact_q2, qq2, q2_inv, iorder_q, shift_Q     )
+
+            ! ----------------------------------------------------------------------------------------------------
+
+          enddo
+
+          j1b_gauss_erf_acc = j1b_gauss_erf_acc - coef4 * ( cx + cy + cz )
+        enddo ! s
+      enddo  ! r
+    enddo   ! q
+  enddo    ! p
+
+  return
+end function j1b_gauss_erf_acc

src/ao_tc_eff_map/two_e_ints_gauss.irp.f

@@ -0,0 +1,326 @@
+double precision function ao_tc_sym_two_e_pot(i,j,k,l)
+  implicit none
+  BEGIN_DOC
+  !  integral of the AO basis <ik|jl> or (ij|kl)
+  !     i(r1) j(r1) (tc_pot(r12,mu)) k(r2) l(r2)
+  !
+  ! where (tc_pot(r12,mu)) is the scalar part of the potential EXCLUDING the term erf(mu r12)/r12. 
+  !
+  ! See Eq. (32) of JCP 154, 084119 (2021). 
+  END_DOC
+  integer,intent(in)             :: i,j,k,l
+  integer                        :: p,q,r,s
+  double precision               :: I_center(3),J_center(3),K_center(3),L_center(3)
+  integer                        :: num_i,num_j,num_k,num_l,dim1,I_power(3),J_power(3),K_power(3),L_power(3)
+  double precision               :: integral
+  include 'utils/constants.include.F'
+  double precision               :: P_new(0:max_dim,3),P_center(3),fact_p,pp
+  double precision               :: Q_new(0:max_dim,3),Q_center(3),fact_q,qq
+  integer                        :: iorder_p(3), iorder_q(3)
+  double precision, allocatable  :: schwartz_kl(:,:)
+  double precision               :: schwartz_ij
+  double precision :: scw_gauss_int,general_primitive_integral_gauss
+
+  dim1 = n_pt_max_integrals
+
+  num_i = ao_nucl(i)
+  num_j = ao_nucl(j)
+  num_k = ao_nucl(k)
+  num_l = ao_nucl(l)
+  ao_tc_sym_two_e_pot = 0.d0
+  double precision               :: thr
+  thr = ao_integrals_threshold*ao_integrals_threshold
+
+  allocate(schwartz_kl(0:ao_prim_num(l),0:ao_prim_num(k)))
+
+      double precision               :: coef3
+      double precision               :: coef2
+      double precision               :: p_inv,q_inv
+      double precision               :: coef1
+      double precision               :: coef4
+
+    do p = 1, 3
+      I_power(p) = ao_power(i,p)
+      J_power(p) = ao_power(j,p)
+      K_power(p) = ao_power(k,p)
+      L_power(p) = ao_power(l,p)
+      I_center(p) = nucl_coord(num_i,p)
+      J_center(p) = nucl_coord(num_j,p)
+      K_center(p) = nucl_coord(num_k,p)
+      L_center(p) = nucl_coord(num_l,p)
+    enddo
+
+    schwartz_kl(0,0) = 0.d0
+    do r = 1, ao_prim_num(k)
+      coef1 = ao_coef_normalized_ordered_transp(r,k)*ao_coef_normalized_ordered_transp(r,k)
+      schwartz_kl(0,r) = 0.d0
+      do s = 1, ao_prim_num(l)
+        coef2 = coef1 * ao_coef_normalized_ordered_transp(s,l) * ao_coef_normalized_ordered_transp(s,l)
+        call give_explicit_poly_and_gaussian(Q_new,Q_center,qq,fact_q,iorder_q,&
+            ao_expo_ordered_transp(r,k),ao_expo_ordered_transp(s,l),                 &
+            K_power,L_power,K_center,L_center,dim1)
+        q_inv = 1.d0/qq
+        scw_gauss_int = general_primitive_integral_gauss(dim1,              &
+                Q_new,Q_center,fact_q,qq,q_inv,iorder_q,             &
+                Q_new,Q_center,fact_q,qq,q_inv,iorder_q)
+
+        schwartz_kl(s,r) = dabs(scw_gauss_int * coef2)
+        schwartz_kl(0,r) = max(schwartz_kl(0,r),schwartz_kl(s,r))
+      enddo
+      schwartz_kl(0,0) = max(schwartz_kl(0,r),schwartz_kl(0,0))
+    enddo
+    do p = 1, ao_prim_num(i)
+      coef1 = ao_coef_normalized_ordered_transp(p,i)
+      do q = 1, ao_prim_num(j)
+        coef2 = coef1*ao_coef_normalized_ordered_transp(q,j)
+        call give_explicit_poly_and_gaussian(P_new,P_center,pp,fact_p,iorder_p,&
+            ao_expo_ordered_transp(p,i),ao_expo_ordered_transp(q,j),                 &
+            I_power,J_power,I_center,J_center,dim1)
+        p_inv = 1.d0/pp
+        scw_gauss_int = general_primitive_integral_gauss(dim1,              &
+                P_new,P_center,fact_p,pp,p_inv,iorder_p,             &
+                P_new,P_center,fact_p,pp,p_inv,iorder_p)
+        schwartz_ij = dabs(scw_gauss_int * coef2*coef2)
+        if (schwartz_kl(0,0)*schwartz_ij < thr) then
+           cycle
+        endif
+        do r = 1, ao_prim_num(k)
+          if (schwartz_kl(0,r)*schwartz_ij < thr) then
+             cycle
+          endif
+          coef3 = coef2*ao_coef_normalized_ordered_transp(r,k)
+          do s = 1, ao_prim_num(l)
+            if (schwartz_kl(s,r)*schwartz_ij < thr) then
+               cycle
+            endif
+            coef4 = coef3*ao_coef_normalized_ordered_transp(s,l)
+            call give_explicit_poly_and_gaussian(Q_new,Q_center,qq,fact_q,iorder_q, &
+                ao_expo_ordered_transp(r,k),ao_expo_ordered_transp(s,l),            &
+                K_power,L_power,K_center,L_center,dim1)
+            q_inv = 1.d0/qq
+            integral = general_primitive_integral_gauss(dim1,              &
+                P_new,P_center,fact_p,pp,p_inv,iorder_p,             &
+                Q_new,Q_center,fact_q,qq,q_inv,iorder_q)
+            ao_tc_sym_two_e_pot = ao_tc_sym_two_e_pot + coef4 * integral
+          enddo ! s
+        enddo  ! r
+      enddo   ! q
+    enddo    ! p
+
+  deallocate (schwartz_kl)
+
+end
+
+
+double precision function general_primitive_integral_gauss(dim,      &
+      P_new,P_center,fact_p,p,p_inv,iorder_p,                        &
+      Q_new,Q_center,fact_q,q,q_inv,iorder_q)
+  implicit none
+  BEGIN_DOC
+  ! Computes the integral <pq|rs> where p,q,r,s are Gaussian primitives
+  END_DOC
+  integer,intent(in)             :: dim
+  include 'utils/constants.include.F'
+  double precision, intent(in)   :: P_new(0:max_dim,3),P_center(3),fact_p,p,p_inv
+  double precision, intent(in)   :: Q_new(0:max_dim,3),Q_center(3),fact_q,q,q_inv
+  integer, intent(in)            :: iorder_p(3)
+  integer, intent(in)            :: iorder_q(3)
+
+  double precision               :: r_cut,gama_r_cut,rho,dist
+  double precision               :: dx(0:max_dim),Ix_pol(0:max_dim),dy(0:max_dim),Iy_pol(0:max_dim),dz(0:max_dim),Iz_pol(0:max_dim)
+  integer                        :: n_Ix,n_Iy,n_Iz,nx,ny,nz
+  double precision               :: bla
+  integer                        :: ix,iy,iz,jx,jy,jz,i
+  double precision               :: a,b,c,d,e,f,accu,pq,const
+  double precision               :: pq_inv, p10_1, p10_2, p01_1, p01_2,pq_inv_2
+  integer                        :: n_pt_tmp,n_pt_out, iorder
+  double precision               :: d1(0:max_dim),d_poly(0:max_dim),rint,d1_screened(0:max_dim)
+  double precision :: thr
+
+  thr = ao_integrals_threshold
+
+  general_primitive_integral_gauss = 0.d0
+
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: dx,Ix_pol,dy,Iy_pol,dz,Iz_pol
+  !DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: d1, d_poly
+
+  ! Gaussian Product
+  ! ----------------
+
+  pq = p_inv*0.5d0*q_inv
+  pq_inv = 0.5d0/(p+q)
+  p10_1 = q*pq  ! 1/(2p)
+  p01_1 = p*pq  ! 1/(2q)
+  pq_inv_2 = pq_inv+pq_inv
+  p10_2 = pq_inv_2 * p10_1*q !0.5d0*q/(pq + p*p)
+  p01_2 = pq_inv_2 * p01_1*p !0.5d0*p/(q*q + pq)
+
+
+  accu = 0.d0
+  iorder = iorder_p(1)+iorder_q(1)+iorder_p(1)+iorder_q(1)
+  do ix=0,iorder
+    Ix_pol(ix) = 0.d0
+  enddo
+  n_Ix = 0
+  do ix = 0, iorder_p(1)
+    if (abs(P_new(ix,1)) < thr) cycle
+    a = P_new(ix,1)
+    do jx = 0, iorder_q(1)
+      d = a*Q_new(jx,1)
+      if (abs(d) < thr) cycle
+      !DIR$ FORCEINLINE
+      call give_polynom_mult_center_x(P_center(1),Q_center(1),ix,jx,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dx,nx)
+      !DIR$ FORCEINLINE
+      call add_poly_multiply(dx,nx,d,Ix_pol,n_Ix)
+    enddo
+  enddo
+  if (n_Ix == -1) then
+    return
+  endif
+  iorder = iorder_p(2)+iorder_q(2)+iorder_p(2)+iorder_q(2)
+  do ix=0, iorder
+    Iy_pol(ix) = 0.d0
+  enddo
+  n_Iy = 0
+  do iy = 0, iorder_p(2)
+    if (abs(P_new(iy,2)) > thr) then
+      b = P_new(iy,2)
+      do jy = 0, iorder_q(2)
+        e = b*Q_new(jy,2)
+        if (abs(e) < thr) cycle
+        !DIR$ FORCEINLINE
+        call   give_polynom_mult_center_x(P_center(2),Q_center(2),iy,jy,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dy,ny)
+        !DIR$ FORCEINLINE
+        call add_poly_multiply(dy,ny,e,Iy_pol,n_Iy)
+      enddo
+    endif
+  enddo
+  if (n_Iy == -1) then
+    return
+  endif
+
+  iorder = iorder_p(3)+iorder_q(3)+iorder_p(3)+iorder_q(3)
+  do ix=0,iorder
+    Iz_pol(ix) = 0.d0
+  enddo
+  n_Iz = 0
+  do iz = 0, iorder_p(3)
+    if (abs(P_new(iz,3)) > thr) then
+      c = P_new(iz,3)
+      do jz = 0, iorder_q(3)
+        f = c*Q_new(jz,3)
+        if (abs(f) < thr) cycle
+        !DIR$ FORCEINLINE
+        call   give_polynom_mult_center_x(P_center(3),Q_center(3),iz,jz,p,q,iorder,pq_inv,pq_inv_2,p10_1,p01_1,p10_2,p01_2,dz,nz)
+        !DIR$ FORCEINLINE
+        call add_poly_multiply(dz,nz,f,Iz_pol,n_Iz)
+      enddo
+    endif
+  enddo
+  if (n_Iz == -1) then
+    return
+  endif
+
+  rho = p*q *pq_inv_2
+  dist =  (P_center(1) - Q_center(1))*(P_center(1) - Q_center(1)) +  &
+      (P_center(2) - Q_center(2))*(P_center(2) - Q_center(2)) +      &
+      (P_center(3) - Q_center(3))*(P_center(3) - Q_center(3))
+  const = dist*rho
+
+  n_pt_tmp = n_Ix+n_Iy
+  do i=0,n_pt_tmp
+    d_poly(i)=0.d0
+  enddo
+
+  !DIR$ FORCEINLINE
+  call multiply_poly(Ix_pol,n_Ix,Iy_pol,n_Iy,d_poly,n_pt_tmp)
+  if (n_pt_tmp == -1) then
+    return
+  endif
+  n_pt_out = n_pt_tmp+n_Iz
+  do i=0,n_pt_out
+    d1(i)=0.d0
+  enddo
+
+  !DIR$ FORCEINLINE
+  call multiply_poly(d_poly ,n_pt_tmp ,Iz_pol,n_Iz,d1,n_pt_out)
+
+  double precision :: aa,c_a,t_a,rho_old,w_a,pi_3,prefactor,inv_pq_3_2
+  double precision :: gauss_int
+  integer :: m
+  gauss_int = 0.d0
+  pi_3 = pi*pi*pi
+  inv_pq_3_2 = (p_inv * q_inv)**(1.5d0)
+  rho_old = (p*q)/(p+q)
+  prefactor = pi_3 * inv_pq_3_2 * fact_p * fact_q 
+  do i = 1, n_gauss_eff_pot ! browse the gaussians with different expo/coef
+   aa = expo_gauss_eff_pot(i) 
+   c_a = coef_gauss_eff_pot(i)
+   t_a = dsqrt( aa /(rho_old + aa) ) 
+   w_a = dexp(-t_a*t_a*rho_old*dist)
+   accu = 0.d0
+   ! evaluation of the polynom Ix(t_a) * Iy(t_a) * Iz(t_a)
+   do m = 0, n_pt_out,2
+    accu += d1(m) * (t_a)**(dble(m)) 
+   enddo
+   ! equation A8 of PRA-70-062505 (2004) of Toul. Col. Sav. 
+   gauss_int = gauss_int + c_a * prefactor * (1.d0 - t_a*t_a)**(1.5d0) * w_a * accu
+  enddo
+
+  general_primitive_integral_gauss = gauss_int
+end
+
+subroutine compute_ao_integrals_gauss_jl(j,l,n_integrals,buffer_i,buffer_value)
+  implicit none
+  use map_module
+  BEGIN_DOC
+  !  Parallel client for AO integrals
+  END_DOC
+
+  integer, intent(in)            :: j,l
+  integer,intent(out)            :: n_integrals
+  integer(key_kind),intent(out)  :: buffer_i(ao_num*ao_num)
+  real(integral_kind),intent(out) :: buffer_value(ao_num*ao_num)
+
+  integer                        :: i,k
+  double precision               :: cpu_1,cpu_2, wall_1, wall_2
+  double precision               :: integral, wall_0
+  double precision               :: thr,ao_tc_sym_two_e_pot
+  integer                        :: kk, m, j1, i1
+  logical, external              :: ao_two_e_integral_zero
+
+  thr = ao_integrals_threshold
+
+  n_integrals = 0
+
+  j1 = j+ishft(l*l-l,-1)
+  do k = 1, ao_num           ! r1
+    i1 = ishft(k*k-k,-1)
+    if (i1 > j1) then
+      exit
+    endif
+    do i = 1, k
+      i1 += 1
+      if (i1 > j1) then
+        exit
+      endif
+!      if (ao_two_e_integral_zero(i,j,k,l)) then
+      if (.False.) then
+        cycle
+      endif
+      if (ao_two_e_integral_erf_schwartz(i,k)*ao_two_e_integral_erf_schwartz(j,l) < thr ) then
+        cycle
+      endif
+      !DIR$ FORCEINLINE
+      integral = ao_tc_sym_two_e_pot(i,k,j,l)  ! i,k : r1    j,l : r2
+      if (abs(integral) < thr) then
+        cycle
+      endif
+      n_integrals += 1
+      !DIR$ FORCEINLINE
+      call two_e_integrals_index(i,j,k,l,buffer_i(n_integrals))
+      buffer_value(n_integrals) = integral
+    enddo
+  enddo
+
+end

src/ao_two_e_ints/EZFIO.cfg

@@ -4,13 +4,6 @@ doc: Read/Write |AO| integrals from/to disk [ Write | Read | None ]
 interface: ezfio,provider,ocaml
 default: None
 
-[ao_integrals_threshold]
-type: Threshold
-doc: If | (pq|rs) | < `ao_integrals_threshold` then (pq|rs) is zero
-interface: ezfio,provider,ocaml
-default: 1.e-15
-ezfio_name: threshold_ao
-
 [do_direct_integrals]
 type: logical
 doc: Compute integrals on the fly (very slow, only for debugging)

src/ao_two_e_ints/gauss_legendre.irp.f

@@ -1,57 +0,0 @@
- BEGIN_PROVIDER [ double precision, gauleg_t2, (n_pt_max_integrals,n_pt_max_integrals/2) ]
-&BEGIN_PROVIDER [ double precision, gauleg_w, (n_pt_max_integrals,n_pt_max_integrals/2) ]
-   implicit none
-   BEGIN_DOC
-   ! t_w(i,1,k) = w(i)
-   ! t_w(i,2,k) = t(i)
-   END_DOC
-   integer                        :: i,j,l
-   l=0
-   do i = 2,n_pt_max_integrals,2
-     l = l+1
-     call gauleg(0.d0,1.d0,gauleg_t2(1,l),gauleg_w(1,l),i)
-     do j=1,i
-       gauleg_t2(j,l) *= gauleg_t2(j,l)
-     enddo
-   enddo
-
-END_PROVIDER
-
-subroutine gauleg(x1,x2,x,w,n)
-   implicit none
-   BEGIN_DOC
-   ! Gauss-Legendre
-   END_DOC
-   integer, intent(in)            :: n
-   double precision, intent(in)   :: x1, x2
-   double precision, intent (out) :: x(n),w(n)
-   double precision, parameter    :: eps=3.d-14
-
-   integer                        :: m,i,j
-   double precision               :: xm, xl, z, z1, p1, p2, p3, pp, dn
-   m=(n+1)/2
-   xm=0.5d0*(x2+x1)
-   xl=0.5d0*(x2-x1)
-   dn = dble(n)
-   do i=1,m
-     z=dcos(3.141592654d0*(dble(i)-.25d0)/(dble(n)+.5d0))
-     z1 = z+1.d0
-     do while (dabs(z-z1) > eps)
-       p1=1.d0
-       p2=0.d0
-       do j=1,n
-         p3=p2
-         p2=p1
-         p1=(dble(j+j-1)*z*p2-dble(j-1)*p3)/j
-       enddo
-       pp=dn*(z*p1-p2)/(z*z-1.d0)
-       z1=z
-       z=z1-p1/pp
-     end do
-     x(i)=xm-xl*z
-     x(n+1-i)=xm+xl*z
-     w(i)=(xl+xl)/((1.d0-z*z)*pp*pp)
-     w(n+1-i)=w(i)
-   enddo
-end
-

src/ao_two_e_ints/map_integrals.irp.f

@@ -326,9 +326,9 @@ double precision function get_ao_two_e_integral(i,j,k,l,map) result(result)
   use map_module
   implicit none
   BEGIN_DOC
-  ! Gets one AO bi-electronic integral from the AO map
+  ! Gets one AO bi-electronic integral from the AO map in PHYSICIST NOTATION
   !
-  ! i,j,k,l in physicist notation <ij|kl>
+  ! <1:k, 2:l |1:i, 2:j> 
   END_DOC
   integer, intent(in)            :: i,j,k,l
   integer(key_kind)              :: idx

src/ao_two_e_ints/test_cosgtos_1e.irp.f

@@ -0,0 +1,191 @@
+
+! ---
+
+program test_cosgtos
+
+  implicit none
+  integer :: i, j
+
+  call init_expo()
+
+!  call test_coef()
+  call test_1e_kin()
+  call test_1e_coul()
+
+  i = 1
+  j = 1
+!  call test_1e_coul_real(i, j)
+!  call test_1e_coul_cpx (i, j)
+
+end
+
+! ---
+
+subroutine init_expo()
+
+  implicit none
+
+  integer                       :: i, j
+  double precision, allocatable :: expo_im(:,:)
+
+  allocate(expo_im(ao_num, ao_prim_num_max))
+
+  do j = 1, ao_prim_num_max
+    do i = 1, ao_num
+      ao_expoim_cosgtos(i,j) = 0.d0
+    enddo
+  enddo
+
+  call ezfio_set_cosgtos_ao_int_ao_expoim_cosgtos(expo_im)
+
+  deallocate(expo_im)
+
+end subroutine init_expo
+
+! ---
+
+subroutine test_coef()
+
+  implicit none
+
+  integer          :: i, j
+  double precision :: coef, coef_gtos, coef_cosgtos 
+  double precision :: delta, accu_abs
+
+  print*, ' check coefs' 
+
+  accu_abs = 0.d0
+  accu_abs = 0.d0
+  do i = 1, ao_num
+    do j = 1, ao_prim_num(i)
+
+      coef         = ao_coef(i,j)
+      coef_gtos    = 1.d0 * ao_coef_normalized_ordered_transp(j,i)
+      coef_cosgtos = 2.d0 * ao_coef_norm_ord_transp_cosgtos  (j,i)
+
+      delta = dabs(coef_gtos - coef_cosgtos)
+      accu_abs += delta
+
+      if(delta .gt. 1.d-10) then
+        print*, ' problem on: '
+        print*, i, j
+        print*, coef_gtos, coef_cosgtos, delta
+        print*, coef 
+        stop
+      endif
+
+    enddo
+  enddo
+
+  print*, 'accu_abs = ', accu_abs 
+
+end subroutine test_coef
+
+! ---
+
+subroutine test_1e_kin()
+
+  implicit none
+
+  integer          :: i, j
+  double precision :: integral_gtos, integral_cosgtos
+  double precision :: delta, accu_abs
+
+  print*, ' check kin 1e integrals' 
+
+  accu_abs = 0.d0
+  accu_abs = 0.d0
+
+  do j = 1, ao_num
+    do i = 1, ao_num
+
+      integral_gtos    = ao_kinetic_integrals        (i,j) 
+      integral_cosgtos = ao_kinetic_integrals_cosgtos(i,j) 
+
+
+      delta = dabs(integral_gtos - integral_cosgtos)
+      accu_abs += delta
+
+      if(delta .gt. 1.d-7) then
+        print*, ' problem on: '
+        print*, i, j
+        print*, integral_gtos, integral_cosgtos, delta
+        !stop
+      endif
+
+    enddo
+  enddo
+
+ print*,'accu_abs = ', accu_abs
+
+end subroutine test_1e_kin
+
+! ---
+
+subroutine test_1e_coul()
+
+  implicit none
+
+  integer          :: i, j
+  double precision :: integral_gtos, integral_cosgtos
+  double precision :: delta, accu_abs
+
+  print*, ' check Coulomb 1e integrals' 
+
+  accu_abs = 0.d0
+  accu_abs = 0.d0
+
+  do j = 1, ao_num
+    do i = 1, ao_num
+
+      integral_gtos    = ao_integrals_n_e        (i,j) 
+      integral_cosgtos = ao_integrals_n_e_cosgtos(i,j) 
+
+      delta = dabs(integral_gtos - integral_cosgtos)
+      accu_abs += delta
+
+      if(delta .gt. 1.d-7) then
+        print*, ' problem on: '
+        print*, i, j
+        print*, integral_gtos, integral_cosgtos, delta
+        !stop
+      endif
+
+    enddo
+  enddo
+
+ print*,'accu_abs = ', accu_abs
+
+end subroutine test_1e_coul
+
+! ---
+
+subroutine test_1e_coul_cpx(i, j)
+
+  implicit none
+
+  integer, intent(in) :: i, j
+  double precision    :: integral
+
+  integral = ao_integrals_n_e_cosgtos(i,j) 
+
+  print*, ' cpx Coulomb 1e integrals', integral
+
+end subroutine test_1e_coul_cpx
+
+! ---
+
+subroutine test_1e_coul_real(i, j)
+
+  implicit none
+
+  integer, intent(in) :: i, j
+  double precision    :: integral
+
+  integral = ao_integrals_n_e(i,j) 
+
+  print*, ' real Coulomb 1e integrals', integral
+
+end subroutine test_1e_coul_real
+
+! ---

src/ao_two_e_ints/test_cosgtos_2e.irp.f

@@ -0,0 +1,165 @@
+
+! ---
+
+program test_cosgtos
+
+  implicit none
+  integer :: iao, jao, kao, lao
+
+  call init_expo()
+
+!  call test_coef()
+  call test_2e()
+
+  iao = 1
+  jao = 1
+  kao = 1
+  lao = 21
+!  call test_2e_cpx (iao, jao, kao, lao)
+!  call test_2e_real(iao, jao, kao, lao)
+
+end
+
+! ---
+
+subroutine init_expo()
+
+  implicit none
+
+  integer                       :: i, j
+  double precision, allocatable :: expo_im(:,:)
+
+  allocate(expo_im(ao_num, ao_prim_num_max))
+
+  do j = 1, ao_prim_num_max
+    do i = 1, ao_num
+      ao_expoim_cosgtos(i,j) = 0.d0
+    enddo
+  enddo
+
+  call ezfio_set_cosgtos_ao_int_ao_expoim_cosgtos(expo_im)
+
+  deallocate(expo_im)
+
+end subroutine init_expo
+
+! ---
+
+subroutine test_coef()
+
+  implicit none
+
+  integer          :: i, j
+  double precision :: coef, coef_gtos, coef_cosgtos 
+  double precision :: delta, accu_abs
+
+  print*, ' check coefs' 
+
+  accu_abs = 0.d0
+  accu_abs = 0.d0
+  do i = 1, ao_num
+    do j = 1, ao_prim_num(i)
+
+      coef         = ao_coef(i,j)
+      coef_gtos    = 1.d0 * ao_coef_normalized_ordered_transp(j,i)
+      coef_cosgtos = 2.d0 * ao_coef_norm_ord_transp_cosgtos  (j,i)
+
+      delta = dabs(coef_gtos - coef_cosgtos)
+      accu_abs += delta
+
+      if(delta .gt. 1.d-10) then
+        print*, ' problem on: '
+        print*, i, j
+        print*, coef_gtos, coef_cosgtos, delta
+        print*, coef 
+        stop
+      endif
+
+    enddo
+  enddo
+
+  print*, 'accu_abs = ', accu_abs 
+
+end subroutine test_coef
+
+
+! ---
+
+subroutine test_2e()
+
+  implicit none
+
+  integer          :: iao, jao, kao, lao
+  double precision :: integral_gtos, integral_cosgtos
+  double precision :: delta, accu_abs
+
+  double precision :: ao_two_e_integral, ao_two_e_integral_cosgtos
+
+  print*, ' check integrals' 
+
+  accu_abs = 0.d0
+  accu_abs = 0.d0
+
+ ! iao = 1
+ ! jao = 1
+ ! kao = 1
+ ! lao = 24
+
+  do iao = 1, ao_num ! r1
+    do jao = 1, ao_num ! r2
+      do kao = 1, ao_num ! r1
+        do lao = 1, ao_num ! r2
+
+          integral_gtos    = ao_two_e_integral        (iao, kao, jao, lao)
+          integral_cosgtos = ao_two_e_integral_cosgtos(iao, kao, jao, lao)
+
+          delta = dabs(integral_gtos - integral_cosgtos)
+          accu_abs += delta
+
+          if(delta .gt. 1.d-7) then
+            print*, ' problem on: '
+            print*, iao, jao, kao, lao
+            print*, integral_gtos, integral_cosgtos, delta
+            !stop
+          endif
+
+        enddo
+      enddo
+    enddo
+  enddo
+
+ print*,'accu_abs = ', accu_abs
+
+end subroutine test_2e
+
+! ---
+
+subroutine test_2e_cpx(iao, jao, kao, lao)
+
+  implicit none
+  integer, intent(in) :: iao, jao, kao, lao
+  double precision    :: integral
+  double precision    :: ao_two_e_integral_cosgtos
+
+  integral = ao_two_e_integral_cosgtos(iao, kao, jao, lao)
+  print *, ' cosgtos: ', integral
+
+end subroutine test_2e_cpx
+
+! ---
+
+subroutine test_2e_real(iao, jao, kao, lao)
+
+  implicit none
+  integer, intent(in) :: iao, jao, kao, lao
+  double precision    :: integral
+  double precision    :: ao_two_e_integral
+
+  integral = ao_two_e_integral(iao, kao, jao, lao)
+  print *, ' gtos: ', integral
+
+end subroutine test_2e_real
+
+! ---
+
+

src/ao_two_e_ints/two_e_integrals.irp.f

@@ -1,23 +1,42 @@
+
+! ---
+
 double precision function ao_two_e_integral(i,j,k,l)
-  implicit none
+
   BEGIN_DOC
   !  integral of the AO basis <ik|jl> or (ij|kl)
   !     i(r1) j(r1) 1/r12 k(r2) l(r2)
   END_DOC
 
-  integer,intent(in)             :: i,j,k,l
+  implicit none
-  integer                        :: p,q,r,s
-  double precision               :: I_center(3),J_center(3),K_center(3),L_center(3)
-  integer                        :: num_i,num_j,num_k,num_l,dim1,I_power(3),J_power(3),K_power(3),L_power(3)
-  double precision               :: integral
   include 'utils/constants.include.F'
+
+  integer, intent(in)            :: i, j, k, l
+
+  integer                        :: p, q, r, s
+  integer                        :: num_i,num_j,num_k,num_l,dim1,I_power(3),J_power(3),K_power(3),L_power(3)
+  integer                        :: iorder_p(3), iorder_q(3)
+  double precision               :: I_center(3), J_center(3), K_center(3), L_center(3)
+  double precision               :: integral
   double precision               :: P_new(0:max_dim,3),P_center(3),fact_p,pp
   double precision               :: Q_new(0:max_dim,3),Q_center(3),fact_q,qq
-  integer                        :: iorder_p(3), iorder_q(3)
+
   double precision               :: ao_two_e_integral_schwartz_accel
 
+  double precision               :: ao_two_e_integral_cosgtos
+
+
+  if(use_cosgtos) then
+    !print *, ' use_cosgtos for ao_two_e_integral ?', use_cosgtos
+
+    ao_two_e_integral = ao_two_e_integral_cosgtos(i,j,k,l)
+
+  else
+
     if (ao_prim_num(i) * ao_prim_num(j) * ao_prim_num(k) * ao_prim_num(l) > 1024 ) then
+
        ao_two_e_integral = ao_two_e_integral_schwartz_accel(i,j,k,l)
+
     else
 
       dim1 = n_pt_max_integrals
@@ -101,8 +120,13 @@ double precision function ao_two_e_integral(i,j,k,l)
       endif
 
     endif
+
+  endif
+
 end
 
+! ---
+
 double precision function ao_two_e_integral_schwartz_accel(i,j,k,l)
   implicit none
   BEGIN_DOC
@@ -420,13 +444,16 @@ BEGIN_PROVIDER [ logical, ao_two_e_integrals_in_map ]
 
 END_PROVIDER
 
-BEGIN_PROVIDER [ double precision, ao_two_e_integral_schwartz,(ao_num,ao_num)  ]
+! ---
-  implicit none
+
+BEGIN_PROVIDER [ double precision, ao_two_e_integral_schwartz, (ao_num, ao_num) ]
+
   BEGIN_DOC
   !  Needed to compute Schwartz inequalities
   END_DOC
 
-  integer                        :: i,k
+  implicit none
+  integer          :: i, k
   double precision :: ao_two_e_integral,cpu_1,cpu_2, wall_1, wall_2
 
   ao_two_e_integral_schwartz(1,1) = ao_two_e_integral(1,1,1,1)
@@ -444,6 +471,7 @@ BEGIN_PROVIDER [ double precision, ao_two_e_integral_schwartz,(ao_num,ao_num)  ]
 
 END_PROVIDER
 
+! ---
 
 double precision function general_primitive_integral(dim,            &
       P_new,P_center,fact_p,p,p_inv,iorder_p,                        &
@@ -575,7 +603,10 @@ double precision function general_primitive_integral(dim,            &
   !DIR$ FORCEINLINE
   call multiply_poly(d_poly ,n_pt_tmp ,Iz_pol,n_Iz,d1,n_pt_out)
   double precision               :: rint_sum
+
   accu = accu + rint_sum(n_pt_out,const,d1)
+!  print *, n_pt_out, d1(0:n_pt_out)
+!  print *, accu
 
   general_primitive_integral = fact_p * fact_q * accu *pi_5_2*p_inv*q_inv/dsqrt(p+q)
 end
@@ -840,6 +871,15 @@ subroutine give_polynom_mult_center_x(P_center,Q_center,a_x,d_x,p,q,n_pt_in,pq_i
   !DIR$ FORCEINLINE
   call I_x1_pol_mult(a_x,d_x,B10,B01,B00,C00,D00,d,n_pt1,n_pt_in)
   n_pt_out = n_pt1
+
+!  print *, ' '
+!  print *, a_x, d_x
+!  print *, B10, B01, B00, C00, D00
+!  print *, n_pt1, d(0:n_pt1)
+!  print *, ' '
+
+
+
   if(n_pt1<0)then
     n_pt_out = -1
     do i = 0,n_pt_in

src/basis/EZFIO.cfg

@@ -72,4 +72,3 @@ doc: Exponents in the shell
 size: (basis.prim_num)
 interface: ezfio, provider
 
-

src/basis/basis.irp.f

@@ -1,67 +1,11 @@
-BEGIN_PROVIDER [ double precision, shell_normalization_factor , (shell_num) ]
+BEGIN_PROVIDER [ integer, shell_prim_num_max ]
  implicit none
  BEGIN_DOC
-  ! Number of primitives per |AO|
+ ! Max number of primitives.
  END_DOC
-
+ shell_prim_num_max = maxval(shell_prim_num)
-  logical                        :: has
-  PROVIDE ezfio_filename
-  if (mpi_master) then
-    if (size(shell_normalization_factor) == 0) return
-
-    call ezfio_has_basis_shell_normalization_factor(has)
-    if (has) then
-      write(6,'(A)') '.. >>>>> [ IO READ: shell_normalization_factor ] <<<<< ..'
-      call ezfio_get_basis_shell_normalization_factor(shell_normalization_factor)
-    else
-
-      double precision               :: norm,overlap_x,overlap_y,overlap_z,C_A(3), c
-      integer                        :: l, powA(3), nz
-      integer                        :: i,j,k
-      nz=100
-      C_A(1) = 0.d0
-      C_A(2) = 0.d0
-      C_A(3) = 0.d0
-
-      do i=1,shell_num
-
-        powA(1) = shell_ang_mom(i)
-        powA(2) = 0
-        powA(3) = 0
-
-        norm = 0.d0
-        do k=1, prim_num
-          if (shell_index(k) /= i) cycle
-          do j=1, prim_num
-            if (shell_index(j) /= i) cycle
-            call overlap_gaussian_xyz(C_A,C_A,prim_expo(j),prim_expo(k), &
-              powA,powA,overlap_x,overlap_y,overlap_z,c,nz)
-            norm = norm+c*prim_coef(j)*prim_coef(k) * prim_normalization_factor(j) * prim_normalization_factor(k)
-          enddo
-        enddo
-        shell_normalization_factor(i) = 1.d0/dsqrt(norm)
-      enddo
-
-    endif
-  endif
-  IRP_IF MPI_DEBUG
-  print *,  irp_here, mpi_rank
-  call MPI_BARRIER(MPI_COMM_WORLD, ierr)
-  IRP_ENDIF
-  IRP_IF MPI
-  include 'mpif.h'
-  integer                        :: ierr
-  call MPI_BCAST( shell_normalization_factor, (shell_num), MPI_DOUBLE_PRECISION, 0, MPI_COMM_WORLD, ierr)
-  if (ierr /= MPI_SUCCESS) then
-    stop 'Unable to read shell_normalization_factor with MPI'
-  endif
-  IRP_ENDIF
-
-  call write_time(6)
-
 END_PROVIDER
 
-
 BEGIN_PROVIDER [ double precision, prim_normalization_factor , (prim_num) ]
   implicit none
   BEGIN_DOC
@@ -120,3 +64,94 @@ BEGIN_PROVIDER [ double precision, prim_normalization_factor , (prim_num) ]
   call write_time(6)
 
 END_PROVIDER
+
+ BEGIN_PROVIDER [ double precision, shell_coef , (shell_num, shell_prim_num_max) ]
+&BEGIN_PROVIDER [ double precision, shell_expo , (shell_num, shell_prim_num_max) ]
+  implicit none
+  BEGIN_DOC
+! Primitive coefficients and exponents for each shell.
+  END_DOC
+
+  integer :: i, idx
+  integer :: count(shell_num)
+
+  count(:) = 0
+  do i=1, prim_num
+    idx = shell_index(i)
+    count(idx) += 1
+    shell_coef(idx, count(idx)) = prim_coef(i)
+    shell_expo(idx, count(idx)) = prim_expo(i)
+  end do
+END_PROVIDER
+
+
+ BEGIN_PROVIDER [ double precision, shell_coef_normalized, (shell_num,shell_prim_num_max) ]
+&BEGIN_PROVIDER [ double precision, shell_normalization_factor, (shell_num) ]
+  implicit none
+  BEGIN_DOC
+  ! Coefficients including the |shell| normalization
+  END_DOC
+  logical                        :: has
+  PROVIDE ezfio_filename
+
+  shell_normalization_factor(:) = 1.d0
+  if (mpi_master) then
+    if (size(shell_normalization_factor) == 0) return
+
+    call ezfio_has_basis_shell_normalization_factor(has)
+    if (has) then
+      write(6,'(A)') '.. >>>>> [ IO READ: shell_normalization_factor ] <<<<< ..'
+      call ezfio_get_basis_shell_normalization_factor(shell_normalization_factor)
+    endif
+  endif
+  IRP_IF MPI_DEBUG
+  print *,  irp_here, mpi_rank
+  call MPI_BARRIER(MPI_COMM_WORLD, ierr)
+  IRP_ENDIF
+  IRP_IF MPI
+  include 'mpif.h'
+  integer                        :: ierr
+  call MPI_BCAST( shell_normalization_factor, (shell_num), MPI_DOUBLE_PRECISION, 0, MPI_COMM_WORLD, ierr)
+  if (ierr /= MPI_SUCCESS) then
+    stop 'Unable to read shell_normalization_factor with MPI'
+  endif
+  IRP_ENDIF
+
+  call write_time(6)
+  double precision               :: norm,overlap_x,overlap_y,overlap_z,C_A(3), c
+  integer                        :: l, powA(3), nz
+  integer                        :: i,j,k
+  nz=100
+  C_A = 0.d0
+  powA = 0
+  shell_coef_normalized = 0.d0
+
+  do i=1,shell_num
+
+    powA(1) = shell_ang_mom(i)
+
+    ! Normalization of the primitives
+    if (primitives_normalized) then
+      do j=1,shell_prim_num(i)
+        call overlap_gaussian_xyz(C_A,C_A,shell_expo(i,j),shell_expo(i,j), &
+           powA,powA,overlap_x,overlap_y,overlap_z,norm,nz)
+        shell_coef_normalized(i,j) = shell_coef(i,j)/dsqrt(norm)
+      enddo
+    else
+      do j=1,shell_prim_num(i)
+        shell_coef_normalized(i,j) = shell_coef(i,j)
+      enddo
+    endif
+
+    ! Normalization of the contracted basis functions
+    norm = 0.d0
+    do j=1,shell_prim_num(i)
+      do k=1,shell_prim_num(i)
+        call overlap_gaussian_xyz(C_A,C_A,shell_expo(i,j),shell_expo(i,k),powA,powA,overlap_x,overlap_y,overlap_z,c,nz)
+        norm = norm+c*shell_coef_normalized(i,j)*shell_coef_normalized(i,k)
+      enddo
+    enddo
+    shell_normalization_factor(i) *= 1.d0/dsqrt(norm)
+  enddo
+END_PROVIDER
+

src/basis_correction/pbe_ueg_self_contained.irp.f

@@ -0,0 +1,57 @@
+double precision function ecmd_pbe_ueg_self_cont(dens,spin_pol,mu,e_PBE)
+ implicit none
+ ! dens = total density 
+ ! spin_pol = spin_polarization (n_a - n_b)/dens
+ ! e_PBE = PBE correlation (mu=0) energy evaluated at  dens,spin_pol (and grad_rho) 
+ ! e_PBE = epsilon_PBE * dens which means that it is not the energy density but the energy density X the density
+ double precision, intent(in) :: dens,spin_pol,mu,e_PBE
+ double precision :: rho_a,rho_b,pi,g0_UEG_func,denom,beta
+ pi = dacos(-1.d0)
+ rho_a = (dens * spin_pol + dens)*0.5d0
+ rho_b = (dens - dens * spin_pol)*0.5d0 
+ if(mu == 0.d0) then
+  ecmd_pbe_ueg_self_cont = e_PBE
+ else
+! note: the on-top pair density is (1-zeta^2) rhoc^2 g0 = 4 rhoa * rhob * g0
+  denom = (-2.d0+sqrt(2d0))*sqrt(2.d0*pi) * 4.d0*rho_a*rho_b*g0_UEG_func(rho_a,rho_b)
+  if (dabs(denom) > 1.d-12) then
+   beta = (3.d0*e_PBE)/denom
+   ecmd_pbe_ueg_self_cont=e_PBE/(1.d0+beta*mu**3)
+  else
+   ecmd_pbe_ueg_self_cont=0.d0
+  endif
+ endif
+end
+
+double precision function g0_UEG_func(rho_a,rho_b)
+! Pair distribution function g0(n_alpha,n_beta) of the Colombic UEG 
+!
+! Taken from Eq. (46)  P. Gori-Giorgi and A. Savin, Phys. Rev. A 73, 032506 (2006). 
+ implicit none
+ double precision, intent(in) :: rho_a,rho_b
+ double precision :: rho,pi,x
+ double precision :: B, C, D, E, d2, rs, ahd
+ rho = rho_a+rho_b
+ pi = 4d0 * datan(1d0)
+ ahd = -0.36583d0
+ d2 = 0.7524d0
+ B = -2d0 * ahd - d2
+ C = 0.08193d0
+ D = -0.01277d0
+ E = 0.001859d0
+ x = -d2*rs
+ if (dabs(rho) > 1.d-20) then
+  rs = (3d0 / (4d0*pi*rho))**(1d0/3d0) 
+  x = -d2*rs
+  if(dabs(x).lt.50.d0)then
+   g0_UEG_func= 0.5d0 * (1d0+ rs* (-B + rs*(C + rs*(D + rs*E))))*dexp(x)
+  else
+   g0_UEG_func= 0.d0
+  endif
+ else
+  g0_UEG_func= 0.d0
+ endif
+ g0_UEG_func = max(g0_UEG_func,1.d-14)
+
+end
+

src/basis_correction/print_routine.irp.f

@@ -38,7 +38,7 @@ subroutine print_basis_correction
     write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ECMD PBE-UEG       , state ',istate,' = ',ecmd_pbe_ueg_mu_of_r(istate)
    enddo
 
-  else if(mu_of_r_potential.EQ."cas_ful".or.mu_of_r_potential.EQ."cas_truncated".or.mu_of_r_potential.EQ."pure_act")then
+  else if(mu_of_r_potential.EQ."cas_ful")then
    print*, ''
    print*,'Using a CAS-like two-body density to define mu(r)'
    print*,'This assumes that the CAS is a qualitative representation of the wave function ' 
@@ -80,3 +80,64 @@ subroutine print_basis_correction
 end
 
 
+
+subroutine print_all_basis_correction
+ implicit none
+ integer :: istate
+ provide mu_average_prov
+ provide ecmd_lda_mu_of_r ecmd_pbe_ueg_mu_of_r 
+ provide ecmd_pbe_on_top_mu_of_r ecmd_pbe_on_top_su_mu_of_r
+
+ print*, ''
+ print*, ''
+ print*, '****************************************'
+ print*, '****************************************'
+ print*, 'Basis set correction for WFT using DFT Ecmd functionals'
+ print*, 'These functionals are accurate for short-range correlation'
+ print*, ''
+ print*, 'For more details look at Journal of Chemical Physics 149, 194301 1-15 (2018)        '
+ print*, '                         Journal of Physical Chemistry Letters 10, 2931-2937 (2019) '
+ print*, '                         ???REF SC?'
+ print*, '****************************************'
+ print*, '****************************************'
+ print*, 'mu_of_r_potential = ',mu_of_r_potential
+ print*, ''
+ print*,'Using a CAS-like two-body density to define mu(r)'
+ print*,'This assumes that the CAS is a qualitative representation of the wave function ' 
+ print*,'********************************************'
+ print*,'Functionals more suited for weak correlation'
+ print*,'********************************************'
+ print*,'+) LDA Ecmd functional     : purely based on the UEG (JCP,149,194301,1-15 (2018)) '
+ do istate = 1, N_states
+  write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ECMD LDA           , state ',istate,' = ',ecmd_lda_mu_of_r(istate)
+ enddo
+ print*,'+) PBE-UEG Ecmd functional : PBE at mu=0, UEG ontop pair density at large mu (JPCL, 10, 2931-2937 (2019))'
+ do istate = 1, N_states
+  write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ECMD PBE-UEG       , state ',istate,' = ',ecmd_pbe_ueg_mu_of_r(istate)
+ enddo
+ print*,''
+ print*,'********************************************'
+ print*,'********************************************'
+ print*,'+) PBE-on-top Ecmd functional : (??????? REF-SCF ??????????)' 
+ print*,'PBE at mu=0, extrapolated ontop pair density at large mu, usual spin-polarization'
+ do istate = 1, N_states
+  write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ECMD PBE-OT        , state ',istate,' = ',ecmd_pbe_on_top_mu_of_r(istate)
+ enddo
+ print*,''
+ print*,'********************************************'
+ print*,'+) PBE-on-top no spin polarization Ecmd functional : (??????? REF-SCF ??????????)' 
+ print*,'PBE at mu=0, extrapolated ontop pair density at large mu, and ZERO SPIN POLARIZATION'
+ do istate = 1, N_states
+  write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ECMD SU-PBE-OT     , state ',istate,' = ',ecmd_pbe_on_top_su_mu_of_r(istate)
+ enddo
+ print*,''
+
+  print*,''
+  print*,'**************'
+  do istate = 1, N_states
+    write(*, '(A29,X,I3,X,A3,X,F16.10)') '  Average mu(r)      , state ',istate,' = ',mu_average_prov(istate)
+  enddo
+
+end
+
+

src/basis_correction/print_su_pbe_ot.irp.f

@@ -20,9 +20,10 @@ subroutine print_su_pbe_ot
  integer :: istate 
  do istate = 1, N_states
   write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ECMD PBE-UEG       , state ',istate,' = ',ecmd_pbe_ueg_mu_of_r(istate)
+  write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ecmd_pbe_ueg_test  , state ',istate,' = ',ecmd_pbe_ueg_test(istate)
  enddo
- do istate = 1, N_states
+! do istate = 1, N_states
-  write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ECMD SU-PBE-OT     , state ',istate,' = ',ecmd_pbe_on_top_su_mu_of_r(istate)
+!  write(*, '(A29,X,I3,X,A3,X,F16.10)') '  ECMD SU-PBE-OT     , state ',istate,' = ',ecmd_pbe_on_top_su_mu_of_r(istate)
- enddo
+! enddo
 
 end

src/basis_correction/test_ueg_self_contained.irp.f

@@ -0,0 +1,84 @@
+program test_sc
+ implicit none
+ integer :: m
+ double precision :: r(3),f_hf,on_top,mu,sqpi
+ double precision :: rho_a,rho_b,w_hf,dens,delta_rho,e_pbe
+ double precision :: grad_rho_a(3),grad_rho_b(3),grad_rho_a_2(3),grad_rho_b_2(3),grad_rho_a_b(3)
+ double precision :: sigmacc,sigmaco,sigmaoo,spin_pol
+ double precision :: eps_c_md_PBE , ecmd_pbe_ueg_self_cont
+ r = 0.D0
+ r(3) = 1.D0
+ call f_HF_valence_ab(r,r,f_hf,on_top)
+ sqpi = dsqrt(dacos(-1.d0))
+ if(on_top.le.1.d-12.or.f_hf.le.0.d0.or.f_hf * on_top.lt.0.d0)then
+  w_hf   = 1.d+10
+ else
+  w_hf  = f_hf /  on_top
+ endif                            
+ mu = sqpi * 0.5d0 * w_hf
+ call density_and_grad_alpha_beta(r,rho_a,rho_b, grad_rho_a, grad_rho_b)                                                                              
+ dens = rho_a + rho_b
+ delta_rho = rho_a - rho_b
+ spin_pol = delta_rho/(max(1.d-10,dens))
+ grad_rho_a_2 = 0.d0
+ grad_rho_b_2 = 0.d0
+ grad_rho_a_b = 0.d0
+ do m = 1, 3
+  grad_rho_a_2 += grad_rho_a(m)*grad_rho_a(m)
+  grad_rho_b_2 += grad_rho_b(m)*grad_rho_b(m)
+  grad_rho_a_b += grad_rho_a(m)*grad_rho_b(m)
+ enddo
+ call grad_rho_ab_to_grad_rho_oc(grad_rho_a_2,grad_rho_b_2,grad_rho_a_b,sigmaoo,sigmacc,sigmaco)
+
+ ! call the PBE energy 
+ print*,'f_hf,on_top = ',f_hf,on_top
+ print*,'mu = ',mu
+ print*,'dens,spin_pol',dens,spin_pol
+ call ec_pbe_only(0.d0,dens,delta_rho,sigmacc,sigmaco,sigmaoo,e_PBE)
+ print*,'e_PBE = ',e_PBE
+ eps_c_md_PBE  = ecmd_pbe_ueg_self_cont(dens,spin_pol,mu,e_PBE)
+ print*,'eps_c_md_PBE = ',eps_c_md_PBE
+
+ print*,''
+ print*,''
+ print*,''
+ print*,'energy_c' ,energy_c
+
+ integer::ipoint
+ double precision :: weight , accu
+ accu = 0.d0
+ do ipoint = 1, n_points_final_grid
+  r =  final_grid_points(:,ipoint)
+  weight = final_weight_at_r_vector(ipoint)
+  call f_HF_valence_ab(r,r,f_hf,on_top)
+  sqpi = dsqrt(dacos(-1.d0))
+  if(on_top.le.1.d-12.or.f_hf.le.0.d0.or.f_hf * on_top.lt.0.d0)then
+   w_hf   = 1.d+10
+  else
+   w_hf  = f_hf /  on_top
+  endif
+  mu = sqpi * 0.5d0 * w_hf
+  call density_and_grad_alpha_beta(r,rho_a,rho_b, grad_rho_a, grad_rho_b)
+  dens = rho_a + rho_b
+  delta_rho = rho_a - rho_b
+  spin_pol = delta_rho/(max(1.d-10,dens))
+  grad_rho_a_2 = 0.d0
+  grad_rho_b_2 = 0.d0
+  grad_rho_a_b = 0.d0
+  do m = 1, 3
+   grad_rho_a_2 += grad_rho_a(m)*grad_rho_a(m)
+   grad_rho_b_2 += grad_rho_b(m)*grad_rho_b(m)
+   grad_rho_a_b += grad_rho_a(m)*grad_rho_b(m)
+  enddo
+  call grad_rho_ab_to_grad_rho_oc(grad_rho_a_2,grad_rho_b_2,grad_rho_a_b,sigmaoo,sigmacc,sigmaco)
+  ! call the PBE energy 
+  call ec_pbe_only(0.d0,dens,delta_rho,sigmacc,sigmaco,sigmaoo,e_PBE)
+  eps_c_md_PBE  = ecmd_pbe_ueg_self_cont(dens,spin_pol,mu,e_PBE)
+  write(33,'(100(F16.10,X))')r(:), weight, w_hf, on_top, mu, dens, spin_pol, e_PBE, eps_c_md_PBE
+  accu += weight * eps_c_md_PBE
+ enddo
+ print*,'accu = ',accu
+  write(*, *) '  ECMD PBE-UEG       ',ecmd_pbe_ueg_mu_of_r(1)
+  write(*, *) '  ecmd_pbe_ueg_test  ',ecmd_pbe_ueg_test(1)
+ 
+end

src/basis_correction/weak_corr_func.irp.f

@@ -81,3 +81,54 @@ BEGIN_PROVIDER [double precision, ecmd_pbe_ueg_mu_of_r, (N_states)]
  print*,'Time for the ecmd_pbe_ueg_mu_of_r:',wall1-wall0
 
 END_PROVIDER
+
+BEGIN_PROVIDER [double precision, ecmd_pbe_ueg_test, (N_states)]
+BEGIN_DOC
+! test of the routines contained in pbe_ueg_self_contained.irp.f
+END_DOC
+implicit none
+double precision :: weight
+integer :: ipoint,istate,m
+double precision :: mu,rho_a,rho_b
+double precision :: dens,spin_pol,grad_rho,e_PBE,delta_rho
+double precision :: ecmd_pbe_ueg_self_cont,eps_c_md_PBE
+ecmd_pbe_ueg_test = 0.d0
+ 
+do istate = 1, N_states
+ do ipoint = 1, n_points_final_grid
+  weight=final_weight_at_r_vector(ipoint)
+
+  ! mu(r) defined by Eq. (37) of J. Chem. Phys. 149, 194301 (2018)
+  mu    = mu_of_r_prov(ipoint,istate)
+
+  ! conversion from rho_a,rho_b --> dens,spin_pol
+  rho_a = one_e_dm_and_grad_alpha_in_r(4,ipoint,istate)
+  rho_b = one_e_dm_and_grad_beta_in_r(4,ipoint,istate)
+  dens = rho_a + rho_b
+  spin_pol = (rho_a - rho_b)/(max(dens,1.d-12))
+  delta_rho = rho_a - rho_b
+
+  ! conversion from grad_rho_a ... to sigma 
+  double precision :: grad_rho_a(3),grad_rho_b(3),grad_rho_a_2(3),grad_rho_b_2(3),grad_rho_a_b(3)
+  double precision :: sigmacc,sigmaco,sigmaoo
+  grad_rho_b(1:3) = one_e_dm_and_grad_beta_in_r(1:3,ipoint,istate)
+  grad_rho_a(1:3) = one_e_dm_and_grad_alpha_in_r(1:3,ipoint,istate)
+  grad_rho_a_2 = 0.d0
+  grad_rho_b_2 = 0.d0
+  grad_rho_a_b = 0.d0
+  do m = 1, 3
+   grad_rho_a_2 += grad_rho_a(m)*grad_rho_a(m)
+   grad_rho_b_2 += grad_rho_b(m)*grad_rho_b(m)
+   grad_rho_a_b += grad_rho_a(m)*grad_rho_b(m)
+  enddo
+  call grad_rho_ab_to_grad_rho_oc(grad_rho_a_2,grad_rho_b_2,grad_rho_a_b,sigmaoo,sigmacc,sigmaco)
+
+  ! call the PBE energy 
+  call ec_pbe_only(0.d0,dens,delta_rho,sigmacc,sigmaco,sigmaoo,e_PBE)
+  eps_c_md_PBE  = ecmd_pbe_ueg_self_cont(dens,spin_pol,mu,e_PBE)
+
+  ecmd_pbe_ueg_test(istate) += eps_c_md_PBE * weight
+ enddo
+enddo
+!
+END_PROVIDER

src/becke_numerical_grid/grid_becke.irp.f

@@ -64,7 +64,8 @@ END_PROVIDER
 
 END_PROVIDER
 
-BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_angular,n_points_radial_grid,nucl_num)]
+ BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_angular,n_points_radial_grid,nucl_num)]
+&BEGIN_PROVIDER [double precision, radial_points_per_atom, (n_points_radial_grid,nucl_num)]
   BEGIN_DOC
   ! x,y,z coordinates of grid points used for integration in 3d space
   END_DOC
@@ -72,6 +73,7 @@ BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_
   integer                        :: i,j,k
   double precision               :: dr,x_ref,y_ref,z_ref
   double precision               :: knowles_function
+  radial_points_per_atom = 0.D0
   do i = 1, nucl_num
     x_ref = nucl_coord(i,1)
     y_ref = nucl_coord(i,2)
@@ -83,7 +85,7 @@ BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_
 
       ! value of the radial coordinate for the integration
       r = knowles_function(alpha_knowles(grid_atomic_number(i)),m_knowles,x)
-
+      radial_points_per_atom(j,i) = r
       ! explicit values of the grid points centered around each atom
       do k = 1, n_points_integration_angular
         grid_points_per_atom(1,k,j,i) =                              &

src/becke_numerical_grid/grid_becke_vector.irp.f

@@ -58,17 +58,3 @@ END_PROVIDER
   enddo
 
 END_PROVIDER
-
-BEGIN_PROVIDER [double precision, final_grid_points_transp, (n_points_final_grid,3)]
-  implicit none
-  BEGIN_DOC
-! Transposed final_grid_points
-  END_DOC
-
-  integer :: i,j
-  do j=1,3
-    do i=1,n_points_final_grid
-      final_grid_points_transp(i,j) = final_grid_points(j,i)
-    enddo
-  enddo
-END_PROVIDER

src/bi_ort_ints/NEED

@@ -0,0 +1,3 @@
+non_h_ints_mu
+ao_tc_eff_map
+bi_ortho_mos

src/bi_ort_ints/README.rst

@@ -0,0 +1,25 @@
+===========
+bi_ort_ints
+===========
+
+This module contains all necessary integrals for the TC Hamiltonian in a bi-orthonormal (BO) MO Basis.
+See in bi_ortho_basis for more information. 
+The main providers are : 
+
+One-electron integrals 
+----------------------
++) ao_one_e_integrals_tc_tot : total one-electron Hamiltonian which might include non hermitian part coming from one-e correlation factor. 
++) mo_bi_ortho_tc_one_e : one-electron Hamiltonian (h_core+one-J terms) on the BO-MO basis. 
++) mo_bi_orth_bipole_x  : x-component of the dipole operator on the BO-MO basis. (Same for y,z) 
+
+Two-electron integrals 
+----------------------
++) ao_two_e_tc_tot : Total two-electron operator (including the non-hermitian term of the TC Hamiltonian) on the AO basis
++) mo_bi_ortho_tc_two_e : Total two-electron operator on the BO-MO basis
+
+Three-electron integrals 
+------------------------
++) three_body_ints_bi_ort : 6-indices three-electron tensor (-L) on the BO-MO basis. WARNING :: N^6 storage !
++) three_e_3_idx_direct_bi_ort : DIRECT term with 3 different indices of the -L operator. These terms appear in the DIAGONAL matrix element of the -L operator. The 5 other permutations needed to compute matrix elements can be found in three_body_ijm.irp.f 
++) three_e_4_idx_direct_bi_ort : DIRECT term with 4 different indices of the -L operator. These terms appear in the OFF-DIAGONAL matrix element of the -L operator including SINGLE EXCITATIONS. The 5 other permutations needed to compute matrix elements can be found in three_body_ijmk.irp.f 
++) three_e_5_idx_direct_bi_ort : DIRECT term with 5 different indices of the -L operator. These terms appear in the OFF-DIAGONAL matrix element of the -L operator including DOUBLE EXCITATIONS. The 5 other permutations needed to compute matrix elements can be found in three_body_ijmkl.irp.f 

src/bi_ort_ints/bi_ort_ints.irp.f

@@ -0,0 +1,21 @@
+program bi_ort_ints
+  implicit none
+  BEGIN_DOC
+! TODO : Put the documentation of the program here
+  END_DOC
+  my_grid_becke = .True.
+  my_n_pt_r_grid = 30
+  my_n_pt_a_grid = 50
+  touch  my_grid_becke my_n_pt_r_grid my_n_pt_a_grid
+!  call test_overlap
+!  call routine_twoe
+!  call routine_onee
+!  call test_v_ki_bi_ortho
+!  call test_x_v_ki_bi_ortho
+!  call test_3_body_bi_ort
+!  call test_3_e_diag
+!  call test_3_e_diag_cycle1
+! call test_3_e
+!  call routine_test_one_int
+end
+

src/bi_ort_ints/one_e_bi_ort.irp.f

@@ -0,0 +1,70 @@
+
+! ---
+
+BEGIN_PROVIDER [double precision, ao_one_e_integrals_tc_tot, (ao_num,ao_num)]
+
+  implicit none
+  integer :: i, j
+
+  ao_one_e_integrals_tc_tot = ao_one_e_integrals      
+
+  provide j1b_gauss
+
+  if(j1b_gauss .eq. 1) then
+
+    do i = 1, ao_num
+      do j = 1, ao_num
+        ao_one_e_integrals_tc_tot(j,i) += ( j1b_gauss_hermI  (j,i) &
+                                          + j1b_gauss_hermII (j,i) &
+                                          + j1b_gauss_nonherm(j,i) )
+      enddo
+    enddo
+
+  endif
+
+END_PROVIDER
+
+BEGIN_PROVIDER [ double precision, mo_bi_ortho_tc_one_e, (mo_num, mo_num)]
+ implicit none
+ BEGIN_DOC
+! mo_bi_ortho_tc_one_e(k,i) = <MO^L_k | h_c | MO^R_i>
+ END_DOC
+ integer :: i,k,p,q
+ 
+  call ao_to_mo_bi_ortho(ao_one_e_integrals_tc_tot, ao_num, mo_bi_ortho_tc_one_e, mo_num)
+
+END_PROVIDER 
+
+! ---
+
+ BEGIN_PROVIDER [double precision, mo_bi_orth_bipole_x , (mo_num,mo_num)]
+&BEGIN_PROVIDER [double precision, mo_bi_orth_bipole_y , (mo_num,mo_num)]
+&BEGIN_PROVIDER [double precision, mo_bi_orth_bipole_z , (mo_num,mo_num)]
+ BEGIN_DOC
+ ! array of the integrals of MO_i * x MO_j
+ ! array of the integrals of MO_i * y MO_j
+ ! array of the integrals of MO_i * z MO_j
+ END_DOC
+ implicit none
+
+  call ao_to_mo_bi_ortho(                                                     &
+      ao_dipole_x,                                                   &
+      size(ao_dipole_x,1),                                           &
+      mo_bi_orth_bipole_x,                                                   &
+      size(mo_bi_orth_bipole_x,1)                                            &
+      )
+  call ao_to_mo_bi_ortho(                                                     &
+      ao_dipole_y,                                                   &
+      size(ao_dipole_y,1),                                           &
+      mo_bi_orth_bipole_y,                                                   &
+      size(mo_bi_orth_bipole_y,1)                                            &
+      )
+  call ao_to_mo_bi_ortho(                                                     &
+      ao_dipole_z,                                                   &
+      size(ao_dipole_z,1),                                           &
+      mo_bi_orth_bipole_z,                                                   &
+      size(mo_bi_orth_bipole_z,1)                                            &
+      )
+
+END_PROVIDER
+

src/bi_ort_ints/semi_num_ints_mo.irp.f

@@ -0,0 +1,177 @@
+BEGIN_PROVIDER [ double precision, mo_v_ki_bi_ortho_erf_rk_cst_mu, ( mo_num, mo_num,n_points_final_grid)]
+ implicit none
+ BEGIN_DOC
+! mo_v_ki_bi_ortho_erf_rk_cst_mu(k,i,ip) = int dr chi_k(r) phi_i(r) (erf(mu |r - R_ip|) - 1 )/(2|r - R_ip|) on the BI-ORTHO MO basis 
+! 
+! where phi_k(r) is a LEFT MOs and phi_i(r) is a RIGHT MO
+!
+! R_ip = the "ip"-th point of the DFT Grid
+ END_DOC
+ integer :: ipoint
+ !$OMP PARALLEL                  &
+ !$OMP DEFAULT (NONE)            &
+ !$OMP PRIVATE (ipoint) & 
+ !$OMP SHARED (n_points_final_grid,v_ij_erf_rk_cst_mu,mo_v_ki_bi_ortho_erf_rk_cst_mu)
+ !$OMP DO SCHEDULE (dynamic)
+! TODO :: optimization : transform into a DGEMM
+ do ipoint = 1, n_points_final_grid
+   call ao_to_mo_bi_ortho(v_ij_erf_rk_cst_mu(1,1,ipoint),size(v_ij_erf_rk_cst_mu,1),mo_v_ki_bi_ortho_erf_rk_cst_mu(1,1,ipoint),size(mo_v_ki_bi_ortho_erf_rk_cst_mu,1))
+ enddo
+ !$OMP END DO
+ !$OMP END PARALLEL
+ mo_v_ki_bi_ortho_erf_rk_cst_mu = mo_v_ki_bi_ortho_erf_rk_cst_mu * 0.5d0
+END_PROVIDER 
+
+
+BEGIN_PROVIDER [ double precision, mo_v_ki_bi_ortho_erf_rk_cst_mu_transp, ( n_points_final_grid,mo_num, mo_num)]
+ implicit none
+ BEGIN_DOC
+! int dr phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/(2|r - R|) on the BI-ORTHO MO basis
+ END_DOC
+ integer :: ipoint,i,j
+ do i = 1, mo_num
+  do j = 1, mo_num
+   do ipoint = 1, n_points_final_grid
+    mo_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,j,i) = mo_v_ki_bi_ortho_erf_rk_cst_mu(j,i,ipoint)
+   enddo
+  enddo
+ enddo
+! FREE mo_v_ki_bi_ortho_erf_rk_cst_mu
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, mo_x_v_ki_bi_ortho_erf_rk_cst_mu, ( mo_num, mo_num,3,n_points_final_grid)]
+ implicit none
+ BEGIN_DOC
+! mo_x_v_ki_bi_ortho_erf_rk_cst_mu(k,i,m,ip) = int dr x(m) * chi_k(r) phi_i(r) (erf(mu |r - R_ip|) - 1)/2|r - R_ip| on the BI-ORTHO MO basis 
+!
+! where chi_k(r)/phi_i(r) are left/right MOs, m=1 => x(m) = x, m=2 => x(m) = y, m=3 => x(m) = z,
+!
+! R_ip = the "ip"-th point of the DFT Grid
+ END_DOC
+ integer :: ipoint,m
+ !$OMP PARALLEL                  &
+ !$OMP DEFAULT (NONE)            &
+ !$OMP PRIVATE (ipoint,m) & 
+ !$OMP SHARED (n_points_final_grid,x_v_ij_erf_rk_cst_mu_transp,mo_x_v_ki_bi_ortho_erf_rk_cst_mu)
+ !$OMP DO SCHEDULE (dynamic)
+! TODO :: optimization : transform into a DGEMM
+ do ipoint = 1, n_points_final_grid
+  do m = 1, 3
+   call ao_to_mo_bi_ortho(x_v_ij_erf_rk_cst_mu_transp(1,1,m,ipoint),size(x_v_ij_erf_rk_cst_mu_transp,1),mo_x_v_ki_bi_ortho_erf_rk_cst_mu(1,1,m,ipoint),size(mo_x_v_ki_bi_ortho_erf_rk_cst_mu,1))
+  enddo
+ enddo
+ !$OMP END DO
+ !$OMP END PARALLEL
+ mo_x_v_ki_bi_ortho_erf_rk_cst_mu = 0.5d0 * mo_x_v_ki_bi_ortho_erf_rk_cst_mu
+
+END_PROVIDER 
+
+! ---
+BEGIN_PROVIDER [ double precision, mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp, (n_points_final_grid, 3, mo_num, mo_num)]
+  implicit none
+  integer :: i, j, m, ipoint
+  do i = 1, mo_num
+    do j = 1, mo_num
+      do m = 1, 3
+        do ipoint = 1, n_points_final_grid
+          mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,m,j,i) = mo_x_v_ki_bi_ortho_erf_rk_cst_mu(j,i,m,ipoint)
+        enddo
+      enddo
+    enddo
+  enddo
+END_PROVIDER 
+
+! ---
+
+
+BEGIN_PROVIDER [ double precision, x_W_ki_bi_ortho_erf_rk, (n_points_final_grid, 3, mo_num, mo_num)]
+  BEGIN_DOC
+  ! x_W_ki_bi_ortho_erf_rk(ip,m,k,i) = \int dr chi_k(r) (1 - erf(mu |r-R_ip|)) (x(m)-X(m)_ip) phi_i(r) ON THE BI-ORTHO MO BASIS 
+!
+! where chi_k(r)/phi_i(r) are left/right MOs, m=1 => X(m) = x, m=2 => X(m) = y, m=3 => X(m) = z,
+!
+! R_ip = the "ip"-th point of the DFT Grid
+  END_DOC
+ 
+  implicit none
+  include 'constants.include.F'
+ 
+  integer          :: ipoint, m, i, k
+  double precision :: xyz
+  double precision :: wall0, wall1
+ 
+  print*,'providing x_W_ki_bi_ortho_erf_rk ...'
+  call wall_time(wall0)
+
+ !$OMP PARALLEL                   &
+ !$OMP DEFAULT (NONE)             &
+ !$OMP PRIVATE (ipoint,m,i,k,xyz) & 
+ !$OMP SHARED (x_W_ki_bi_ortho_erf_rk,n_points_final_grid,mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp,mo_v_ki_bi_ortho_erf_rk_cst_mu_transp,mo_num,final_grid_points) 
+ !$OMP DO SCHEDULE (dynamic)
+  do i = 1, mo_num
+    do k = 1, mo_num
+      do m = 1, 3
+        do ipoint = 1, n_points_final_grid
+          xyz = final_grid_points(m,ipoint)
+          x_W_ki_bi_ortho_erf_rk(ipoint,m,k,i) = mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,m,k,i) - xyz * mo_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,k,i)
+        enddo
+      enddo
+    enddo
+  enddo
+
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+ ! FREE mo_v_ki_bi_ortho_erf_rk_cst_mu_transp 
+ ! FREE mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp
+
+  call wall_time(wall1)
+  print*,'time to provide x_W_ki_bi_ortho_erf_rk = ',wall1 - wall0
+
+END_PROVIDER 
+
+! ---
+
+BEGIN_PROVIDER [ double precision, x_W_ki_bi_ortho_erf_rk_diag, (n_points_final_grid, 3, mo_num)]
+  BEGIN_DOC
+  ! x_W_ki_bi_ortho_erf_rk_diag(ip,m,i) = \int dr chi_i(r) (1 - erf(mu |r-R_ip|)) (x(m)-X(m)_ip) phi_i(r) ON THE BI-ORTHO MO BASIS 
+!
+! where chi_k(r)/phi_i(r) are left/right MOs, m=1 => X(m) = x, m=2 => X(m) = y, m=3 => X(m) = z,
+!
+! R_ip = the "ip"-th point of the DFT Grid
+  END_DOC
+
+  implicit none
+  include 'constants.include.F'
+ 
+  integer          :: ipoint, m, i
+  double precision :: xyz
+  double precision :: wall0, wall1
+ 
+  print*,'providing x_W_ki_bi_ortho_erf_rk_diag ...'
+  call wall_time(wall0)
+
+ !$OMP PARALLEL                 &
+ !$OMP DEFAULT (NONE)           &
+ !$OMP PRIVATE (ipoint,m,i,xyz) & 
+ !$OMP SHARED (x_W_ki_bi_ortho_erf_rk_diag,n_points_final_grid,mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp,mo_v_ki_bi_ortho_erf_rk_cst_mu_transp,mo_num,final_grid_points) 
+ !$OMP DO SCHEDULE (dynamic)
+  do i = 1, mo_num
+    do m = 1, 3
+      do ipoint = 1, n_points_final_grid
+        xyz = final_grid_points(m,ipoint)
+        x_W_ki_bi_ortho_erf_rk_diag(ipoint,m,i) = mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,m,i,i) - xyz * mo_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,i,i)
+      enddo
+    enddo
+  enddo
+
+ !$OMP END DO
+ !$OMP END PARALLEL
+
+  call wall_time(wall1)
+  print*,'time to provide x_W_ki_bi_ortho_erf_rk_diag = ',wall1 - wall0
+
+END_PROVIDER 
+
+! ---
+