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Merge pull request #267 from QuantumPackage/dev-stable
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Dev stable
This commit is contained in:
Anthony Scemama 2023-03-21 17:53:33 +01:00 committed by GitHub
commit 6a5f25f549
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383 changed files with 76300 additions and 1457 deletions
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3
.gitignore vendored
View File

@ -5,7 +5,10 @@ build.ninja
.ninja_deps
bin/
lib/
lib64/
libexec/
config/qp_create_ninja.pickle
src/*/.gitignore
ezfio_interface.irp.f
share
*.swp

52
.travis.yml
View File

@ -1,52 +0,0 @@
#sudo: true
#before_script:
# - sudo apt-get update -q
# - sudo apt-get remove curl
# - sudo apt-get remove zlib1g-dev
# - sudo apt-get install autoconf
# - sudo rm /usr/local/bin/bats
os: linux
dist: bionic
sudo: false
compiler: gfortran
addons:
apt:
packages:
- gfortran
- gcc
- libatlas-base-dev
# - liblapack-dev
# - libblas-dev
- wget
env:
- OPAMROOT=$HOME/.opam
cache:
directories:
- $HOME/.opam/
- $HOME/cache
language: python
python:
- "3.7"
stages:
- configuration
- compilation
- testing
jobs:
include:
- stage: configuration
script: travis/configuration.sh
- stage: compilation
script: travis/compilation.sh
- stage: testing
script: travis/testing.sh

2
INSTALL.rst
View File

@ -316,7 +316,7 @@ OCaml
.. code:: bash
opam install ocamlbuild cryptokit zmq sexplib ppx_sexp_conv ppx_deriving getopt
opam install ocamlbuild zmq sexplib ppx_sexp_conv ppx_deriving getopt
Docopt

130
RELEASE_NOTES.org
View File

@ -1,5 +1,32 @@
#+TITLE: Quantum Package Release notes
* Version 2.3
** Changes
- Introduced DFT-based basis set correction
- Use OpamPack for OCaml
- Configure adapted for ARM
- Added many types of integrals
- Accelerated four-index transformation
- Added transcorrelated SCF
- Added transcorrelated CIPSI
- Added CCSD and CCSD(T)
- Added MO localization
- Changed coupling parameters for ROHF
- General Davidson algorithm
- Accelerated restore_symmetry
- Point charges in the Hamiltonian
- Removed cryptokit dependency in OCaml
- Using now standard convention in RDM
- Added molecular properties
- [ ] Added GTOs with complex exponent
*** TODO: take from dev
- Updated version of f77-zmq
- Started to introduce shells in AOs
- Added ECMD UEG functional
* Version 2.2
** Changes
@ -32,62 +59,61 @@
- Fixed bug with non-contiguous MOs in active space and deleter MOs
- Complete network-free installation
- Fixed bug in selection when computing full PT2
- Updated version of f77-zmq
*** User interface
** User interface
- Added ~qp_basis~ script to install a basis set from the ~bse~
command-line tool
- Introduced ~n_det_qp_edit~, ~psi_det_qp_edit~, and
~psi_coef_qp_edit~ to accelerate the opening of qp_edit with
large wave functions
- Removed ~etc/ninja.rc~
- Added flag to specify if the AOs are normalized
- Added flag to specify if the primitive Gaussians are normalized
- Added ~lin_dep_cutoff~, the cutoff for linear dependencies
- Davidson convergence threshold can be adapted from PT2
- In ~density_for_dft~, ~no_core_density~ is now a logical
- Default for ~weight_selection~ has changed from 2 to 1
- Nullify_small_elements in matrices to keep symmetry
- Default of density functional changed from LDA to PBE
- Added ~no_vvvv_integrals~ flag
- Added ~pt2_min_parallel_tasks~ to control parallelism in PT2
- Added ~print_energy~
- Added ~print_hamiltonian~
- Added input for two body RDM
- Added keyword ~save_wf_after_selection~
- Added a ~restore_symm~ flag to enforce the restoration of
symmetry in matrices
- qp_export_as_tgz exports also plugin codes
- Added a basis module containing basis set information
- Added qp_run truncate_wf
- Added ~qp_basis~ script to install a basis set from the ~bse~
command-line tool
- Introduced ~n_det_qp_edit~, ~psi_det_qp_edit~, and
~psi_coef_qp_edit~ to accelerate the opening of qp_edit with
large wave functions
- Removed ~etc/ninja.rc~
- Added flag to specify if the AOs are normalized
- Added flag to specify if the primitive Gaussians are normalized
- Added ~lin_dep_cutoff~, the cutoff for linear dependencies
- Davidson convergence threshold can be adapted from PT2
- In ~density_for_dft~, ~no_core_density~ is now a logical
- Default for ~weight_selection~ has changed from 2 to 1
- Nullify_small_elements in matrices to keep symmetry
- Default of density functional changed from LDA to PBE
- Added ~no_vvvv_integrals~ flag
- Added ~pt2_min_parallel_tasks~ to control parallelism in PT2
- Added ~print_energy~
- Added ~print_hamiltonian~
- Added input for two body RDM
- Added keyword ~save_wf_after_selection~
- Added a ~restore_symm~ flag to enforce the restoration of
symmetry in matrices
- qp_export_as_tgz exports also plugin codes
- Added a basis module containing basis set information
- Added qp_run truncate_wf
*** Code
** Code
- Many bug fixes
- Changed electron-nucleus from ~e_n~ to ~n_e~ in names of variables
- Changed ~occ_pattern~ to ~configuration~
- Replaced ~List.map~ by a tail-recursive version ~Qputils.list_map~
- Added possible imaginary part in OCaml MO coefficients
- Added ~qp_clean_source_files.sh~ to remove non-ascii characters
- Added flag ~is_periodic~ for periodic systems
- Possibilities to handle complex integrals and complex MOs
- Moved pseuodpotential integrals out of ~ao_one_e_integrals~
- Removed Schwarz test and added logical functions
~ao_two_e_integral_zero~ and ~ao_one_e_integral_zero~
- Introduced type for ~pt2_data~
- Banned excitations are used with far apart localized MOs
- S_z2_Sz is now included in S2
- S^2 in single precision
- Added Shank function
- Added utilities for periodic calculations
- Added ~V_ne_psi_energy~
- Added ~h_core_guess~ routine
- Fixed Laplacians in real space (indices)
- Added LIB file to add extra libs in plugin
- Using Intel IPP for sorting when using Intel compiler
- Removed parallelism in sorting
- Compute banned_excitations from exchange integrals to accelerate with local MOs
- Many bug fixes
- Changed electron-nucleus from ~e_n~ to ~n_e~ in names of variables
- Changed ~occ_pattern~ to ~configuration~
- Replaced ~List.map~ by a tail-recursive version ~Qputils.list_map~
- Added possible imaginary part in OCaml MO coefficients
- Added ~qp_clean_source_files.sh~ to remove non-ascii characters
- Added flag ~is_periodic~ for periodic systems
- Possibilities to handle complex integrals and complex MOs
- Moved pseuodpotential integrals out of ~ao_one_e_integrals~
- Removed Schwarz test and added logical functions
~ao_two_e_integral_zero~ and ~ao_one_e_integral_zero~
- Introduced type for ~pt2_data~
- Banned excitations are used with far apart localized MOs
- S_z2_Sz is now included in S2
- S^2 in single precision
- Added Shank function
- Added utilities for periodic calculations
- Added ~V_ne_psi_energy~
- Added ~h_core_guess~ routine
- Fixed Laplacians in real space (indices)
- Added LIB file to add extra libs in plugin
- Using Intel IPP for sorting when using Intel compiler
- Removed parallelism in sorting
- Compute banned_excitations from exchange integrals to accelerate with local MOs

1
bin/qp_reset
View File

@ -105,6 +105,7 @@ if [[ $mos -eq 1 ]] ; then
echo "Warning: You will need to re-define the MO classes"
fi
rm --recursive --force -- ${ezfio}/mo_basis
rm --recursive --force -- ${ezfio}/bi_ortho_mos
rm --recursive --force -- ${ezfio}/work/mo_ints_*
fi

9
bin/qp_test
View File

@ -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+
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)

66
codemeta.json Normal file
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@ -0,0 +1,66 @@
{
"@context": "https://doi.org/10.5063/schema/codemeta-2.0",
"@type": "SoftwareSourceCode",
"license": "https://spdx.org/licenses/AGPL-3.0",
"codeRepository": "https://github.com/QuantumPackage/qp2",
"dateCreated": "2014-04-01",
"datePublished": "2019-06-11",
"dateModified": "2020-02-21",
"downloadUrl": "https://github.com/QuantumPackage/qp2/releases/tag/2.1.2",
"issueTracker": "https://github.com/QuantumPackage/qp2/issues",
"name": "Quantum Package",
"version": "2.1.2",
"identifier": "https://doi.org/10.5281/zenodo.3677565",
"description": "Programming environment for wave function methods",
"applicationCategory": "Quantum Chemistry",
"funding": "ERC_863481, CoE_952165",
"developmentStatus": "active",
"referencePublication": "https://doi.org/10.1021/acs.jctc.9b00176",
"funder": {
"@type": "Organization",
"name": "CNRS"
},
"keywords": [
"selected configuration interaction",
"CIPSI"
],
"programmingLanguage": [
"Fortran",
"IRPF90",
"OCaml",
"Python",
"C"
],
"operatingSystem": [
"Linux"
],
"softwareRequirements": [
"ZeroMQ"
],
"author": [
{
"@type": "Person",
"@id": "https://orcid.org/0000-0003-4955-7136",
"givenName": "Scemama",
"familyName": "Anthony",
"email": "scemama@irsamc.ups-tlse.fr",
"affiliation": {
"@type": "Organization",
"name": "Laboratoire de chimie et physique quantiques, Toulouse, CNRS"
}
}
],
"contributor": [
{
"@type": "Person",
"givenName": "Emmanuel",
"familyName": "Giner",
"email": "eginer@lct.jussieu.fr",
"affiliation": {
"@type": "Organization",
"name": "Laboratoire de Chimie Theorique, Paris, CNRS"
}
}
]
}

4
config/bull.cfg
View File

@ -6,7 +6,7 @@
# --align=32 : Align all provided arrays on a 32-byte boundary
#
[COMMON]
FC : mpiifort -shared-libgcc -shared-intel -fpic
FC : mpiifort -fpic -xCORE-AVX2
LAPACK_LIB : -mkl=parallel
IRPF90 : irpf90
IRPF90_FLAGS : --ninja --align=32 -DMPI
@ -31,7 +31,7 @@ OPENMP : 1 ; Append OpenMP flags
# -ftz : Flushes denormal results to zero
#
[OPT]
FCFLAGS : -xCORE-AVX2 -O2 -ip -ftz -g -traceback -qopt-prefetch=5 -qopt-prefetch-issue-excl-hint -unroll-aggressive
FCFLAGS : -O2 -ip -ftz -g -traceback -qopt-prefetch=5 -qopt-prefetch-issue-excl-hint -unroll-aggressive
# Profiling flags
#################
#

68
config/cray_gfortran.cfg Normal file
View File

@ -0,0 +1,68 @@
# On LUMI
#
# export SPACK_USER_PREFIX=$HOME/spack
# module swap PrgEnv-cray/8.3.3 PrgEnv-gnu/8.3.3
# module load spack/22.08
# module load openblas/0.3.17-gcc-omp-xi
# Common flags
##############
#
# -ffree-line-length-none : Needed for IRPF90 which produces long lines
# -lblas -llapack : Link with libblas and liblapack libraries provided by the system
# -I . : Include the curent directory (Mandatory)
#
# --ninja : Allow the utilisation of ninja. (Mandatory)
# --align=32 : Align all provided arrays on a 32-byte boundary
#
#
[COMMON]
FC : gfortran -ffree-line-length-none -I . -mavx -g -fPIC
LAPACK_LIB : -L/appl/lumi/spack/22.08/0.18.1/opt/spack/openblas-0.3.17-xinceno/lib -lopenblas
IRPF90 : irpf90
IRPF90_FLAGS : --ninja --align=32 -DSET_NESTED
# Global options
################
#
# 1 : Activate
# 0 : Deactivate
#
[OPTION]
MODE : OPT ; [ OPT | PROFILE | DEBUG ] : Chooses the section below
CACHE : 0 ; Enable cache_compile.py
OPENMP : 1 ; Append OpenMP flags
# Optimization flags
####################
#
# -Ofast : Disregard strict standards compliance. Enables all -O3 optimizations.
# It also enables optimizations that are not valid
# for all standard-compliant programs. It turns on
# -ffast-math and the Fortran-specific
# -fno-protect-parens and -fstack-arrays.
[OPT]
FCFLAGS : -Ofast -march=native
# Profiling flags
#################
#
[PROFILE]
FC : -p -g
FCFLAGS : -Ofast
# Debugging flags
#################
#
# -fcheck=all : Checks uninitialized variables, array subscripts, etc...
# -g : Extra debugging information
#
[DEBUG]
FCFLAGS : -fcheck=all -g
# OpenMP flags
#################
#
[OPENMP]
FC : -fopenmp
IRPF90_FLAGS : --openmp

0
config/cray.cfg → config/cray_intel.cfg
View File

4
config/gfortran.cfg
View File

@ -10,7 +10,7 @@
#
#
[COMMON]
FC : gfortran -g -ffree-line-length-none -I . -fPIC
FC : gfortran -g -ffree-line-length-none -I . -fPIC -march=native
LAPACK_LIB : -lblas -llapack
IRPF90 : irpf90
IRPF90_FLAGS : --ninja --align=32 --assert -DSET_NESTED
@ -22,7 +22,7 @@ IRPF90_FLAGS : --ninja --align=32 --assert -DSET_NESTED
# 0 : Deactivate
#
[OPTION]
MODE : DEBUG ; [ OPT | PROFILE | DEBUG ] : Chooses the section below
MODE : OPT ; [ OPT | PROFILE | DEBUG ] : Chooses the section below
CACHE : 0 ; Enable cache_compile.py
OPENMP : 1 ; Append OpenMP flags

65
config/gfortran_armpl.cfg Normal file
View File

@ -0,0 +1,65 @@
# Common flags
##############
# module load arm
# module load gnu
# module load acfl
#
# -ffree-line-length-none : Needed for IRPF90 which produces long lines
# -lblas -llapack : Link with libblas and liblapack libraries provided by the system
# -I . : Include the curent directory (Mandatory)
#
# --ninja : Allow the utilisation of ninja. (Mandatory)
# --align=32 : Align all provided arrays on a 32-byte boundary
#
#
[COMMON]
FC : gfortran -g -ffree-line-length-none -I . -fPIC -march=native
LAPACK_LIB : -larmpl_lp64
IRPF90 : irpf90
IRPF90_FLAGS : --ninja --align=32 --assert -DSET_NESTED
# Global options
################
#
# 1 : Activate
# 0 : Deactivate
#
[OPTION]
MODE : OPT ; [ OPT | PROFILE | DEBUG ] : Chooses the section below
CACHE : 0 ; Enable cache_compile.py
OPENMP : 1 ; Append OpenMP flags
# Optimization flags
####################
#
# -Ofast : Disregard strict standards compliance. Enables all -O3 optimizations.
# It also enables optimizations that are not valid
# for all standard-compliant programs. It turns on
# -ffast-math and the Fortran-specific
# -fno-protect-parens and -fstack-arrays.
[OPT]
FCFLAGS : -Ofast
# Profiling flags
#################
#
[PROFILE]
FC : -p -g
FCFLAGS : -Ofast
# Debugging flags
#################
#
# -fcheck=all : Checks uninitialized variables, array subscripts, etc...
# -g : Extra debugging information
#
[DEBUG]
FCFLAGS : -g -march=native -fcheck=all -Waliasing -Wampersand -Wconversion -Wsurprising -Wintrinsics-std -Wno-tabs -Wintrinsic-shadow -Wline-truncation -Wreal-q-constant -Wuninitialized -fbacktrace -ffpe-trap=zero,overflow,underflow -finit-real=nan
# OpenMP flags
#################
#
[OPENMP]
FC : -fopenmp
IRPF90_FLAGS : --openmp

62
config/gfortran_openblas.cfg Normal file
View File

@ -0,0 +1,62 @@
# Common flags
##############
#
# -ffree-line-length-none : Needed for IRPF90 which produces long lines
# -lblas -llapack : Link with libblas and liblapack libraries provided by the system
# -I . : Include the curent directory (Mandatory)
#
# --ninja : Allow the utilisation of ninja. (Mandatory)
# --align=32 : Align all provided arrays on a 32-byte boundary
#
#
[COMMON]
FC : gfortran -g -ffree-line-length-none -I . -fPIC -march=native
LAPACK_LIB : -lopenblas
IRPF90 : irpf90
IRPF90_FLAGS : --ninja --align=32 --assert -DSET_NESTED
# Global options
################
#
# 1 : Activate
# 0 : Deactivate
#
[OPTION]
MODE : OPT ; [ OPT | PROFILE | DEBUG ] : Chooses the section below
CACHE : 0 ; Enable cache_compile.py
OPENMP : 1 ; Append OpenMP flags
# Optimization flags
####################
#
# -Ofast : Disregard strict standards compliance. Enables all -O3 optimizations.
# It also enables optimizations that are not valid
# for all standard-compliant programs. It turns on
# -ffast-math and the Fortran-specific
# -fno-protect-parens and -fstack-arrays.
[OPT]
FCFLAGS : -Ofast
# Profiling flags
#################
#
[PROFILE]
FC : -p -g
FCFLAGS : -Ofast
# Debugging flags
#################
#
# -fcheck=all : Checks uninitialized variables, array subscripts, etc...
# -g : Extra debugging information
#
[DEBUG]
FCFLAGS : -g -march=native -fcheck=all -Waliasing -Wampersand -Wconversion -Wsurprising -Wintrinsics-std -Wno-tabs -Wintrinsic-shadow -Wline-truncation -Wreal-q-constant -Wuninitialized -fbacktrace -ffpe-trap=zero,overflow,underflow -finit-real=nan
# OpenMP flags
#################
#
[OPENMP]
FC : -fopenmp
IRPF90_FLAGS : --openmp

2
config/ifort_2019_avx.cfg
View File

@ -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

2
config/ifort_2019_avx_mpi.cfg
View File

@ -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

66
config/ifort_2019_debug.cfg Normal file
View File

@ -0,0 +1,66 @@
# Common flags
##############
#
# -mkl=[parallel|sequential] : Use the MKL library
# --ninja : Allow the utilisation of ninja. It is mandatory !
# --align=32 : Align all provided arrays on a 32-byte boundary
#
[COMMON]
FC : ifort -fpic
LAPACK_LIB : -mkl=parallel -lirc -lsvml -limf -lipps
IRPF90 : irpf90
IRPF90_FLAGS : --ninja --align=32 --assert -DINTEL -DSET_NESTED
# Global options
################
#
# 1 : Activate
# 0 : Deactivate
#
[OPTION]
MODE : DEBUG ; [ OPT | PROFILE | DEBUG ] : Chooses the section below
CACHE : 0 ; Enable cache_compile.py
OPENMP : 1 ; Append OpenMP flags
# Optimization flags
####################
#
# -xHost : Compile a binary optimized for the current architecture
# -O2 : O3 not better than O2.
# -ip : Inter-procedural optimizations
# -ftz : Flushes denormal results to zero
#
[OPT]
FC : -traceback
FCFLAGS : -msse4.2 -O2 -ip -ftz -g
# Profiling flags
#################
#
[PROFILE]
FC : -p -g
FCFLAGS : -msse4.2 -O2 -ip -ftz
# Debugging flags
#################
#
# -traceback : Activate backtrace on runtime
# -fpe0 : All floating point exaceptions
# -C : Checks uninitialized variables, array subscripts, etc...
# -g : Extra debugging information
# -msse4.2 : Valgrind needs a very simple x86 executable
#
[DEBUG]
FC : -g -traceback
FCFLAGS : -msse4.2 -check all -debug all -fpe-all=0 -implicitnone
# OpenMP flags
#################
#
[OPENMP]
FC : -qopenmp
IRPF90_FLAGS : --openmp

2
config/ifort_2019_mpi_rome.cfg
View File

@ -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

2
config/ifort_2019_rome.cfg
View File

@ -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

2
config/ifort_2019_sse4.cfg
View File

@ -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

2
config/ifort_2019_sse4_mpi.cfg
View File

@ -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

2
config/ifort_2019_xHost.cfg
View File

@ -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

2
config/ifort_2021_avx.cfg
View File

@ -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

2
config/ifort_2021_avx_mpi.cfg
View File

@ -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

2
config/ifort_2021_mpi_rome.cfg
View File

@ -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

2
config/ifort_2021_rome.cfg
View File

@ -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

2
config/ifort_2021_sse4.cfg
View File

@ -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

2
config/ifort_2021_sse4_mpi.cfg
View File

@ -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

2
config/ifort_2021_xHost.cfg
View File

@ -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

30
configure vendored
View File

@ -19,19 +19,9 @@ git submodule update
# Update ARM or x86 dependencies
ARCHITECTURE=$(uname -m)
cd ${QP_ROOT}/external/qp2-dependencies
git checkout master
git pull
echo "Architecture: $ARCHITECTURE"
case $ARCHITECTURE in
aarch64)
git checkout arm64
;;
x86_64)
git checkout x86
;;
*)
echo "Unknown architecture. Using x86_64."
git checkout x86
;;
esac
cd ${QP_ROOT}
@ -118,7 +108,7 @@ PACKAGES=$(echo $PACKAGES | xargs)
echo "export QP_ROOT=\"$QP_ROOT\"" > ${QP_ROOT}/etc/00.qp_root.rc
source quantum_package.rc
source ${QP_ROOT}/quantum_package.rc
@ -209,7 +199,7 @@ for PACKAGE in ${PACKAGES} ; do
execute << EOF
rm -f "\${QP_ROOT}"/bin/ninja
tar -zxvf "\${QP_ROOT}"/external/qp2-dependencies/ninja.tar.gz
tar -zxvf "\${QP_ROOT}"/external/qp2-dependencies/${ARCHITECTURE}/ninja.tar.gz
mv ninja "\${QP_ROOT}"/bin/
EOF
@ -256,7 +246,7 @@ EOF
source "${QP_ROOT}"/quantum_package.rc
rm -rf "${QP_ROOT}"/external/opampack
cd "${QP_ROOT}"/external/
tar --gunzip --extract --file qp2-dependencies/opampack.tar.gz
tar --gunzip --extract --file qp2-dependencies/${ARCHITECTURE}/opampack.tar.gz
cd "${QP_ROOT}"/external/opampack
./install.sh
export OPAMROOT="${QP_ROOT}"/external/opampack/opamroot
@ -268,7 +258,7 @@ EOF
execute << EOF
cd "\${QP_ROOT}"/external
tar --gunzip --extract --file qp2-dependencies/bse-v0.8.11.tar.gz
pip install -e basis_set_exchange-*
python3 -m pip install -e basis_set_exchange-*
EOF
elif [[ ${PACKAGE} = zlib ]] ; then
@ -303,8 +293,8 @@ EOF
execute << EOF
cd "\${QP_ROOT}"/external
tar -zxf qp2-dependencies/bats-v1.1.0.tar.gz
( cd bats-core-1.1.0/ ; ./install.sh \${QP_ROOT})
tar -zxf qp2-dependencies/bats-v1.7.0.tar.gz
( cd bats-core-1.7.0/ ; ./install.sh \${QP_ROOT})
EOF
else
@ -315,7 +305,7 @@ EOF
done
source quantum_package.rc
source ${QP_ROOT}/quantum_package.rc
NINJA=$(find_exe ninja)
if [[ ${NINJA} = $(not_found) ]] ; then
@ -416,7 +406,7 @@ else
echo ""
echo "${QP_ROOT}/build.ninja does not exist,"
echo "you need to specify the COMPILATION configuration file."
echo "See ./configure --help for more details."
echo "See ./configure -h for more details."
echo ""
fi

264
data/basis/cc-pcvdz
View File

@ -991,4 +991,266 @@ D 1
1 1.3743000 1.0000000
D 1
1 0.0537000 1.00000000
$END
COPPER
S 20
1 5.430321E+06 7.801026E-06
2 8.131665E+05 6.065666E-05
3 1.850544E+05 3.188964E-04
4 5.241466E+04 1.344687E-03
5 1.709868E+04 4.869050E-03
6 6.171994E+03 1.561013E-02
7 2.406481E+03 4.452077E-02
8 9.972584E+02 1.103111E-01
9 4.339289E+02 2.220342E-01
10 1.962869E+02 3.133739E-01
11 9.104280E+01 2.315121E-01
12 4.138425E+01 7.640920E-02
13 1.993278E+01 1.103818E-01
14 9.581891E+00 1.094372E-01
15 4.234516E+00 1.836311E-02
16 1.985814E+00 -6.043084E-04
17 8.670830E-01 5.092245E-05
18 1.813390E-01 -5.540730E-05
19 8.365700E-02 3.969482E-05
20 3.626700E-02 -1.269538E-05
S 20
1 5.430321E+06 -4.404706E-06
2 8.131665E+05 -3.424801E-05
3 1.850544E+05 -1.801238E-04
4 5.241466E+04 -7.600455E-04
5 1.709868E+04 -2.759348E-03
6 6.171994E+03 -8.900970E-03
7 2.406481E+03 -2.579378E-02
8 9.972584E+02 -6.623861E-02
9 4.339289E+02 -1.445927E-01
10 1.962869E+02 -2.440110E-01
11 9.104280E+01 -2.504837E-01
12 4.138425E+01 2.852577E-02
13 1.993278E+01 5.115874E-01
14 9.581891E+00 4.928061E-01
15 4.234516E+00 8.788437E-02
16 1.985814E+00 -5.820281E-03
17 8.670830E-01 2.013508E-04
18 1.813390E-01 -5.182553E-04
19 8.365700E-02 3.731503E-04
20 3.626700E-02 -1.193171E-04
S 20
1 5.430321E+06 9.704682E-07
2 8.131665E+05 7.549245E-06
3 1.850544E+05 3.968892E-05
4 5.241466E+04 1.677200E-04
5 1.709868E+04 6.095101E-04
6 6.171994E+03 1.978846E-03
7 2.406481E+03 5.798049E-03
8 9.972584E+02 1.534158E-02
9 4.339289E+02 3.540484E-02
10 1.962869E+02 6.702098E-02
11 9.104280E+01 8.026945E-02
12 4.138425E+01 -1.927231E-02
13 1.993278E+01 -3.160129E-01
14 9.581891E+00 -4.573162E-01
15 4.234516E+00 1.550841E-01
16 1.985814E+00 7.202872E-01
17 8.670830E-01 3.885122E-01
18 1.813390E-01 1.924326E-02
19 8.365700E-02 -7.103807E-03
20 3.626700E-02 3.272906E-03
S 20
1 5.430321E+06 -1.959354E-07
2 8.131665E+05 -1.523472E-06
3 1.850544E+05 -8.014808E-06
4 5.241466E+04 -3.383992E-05
5 1.709868E+04 -1.231191E-04
6 6.171994E+03 -3.992085E-04
7 2.406481E+03 -1.171900E-03
8 9.972584E+02 -3.096141E-03
9 4.339289E+02 -7.171993E-03
10 1.962869E+02 -1.356621E-02
11 9.104280E+01 -1.643989E-02
12 4.138425E+01 4.107628E-03
13 1.993278E+01 6.693964E-02
14 9.581891E+00 1.028221E-01
15 4.234516E+00 -4.422945E-02
16 1.985814E+00 -2.031191E-01
17 8.670830E-01 -2.230022E-01
18 1.813390E-01 2.517975E-01
19 8.365700E-02 5.650091E-01
20 3.626700E-02 3.247243E-01
S 20
1 5.430321E+06 -7.508267E-07
2 8.131665E+05 -5.972018E-06
3 1.850544E+05 -3.039682E-05
4 5.241466E+04 -1.340405E-04
5 1.709868E+04 -4.615778E-04
6 6.171994E+03 -1.601064E-03
7 2.406481E+03 -4.330942E-03
8 9.972584E+02 -1.265434E-02
9 4.339289E+02 -2.586864E-02
10 1.962869E+02 -5.835428E-02
11 9.104280E+01 -5.132322E-02
12 4.138425E+01 -1.908953E-02
13 1.993278E+01 3.586116E-01
14 9.581891E+00 3.885818E-01
15 4.234516E+00 -3.057106E-01
16 1.985814E+00 -2.069896E+00
17 8.670830E-01 2.431774E+00
18 1.813390E-01 -2.121974E-02
19 8.365700E-02 -1.820251E+00
20 3.626700E-02 1.434585E+00
S 20
1 5.430321E+06 -3.532229E-07
2 8.131665E+05 -2.798812E-06
3 1.850544E+05 -1.432517E-05
4 5.241466E+04 -6.270946E-05
5 1.709868E+04 -2.179490E-04
6 6.171994E+03 -7.474316E-04
7 2.406481E+03 -2.049271E-03
8 9.972584E+02 -5.885203E-03
9 4.339289E+02 -1.226885E-02
10 1.962869E+02 -2.683147E-02
11 9.104280E+01 -2.479261E-02
12 4.138425E+01 -5.984746E-03
13 1.993278E+01 1.557124E-01
14 9.581891E+00 1.436683E-01
15 4.234516E+00 8.374103E-03
16 1.985814E+00 -7.460711E-01
17 8.670830E-01 1.244367E-01
18 1.813390E-01 1.510110E+00
19 8.365700E-02 -3.477122E-01
20 3.626700E-02 -9.774169E-01
S 1
1 3.626700E-02 1.000000E+00
S 1
1 0.0157200 1.0000000
P 16
1 2.276057E+04 4.000000E-05
2 5.387679E+03 3.610000E-04
3 1.749945E+03 2.083000E-03
4 6.696653E+02 9.197000E-03
5 2.841948E+02 3.266000E-02
6 1.296077E+02 9.379500E-02
7 6.225415E+01 2.082740E-01
8 3.092964E+01 3.339930E-01
9 1.575827E+01 3.324930E-01
10 8.094211E+00 1.547280E-01
11 4.046921E+00 2.127100E-02
12 1.967869E+00 -1.690000E-03
13 9.252950E-01 -1.516000E-03
14 3.529920E-01 -2.420000E-04
15 1.273070E-01 2.300000E-05
16 4.435600E-02 -9.000000E-06
P 16
1 2.276057E+04 -1.500000E-05
2 5.387679E+03 -1.310000E-04
3 1.749945E+03 -7.550000E-04
4 6.696653E+02 -3.359000E-03
5 2.841948E+02 -1.208100E-02
6 1.296077E+02 -3.570300E-02
7 6.225415E+01 -8.250200E-02
8 3.092964E+01 -1.398900E-01
9 1.575827E+01 -1.407290E-01
10 8.094211E+00 3.876600E-02
11 4.046921E+00 3.426950E-01
12 1.967869E+00 4.523100E-01
13 9.252950E-01 2.770540E-01
14 3.529920E-01 4.388500E-02
15 1.273070E-01 -2.802000E-03
16 4.435600E-02 1.152000E-03
P 16
1 2.276057E+04 5.000000E-06
2 5.387679E+03 4.900000E-05
3 1.749945E+03 2.780000E-04
4 6.696653E+02 1.253000E-03
5 2.841948E+02 4.447000E-03
6 1.296077E+02 1.337000E-02
7 6.225415E+01 3.046900E-02
8 3.092964E+01 5.344700E-02
9 1.575827E+01 5.263900E-02
10 8.094211E+00 -1.688100E-02
11 4.046921E+00 -1.794480E-01
12 1.967869E+00 -2.095880E-01
13 9.252950E-01 -3.963300E-02
14 3.529920E-01 5.021300E-01
15 1.273070E-01 5.811110E-01
16 4.435600E-02 4.566600E-02
P 16
1 2.276057E+04 1.100000E-05
2 5.387679E+03 9.600000E-05
3 1.749945E+03 5.900000E-04
4 6.696653E+02 2.484000E-03
5 2.841948E+02 9.463000E-03
6 1.296077E+02 2.645300E-02
7 6.225415E+01 6.568900E-02
8 3.092964E+01 1.027320E-01
9 1.575827E+01 1.370410E-01
10 8.094211E+00 -7.096100E-02
11 4.046921E+00 -5.047080E-01
12 1.967869E+00 -4.780560E-01
13 9.252950E-01 9.428920E-01
14 3.529920E-01 5.446990E-01
15 1.273070E-01 -8.327660E-01
16 4.435600E-02 -1.084160E-01
P 16
1 2.276057E+04 3.000000E-06
2 5.387679E+03 2.500000E-05
3 1.749945E+03 1.470000E-04
4 6.696653E+02 6.560000E-04
5 2.841948E+02 2.351000E-03
6 1.296077E+02 7.004000E-03
7 6.225415E+01 1.613100E-02
8 3.092964E+01 2.777000E-02
9 1.575827E+01 2.756700E-02
10 8.094211E+00 -1.011500E-02
11 4.046921E+00 -8.100900E-02
12 1.967869E+00 -1.104090E-01
13 9.252950E-01 -7.173200E-02
14 3.529920E-01 1.879300E-01
15 1.273070E-01 5.646290E-01
16 4.435600E-02 4.070000E-01
P 1
1 4.435600E-02 1.000000E+00
P 1
1 0.0154500 1.0000000
D 8
1 1.738970E+02 2.700000E-03
2 5.188690E+01 2.090900E-02
3 1.934190E+01 8.440800E-02
4 7.975720E+00 2.139990E-01
5 3.398230E+00 3.359800E-01
6 1.409320E+00 3.573010E-01
7 5.488580E-01 2.645780E-01
8 1.901990E-01 1.039720E-01
D 8
1 1.738970E+02 -3.363000E-03
2 5.188690E+01 -2.607900E-02
3 1.934190E+01 -1.082310E-01
4 7.975720E+00 -2.822170E-01
5 3.398230E+00 -3.471900E-01
6 1.409320E+00 2.671100E-02
7 5.488580E-01 4.920470E-01
8 1.901990E-01 4.384220E-01
D 8
1 1.738970E+02 4.133000E-03
2 5.188690E+01 3.308500E-02
3 1.934190E+01 1.383360E-01
4 7.975720E+00 3.901660E-01
5 3.398230E+00 1.698420E-01
6 1.409320E+00 -6.830180E-01
7 5.488580E-01 -2.657970E-01
8 1.901990E-01 8.380630E-01
D 1
1 1.901990E-01 1.000000E+00
D 1
1 0.0659100 1.0000000
F 1
1 5.082100E+00 1.000000E+00
F 1
1 1.279700E+00 1.000000E+00
F 1
1 0.4617200 1.0000000
G 1
1 3.483500E+00 1.0000000
G 1
1 1.4597900 1.0000000
$END

2
data/basis/cc-pv5z_ecp_bfd
View File

@ -555,7 +555,7 @@ g 1 1.00
g 1 1.00
1 0.457496 1.000000
MAGNESIUM
MAGNESIUM
s 9 1.00
1 0.030975 0.165290
2 0.062959 0.506272

2
external/.gitignore vendored
View File

@ -1,2 +1,2 @@
#*
*

2
external/qp2-dependencies vendored

@ -1 +1 @@
Subproject commit b8cd5815bce14c9b880e3c5ea3d5fc2652f5955c
Subproject commit ce14f57b50511825a9fedb096749200779d3f4d4

8
include/.gitignore vendored
View File

@ -1,7 +1 @@
zmq.h
gmp.h
zconf.h
zconf.h
zlib.h
zmq_utils.h
f77_zmq_free.h
*

2
ocaml/Makefile
View File

@ -43,7 +43,7 @@ $(QP_ROOT)/data/executables: remake_executables element_create_db.byte Qptypes.m
$(QP_ROOT)/ocaml/element_create_db.byte
external_libs:
opam install cryptokit sexplib
opam install sexplib
qpackage.odocl: $(MLIFILES)
ls $(MLIFILES) | sed "s/\.mli//" > qpackage.odocl

4
ocaml/To_md5.ml
View File

@ -4,8 +4,8 @@ open Sexplib
let to_md5 sexp_of_t t =
sexp_of_t t
|> Sexp.to_string
|> Cryptokit.hash_string (Cryptokit.Hash.md5 ())
|> Cryptokit.transform_string (Cryptokit.Hexa.encode ())
|> Digest.string
|> Digest.to_hex
|> MD5.of_string
;;

2
ocaml/_tags
View File

@ -1,4 +1,4 @@
true: package(cryptokit,zarith,zmq,str,sexplib,ppx_sexp_conv,ppx_deriving,getopt)
true: package(zarith,zmq,str,sexplib,ppx_sexp_conv,ppx_deriving,getopt)
true: thread
false: profile
<*byte> : linkdep(c_bindings.o), custom

3
scripts/.gitignore vendored
View File

@ -2,3 +2,6 @@
*.pyo
docopt.py
resultsFile/
verif_omp/a.out
src/*/Makefile
src/*/*/

30
scripts/compilation/qp_create_ninja
View File

@ -99,9 +99,20 @@ def ninja_create_env_variable(pwd_config_file):
l_string = ["builddir = {0}".format(os.path.dirname(ROOT_BUILD_NINJA)),
""]
for flag in ["FC", "FCFLAGS", "IRPF90", "IRPF90_FLAGS"]:
str_ = "{0} = {1}".format(flag, get_compilation_option(pwd_config_file,
flag))
for directory in [real_join(QP_SRC, m) for m in sorted(os.listdir(QP_SRC))]:
includefile = real_join(directory, flag)
try:
content = ""
with open(includefile,'r') as f:
content = f.read()
str_ += " "+content
except IOError:
pass
l_string.append(str_)
lib_lapack = get_compilation_option(pwd_config_file, "LAPACK_LIB")
@ -110,17 +121,20 @@ def ninja_create_env_variable(pwd_config_file):
str_lib = " ".join([lib_lapack, EZFIO_LIB, ZMQ_LIB, LIB, lib_usr])
# Read all LIB files in modules
libfile = "LIB"
try:
content = ""
with open(libfile,'r') as f:
content = f.read()
str_lib += " "+content
except IOError:
pass
for directory in [real_join(QP_SRC, m) for m in sorted(os.listdir(QP_SRC))]:
libfile = real_join(directory, "LIB")
try:
content = ""
with open(libfile,'r') as f:
content = f.read().replace('\n','')
str_lib += " "+content
except IOError:
pass
l_string.append("LIB = {0} ".format(str_lib))
l_string.append("CONFIG_FILE = {0}".format(pwd_config_file))
l_string.append("")
return l_string

6
scripts/ezfio_interface/ezfio_generate_provider.py
View File

@ -52,7 +52,7 @@ BEGIN_PROVIDER [ %(type)s, %(name)s %(size)s ]
%(test_null_size)s
call ezfio_has_%(ezfio_dir)s_%(ezfio_name)s(has)
if (has) then
write(6,'(A)') '.. >>>>> [ IO READ: %(name)s ] <<<<< ..'
! write(6,'(A)') '.. >>>>> [ IO READ: %(name)s ] <<<<< ..'
call ezfio_get_%(ezfio_dir)s_%(ezfio_name)s(%(name)s)
else
print *, '%(ezfio_dir)s/%(ezfio_name)s not found in EZFIO file'
@ -117,7 +117,7 @@ END_PROVIDER
output = self.output
name = self.name
l_write = ["",
" call write_time(%(output)s)",
"! call write_time(%(output)s)",
""]
self.write = "\n".join(l_write) % locals()
@ -129,7 +129,7 @@ END_PROVIDER
write = self.write_correspondance[self.type]
l_write = ["",
" call write_time(%(output)s)",
"! call write_time(%(output)s)",
" call %(write)s(%(output)s, %(name)s, &",
" '%(name)s')",
""]

7
scripts/get_fci_conv.sh Executable file
View File

@ -0,0 +1,7 @@
file=$1
grep "N_det =" $1 | cut -d "=" -f 2 > N_det_tmp
grep "E =" $file | cut -d "=" -f 2 > E_tmp
grep "E+PT2 =" $file | cut -d "=" -f 2 | cut -d "+" -f 1 > E+PT2_tmp
grep "E+rPT2 =" $file | cut -d "=" -f 2 | cut -d "+" -f 1 > E+rPT2_tmp
paste N_det_tmp E_tmp E+PT2_tmp E+rPT2_tmp | column -s ' ' -t > $file.conv_fci
rm N_det_tmp E_tmp E+PT2_tmp E+rPT2_tmp

54
scripts/qp_extract_cipsi_data.py Executable file
View File

@ -0,0 +1,54 @@
#!/usr/bin/env python3
import re
import sys
# Read output file
with open(sys.argv[1], 'r') as file:
output = file.read()
def extract_data(output):
lines = output.split("\n")
data = []
n_det = None
e = None
pt2 = None
err_pt2 = None
rpt2 = None
err_rpt2 = None
e_ex = None
reading = False
for iline, line in enumerate(lines):
if not reading and line.startswith(" N_det "):
n_det = int(re.search(r"N_det\s+=\s+(\d+)", line).group(1))
reading = True
if reading:
if line.startswith(" E "):
e = float(re.search(r"E\s+=\s+(-?\d+\.\d+)", line).group(1))
elif line.startswith(" PT2 "):
pt2 = float(re.search(r"PT2\s+=\s+(-?\d+\.\d+E?.\d*)", line).group(1))
err_pt2 = float(re.search(r"\+/-\s+(-?\d+\.\d+E?.\d*)", line).group(1))
elif line.startswith(" rPT2 "):
rpt2 = float(re.search(r"rPT2\s+=\s+(-?\d+\.\d+E?.\d*)", line).group(1))
err_rpt2 = float(re.search(r"\+/-\s+(-?\d+\.\d+E?.\d*)", line).group(1))
elif "minimum PT2 Extrapolated energy" in line:
e_ex_line = lines[iline+2]
e_ex = float(e_ex_line.split()[1])
reading = False
data.append((n_det, e, pt2, err_pt2, rpt2, err_rpt2, e_ex))
n_det = e = pt2 = err_pt2 = rpt2 = err_rpt2 = e_ex = None
return data
data = extract_data(output)
for item in data:
print(" ".join(str(x) for x in item))

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source ~/qp2/quantum_package.rc
alpha=1.8
input=O
basis=cc-pvdz
mult=3
output=${input}_${basis}_al_${alpha}
qp create_ezfio -b ${basis} ${input}.xyz -m $mult
qp run scf
qp set perturbation pt2_max 0.0001
qp set_frozen_core
########## FCI CALCULATION FOR REFERENCE
qp run fci | tee ${EZFIO_FILE}.fci.out
qp run sort_wf
mv ${EZFIO_FILE}.wf_sorted ${EZFIO_FILE}_fci.wf_sorted
########### TC SCF CALCULATION
qp reset -d
qp set ao_two_e_erf_ints mu_erf 0.87
qp set tc_keywords j1b_type 3
qp set tc_keywords j1b_pen "[${alpha}]"
qp set tc_keywords bi_ortho True
qp set tc_keywords test_cycle_tc True
qp set tc_keywords write_tc_integ True
qp set tc_keywords read_tc_integ False
qp run tc_scf | tee ${EZFIO_FILE}.tc_scf.out
qp set tc_keywords write_tc_integ False
qp set tc_keywords read_tc_integ True
############ TC-FCI CALCULATION
qp run fci_tc_bi_ortho | tee ${EZFIO_FILE}.fci_tc_bi_ortho.out
grep "Ndet,E,E+PT2,E+RPT2,|PT2|=" ${EZFIO_FILE}.fci_tc_bi_ortho.out | cut -d "=" -f 2 > data_al_$alpha
qp run sort_wf
mv ${EZFIO_FILE}.wf_sorted ${EZFIO_FILE}_tc_fci.wf_sorted

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*
!README.rst
!*/
*/*
!*/*.*
*/*.o
*/build.ninja
*/ezfio_interface.irp.f
*/.gitignore
*/*.swp

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ao_one_e_ints
ao_two_e_ints
becke_numerical_grid
mo_one_e_ints
dft_utils_in_r

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==================
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.

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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

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! ---
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
! ---
! TODO :: PUT CYCLES IN LOOPS
double precision function overlap_gauss_r12_ao(D_center, delta, i, j)
BEGIN_DOC
! \int dr AO_i(r) AO_j(r) e^{-delta |r-D_center|^2}
END_DOC
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: D_center(3), delta
integer :: power_A(3), power_B(3), l, k
double precision :: A_center(3), B_center(3), alpha, beta, coef, coef1, analytical_j
double precision, external :: overlap_gauss_r12
overlap_gauss_r12_ao = 0.d0
if(ao_overlap_abs(j,i).lt.1.d-12) then
return
endif
power_A(1:3) = ao_power(i,1:3)
power_B(1:3) = ao_power(j,1:3)
A_center(1:3) = nucl_coord(ao_nucl(i),1:3)
B_center(1:3) = nucl_coord(ao_nucl(j),1:3)
do l = 1, ao_prim_num(i)
alpha = ao_expo_ordered_transp (l,i)
coef1 = ao_coef_normalized_ordered_transp(l,i)
do k = 1, ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
coef = coef1 * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef) .lt. 1d-12) cycle
analytical_j = overlap_gauss_r12(D_center, delta, A_center, B_center, power_A, power_B, alpha, beta)
overlap_gauss_r12_ao += coef * analytical_j
enddo
enddo
end function overlap_gauss_r12_ao
! --
double precision function overlap_abs_gauss_r12_ao(D_center, delta, i, j)
BEGIN_DOC
! \int dr AO_i(r) AO_j(r) e^{-delta |r-D_center|^2}
END_DOC
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: D_center(3), delta
integer :: power_A(3), power_B(3), l, k
double precision :: A_center(3), B_center(3), alpha, beta, coef, coef1, analytical_j
double precision, external :: overlap_abs_gauss_r12
overlap_abs_gauss_r12_ao = 0.d0
if(ao_overlap_abs(j,i).lt.1.d-12) then
return
endif
power_A(1:3) = ao_power(i,1:3)
power_B(1:3) = ao_power(j,1:3)
A_center(1:3) = nucl_coord(ao_nucl(i),1:3)
B_center(1:3) = nucl_coord(ao_nucl(j),1:3)
do l = 1, ao_prim_num(i)
alpha = ao_expo_ordered_transp (l,i)
coef1 = ao_coef_normalized_ordered_transp(l,i)
do k = 1, ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
coef = coef1 * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef) .lt. 1d-12) cycle
analytical_j = overlap_abs_gauss_r12(D_center, delta, A_center, B_center, power_A, power_B, alpha, beta)
overlap_abs_gauss_r12_ao += dabs(coef * analytical_j)
enddo
enddo
end function overlap_gauss_r12_ao
! --
subroutine overlap_gauss_r12_ao_v(D_center, LD_D, delta, i, j, resv, LD_resv, n_points)
BEGIN_DOC
!
! \int dr AO_i(r) AO_j(r) e^{-delta |r-D_center|^2}
!
! n_points: nb of integrals <= min(LD_D, LD_resv)
!
END_DOC
implicit none
integer, intent(in) :: i, j, LD_D, LD_resv, n_points
double precision, intent(in) :: D_center(LD_D,3), delta
double precision, intent(out) :: resv(LD_resv)
integer :: ipoint
integer :: power_A(3), power_B(3), l, k
double precision :: A_center(3), B_center(3), alpha, beta, coef, coef1
double precision, allocatable :: analytical_j(:)
resv(:) = 0.d0
if(ao_overlap_abs(j,i) .lt. 1.d-12) then
return
endif
power_A(1:3) = ao_power(i,1:3)
power_B(1:3) = ao_power(j,1:3)
A_center(1:3) = nucl_coord(ao_nucl(i),1:3)
B_center(1:3) = nucl_coord(ao_nucl(j),1:3)
allocate(analytical_j(n_points))
do l = 1, ao_prim_num(i)
alpha = ao_expo_ordered_transp (l,i)
coef1 = ao_coef_normalized_ordered_transp(l,i)
do k = 1, ao_prim_num(j)
beta = ao_expo_ordered_transp(k,j)
coef = coef1 * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef) .lt. 1d-12) cycle
call overlap_gauss_r12_v(D_center, LD_D, delta, A_center, B_center, power_A, power_B, alpha, beta, analytical_j, n_points, n_points)
do ipoint = 1, n_points
resv(ipoint) = resv(ipoint) + coef * analytical_j(ipoint)
enddo
enddo
enddo
deallocate(analytical_j)
end subroutine overlap_gauss_r12_ao_v
! ---
double precision function overlap_gauss_r12_ao_with1s(B_center, beta, D_center, delta, i, j)
BEGIN_DOC
!
! \int dr AO_i(r) AO_j(r) e^{-beta |r-B_center^2|} e^{-delta |r-D_center|^2}
!
END_DOC
implicit none
integer, intent(in) :: i, j
double precision, intent(in) :: B_center(3), beta, D_center(3), delta
integer :: power_A1(3), power_A2(3), l, k
double precision :: A1_center(3), A2_center(3), alpha1, alpha2, coef1, coef12, analytical_j
double precision :: G_center(3), gama, fact_g, gama_inv
double precision, external :: overlap_gauss_r12, overlap_gauss_r12_ao
if(beta .lt. 1d-10) then
overlap_gauss_r12_ao_with1s = overlap_gauss_r12_ao(D_center, delta, i, j)
return
endif
overlap_gauss_r12_ao_with1s = 0.d0
if(ao_overlap_abs(j,i) .lt. 1.d-12) then
return
endif
! e^{-beta |r-B_center^2|} e^{-delta |r-D_center|^2} = fact_g e^{-gama |r - G|^2}
gama = beta + delta
gama_inv = 1.d0 / gama
G_center(1) = (beta * B_center(1) + delta * D_center(1)) * gama_inv
G_center(2) = (beta * B_center(2) + delta * D_center(2)) * gama_inv
G_center(3) = (beta * B_center(3) + delta * D_center(3)) * gama_inv
fact_g = beta * delta * gama_inv * ( (B_center(1) - D_center(1)) * (B_center(1) - D_center(1)) &
+ (B_center(2) - D_center(2)) * (B_center(2) - D_center(2)) &
+ (B_center(3) - D_center(3)) * (B_center(3) - D_center(3)) )
if(fact_g .gt. 10d0) return
fact_g = dexp(-fact_g)
! ---
power_A1(1:3) = ao_power(i,1:3)
power_A2(1:3) = ao_power(j,1:3)
A1_center(1:3) = nucl_coord(ao_nucl(i),1:3)
A2_center(1:3) = nucl_coord(ao_nucl(j),1:3)
do l = 1, ao_prim_num(i)
alpha1 = ao_expo_ordered_transp (l,i)
coef1 = fact_g * ao_coef_normalized_ordered_transp(l,i)
if(dabs(coef1) .lt. 1d-12) cycle
do k = 1, ao_prim_num(j)
alpha2 = ao_expo_ordered_transp (k,j)
coef12 = coef1 * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef12) .lt. 1d-12) cycle
analytical_j = overlap_gauss_r12(G_center, gama, A1_center, A2_center, power_A1, power_A2, alpha1, alpha2)
overlap_gauss_r12_ao_with1s += coef12 * analytical_j
enddo
enddo
end function overlap_gauss_r12_ao_with1s
! ---
subroutine overlap_gauss_r12_ao_with1s_v(B_center, beta, D_center, LD_D, delta, i, j, resv, LD_resv, n_points)
BEGIN_DOC
!
! \int dr AO_i(r) AO_j(r) e^{-beta |r-B_center^2|} e^{-delta |r-D_center|^2}
! using an array of D_centers.
!
END_DOC
implicit none
integer, intent(in) :: i, j, n_points, LD_D, LD_resv
double precision, intent(in) :: B_center(3), beta, D_center(LD_D,3), delta
double precision, intent(out) :: resv(LD_resv)
integer :: ipoint
integer :: power_A1(3), power_A2(3), l, k
double precision :: A1_center(3), A2_center(3), alpha1, alpha2, coef1
double precision :: coef12, coef12f
double precision :: gama, gama_inv
double precision :: bg, dg, bdg
double precision, allocatable :: fact_g(:), G_center(:,:), analytical_j(:)
if(ao_overlap_abs(j,i) .lt. 1.d-12) then
return
endif
ASSERT(beta .gt. 0.d0)
if(beta .lt. 1d-10) then
call overlap_gauss_r12_ao_v(D_center, LD_D, delta, i, j, resv, LD_resv, n_points)
return
endif
resv(:) = 0.d0
! e^{-beta |r-B_center^2|} e^{-delta |r-D_center|^2} = fact_g e^{-gama |r - G|^2}
gama = beta + delta
gama_inv = 1.d0 / gama
power_A1(1:3) = ao_power(i,1:3)
power_A2(1:3) = ao_power(j,1:3)
A1_center(1:3) = nucl_coord(ao_nucl(i),1:3)
A2_center(1:3) = nucl_coord(ao_nucl(j),1:3)
allocate(fact_g(n_points), G_center(n_points,3), analytical_j(n_points))
bg = beta * gama_inv
dg = delta * gama_inv
bdg = bg * delta
do ipoint = 1, n_points
G_center(ipoint,1) = bg * B_center(1) + dg * D_center(ipoint,1)
G_center(ipoint,2) = bg * B_center(2) + dg * D_center(ipoint,2)
G_center(ipoint,3) = bg * B_center(3) + dg * D_center(ipoint,3)
fact_g(ipoint) = bdg * ( (B_center(1) - D_center(ipoint,1)) * (B_center(1) - D_center(ipoint,1)) &
+ (B_center(2) - D_center(ipoint,2)) * (B_center(2) - D_center(ipoint,2)) &
+ (B_center(3) - D_center(ipoint,3)) * (B_center(3) - D_center(ipoint,3)) )
if(fact_g(ipoint) < 10d0) then
fact_g(ipoint) = dexp(-fact_g(ipoint))
else
fact_g(ipoint) = 0.d0
endif
enddo
do l = 1, ao_prim_num(i)
alpha1 = ao_expo_ordered_transp (l,i)
coef1 = ao_coef_normalized_ordered_transp(l,i)
do k = 1, ao_prim_num(j)
alpha2 = ao_expo_ordered_transp (k,j)
coef12 = coef1 * ao_coef_normalized_ordered_transp(k,j)
if(dabs(coef12) .lt. 1d-12) cycle
call overlap_gauss_r12_v(G_center, n_points, gama, A1_center, A2_center, power_A1, power_A2, alpha1, alpha2, analytical_j, n_points, n_points)
do ipoint = 1, n_points
coef12f = coef12 * fact_g(ipoint)
resv(ipoint) += coef12f * analytical_j(ipoint)
enddo
enddo
enddo
deallocate(fact_g, G_center, analytical_j)
end subroutine overlap_gauss_r12_ao_with1s_v
! ---

94
src/ao_many_one_e_ints/fit_slat_gauss.irp.f Normal file
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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

560
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! ---
BEGIN_PROVIDER [ double precision, int2_grad1u2_grad2u2_j1b2_test, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! -\frac{1}{4} x int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 [1 - erf(mu r12)]^2
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), expo_fit, coef_fit
double precision :: coef, beta, B_center(3)
double precision :: tmp
double precision :: wall0, wall1
double precision :: int_gauss, dsqpi_3_2, int_j1b
double precision :: factor_ij_1s, beta_ij, center_ij_1s(3), sq_pi_3_2
double precision, allocatable :: int_fit_v(:)
double precision, external :: overlap_gauss_r12_ao
double precision, external :: overlap_gauss_r12_ao_with1s
print*, ' providing int2_grad1u2_grad2u2_j1b2_test ...'
sq_pi_3_2 = (dacos(-1.d0))**(1.5d0)
provide mu_erf final_grid_points_transp j1b_pen List_comb_thr_b3_coef
call wall_time(wall0)
int2_grad1u2_grad2u2_j1b2_test(:,:,:) = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit_v, tmp,int_gauss,int_j1b,factor_ij_1s,beta_ij,center_ij_1s) &
!$OMP SHARED (n_points_final_grid, ao_num, final_grid_points,List_comb_thr_b3_size, &
!$OMP final_grid_points_transp, ng_fit_jast, &
!$OMP expo_gauss_1_erf_x_2, coef_gauss_1_erf_x_2, &
!$OMP List_comb_thr_b3_coef, List_comb_thr_b3_expo, &
!$OMP List_comb_thr_b3_cent, int2_grad1u2_grad2u2_j1b2_test, ao_abs_comb_b3_j1b, &
!$OMP ao_overlap_abs,sq_pi_3_2)
!$OMP DO SCHEDULE(dynamic)
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
if(ao_overlap_abs(j,i) .lt. 1.d-12) then
cycle
endif
! --- --- ---
! i_1s = 1
! --- --- ---
int_j1b = ao_abs_comb_b3_j1b(1,j,i)
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_1_erf_x_2(i_fit)
coef_fit = -0.25d0 * coef_gauss_1_erf_x_2(i_fit)
if(dabs(coef_fit*int_j1b*sq_pi_3_2*(expo_fit)**(-1.5d0)).lt.1.d-10)cycle
int_gauss = overlap_gauss_r12_ao(r, expo_fit, i, j)
int2_grad1u2_grad2u2_j1b2_test(j,i,ipoint) += coef_fit * int_gauss
enddo
! --- --- ---
! i_1s > 1
! --- --- ---
do i_1s = 2, List_comb_thr_b3_size(j,i)
coef = List_comb_thr_b3_coef (i_1s,j,i)
beta = List_comb_thr_b3_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b3_j1b(i_1s,j,i)
B_center(1) = List_comb_thr_b3_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b3_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b3_cent(3,i_1s,j,i)
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_1_erf_x_2(i_fit)
!DIR$ FORCEINLINE
call gaussian_product(expo_fit,r,beta,B_center,factor_ij_1s,beta_ij,center_ij_1s)
coef_fit = -0.25d0 * coef_gauss_1_erf_x_2(i_fit) * coef
! if(dabs(coef_fit*factor_ij_1s*int_j1b).lt.1.d-10)cycle ! old version
if(dabs(coef_fit*factor_ij_1s*int_j1b*sq_pi_3_2*(beta_ij)**(-1.5d0)).lt.1.d-10)cycle
! call overlap_gauss_r12_ao_with1s_v(B_center, beta, final_grid_points_transp, &
! expo_fit, i, j, int_fit_v, n_points_final_grid)
int_gauss = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
int2_grad1u2_grad2u2_j1b2_test(j,i,ipoint) += coef_fit * int_gauss
enddo
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
int2_grad1u2_grad2u2_j1b2_test(j,i,ipoint) = int2_grad1u2_grad2u2_j1b2_test(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_grad1u2_grad2u2_j1b2_test', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_grad1u2_grad2u2_j1b2_test_v, (ao_num, ao_num, n_points_final_grid)]
!
! BEGIN_DOC
! !
! ! -\frac{1}{4} x int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 [1 - erf(mu r12)]^2
! !
! END_DOC
!
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), expo_fit, coef_fit
double precision :: coef, beta, B_center(3)
double precision :: tmp
double precision :: wall0, wall1
double precision, allocatable :: int_fit_v(:),big_array(:,:,:)
double precision, external :: overlap_gauss_r12_ao_with1s
print*, ' providing int2_grad1u2_grad2u2_j1b2_test_v ...'
provide mu_erf final_grid_points_transp j1b_pen
call wall_time(wall0)
double precision :: int_j1b
big_array(:,:,:) = 0.d0
allocate(big_array(n_points_final_grid,ao_num, ao_num))
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center,&
!$OMP coef_fit, expo_fit, int_fit_v, tmp,int_j1b) &
!$OMP SHARED (n_points_final_grid, ao_num, List_comb_thr_b3_size,&
!$OMP final_grid_points_transp, ng_fit_jast, &
!$OMP expo_gauss_1_erf_x_2, coef_gauss_1_erf_x_2, &
!$OMP List_comb_thr_b3_coef, List_comb_thr_b3_expo, &
!$OMP List_comb_thr_b3_cent, big_array,&
!$OMP ao_abs_comb_b3_j1b,ao_overlap_abs)
!
allocate(int_fit_v(n_points_final_grid))
!$OMP DO SCHEDULE(dynamic)
do i = 1, ao_num
do j = i, ao_num
if(ao_overlap_abs(j,i) .lt. 1.d-12) then
cycle
endif
do i_1s = 1, List_comb_thr_b3_size(j,i)
coef = List_comb_thr_b3_coef (i_1s,j,i)
beta = List_comb_thr_b3_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b3_j1b(i_1s,j,i)
! if(dabs(coef)*dabs(int_j1b).lt.1.d-15)cycle
B_center(1) = List_comb_thr_b3_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b3_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b3_cent(3,i_1s,j,i)
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_1_erf_x_2(i_fit)
coef_fit = -0.25d0 * coef_gauss_1_erf_x_2(i_fit) * coef
call overlap_gauss_r12_ao_with1s_v(B_center, beta, final_grid_points_transp, size(final_grid_points_transp,1),&
expo_fit, i, j, int_fit_v, size(int_fit_v,1),n_points_final_grid)
do ipoint = 1, n_points_final_grid
big_array(ipoint,j,i) += coef_fit * int_fit_v(ipoint)
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
deallocate(int_fit_v)
!$OMP END PARALLEL
do i = 1, ao_num
do j = i, ao_num
do ipoint = 1, n_points_final_grid
int2_grad1u2_grad2u2_j1b2_test_v(j,i,ipoint) = big_array(ipoint,j,i)
enddo
enddo
enddo
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
int2_grad1u2_grad2u2_j1b2_test_v(j,i,ipoint) = big_array(ipoint,i,j)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_grad1u2_grad2u2_j1b2_test_v', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_u2_j1b2_test, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 [u_12^mu]^2
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit, expo_fit, coef_fit
double precision :: coef, beta, B_center(3), tmp
double precision :: wall0, wall1,int_j1b
double precision, external :: overlap_gauss_r12_ao
double precision, external :: overlap_gauss_r12_ao_with1s
double precision :: factor_ij_1s,beta_ij,center_ij_1s(3),sq_pi_3_2
print*, ' providing int2_u2_j1b2_test ...'
sq_pi_3_2 = (dacos(-1.d0))**(1.5d0)
provide mu_erf final_grid_points j1b_pen
call wall_time(wall0)
int2_u2_j1b2_test = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp, int_j1b,factor_ij_1s,beta_ij,center_ij_1s) &
!$OMP SHARED (n_points_final_grid, ao_num, List_comb_thr_b3_size, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_j_mu_x_2, coef_gauss_j_mu_x_2, &
!$OMP List_comb_thr_b3_coef, List_comb_thr_b3_expo,sq_pi_3_2, &
!$OMP List_comb_thr_b3_cent, int2_u2_j1b2_test,ao_abs_comb_b3_j1b)
!$OMP DO
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
tmp = 0.d0
! --- --- ---
! i_1s = 1
! --- --- ---
int_j1b = ao_abs_comb_b3_j1b(1,j,i)
if(dabs(int_j1b).lt.1.d-10) cycle
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_x_2(i_fit)
coef_fit = coef_gauss_j_mu_x_2(i_fit)
if(dabs(coef_fit*int_j1b*sq_pi_3_2*(expo_fit)**(-1.5d0)).lt.1.d-10)cycle
int_fit = overlap_gauss_r12_ao(r, expo_fit, i, j)
tmp += coef_fit * int_fit
enddo
! --- --- ---
! i_1s > 1
! --- --- ---
do i_1s = 2, List_comb_thr_b3_size(j,i)
coef = List_comb_thr_b3_coef (i_1s,j,i)
beta = List_comb_thr_b3_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b3_j1b(i_1s,j,i)
if(dabs(coef)*dabs(int_j1b).lt.1.d-10)cycle
B_center(1) = List_comb_thr_b3_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b3_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b3_cent(3,i_1s,j,i)
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_x_2(i_fit)
coef_fit = coef_gauss_j_mu_x_2(i_fit)
!DIR$ FORCEINLINE
call gaussian_product(expo_fit,r,beta,B_center,factor_ij_1s,beta_ij,center_ij_1s)
! if(dabs(coef_fit*coef*factor_ij_1s*int_j1b).lt.1.d-10)cycle ! old version
if(dabs(coef_fit*coef*factor_ij_1s*int_j1b*sq_pi_3_2*(beta_ij)**(-1.5d0)).lt.1.d-10)cycle
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
tmp += coef * coef_fit * int_fit
enddo
enddo
int2_u2_j1b2_test(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
int2_u2_j1b2_test(j,i,ipoint) = int2_u2_j1b2_test(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_u2_j1b2_test', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_u_grad1u_x_j1b2_test, (ao_num, ao_num, n_points_final_grid, 3)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 u_12^mu [\grad_1 u_12^mu] r2
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit(3), expo_fit, coef_fit
double precision :: coef, beta, B_center(3), dist
double precision :: alpha_1s, alpha_1s_inv, centr_1s(3), expo_coef_1s, coef_tmp
double precision :: tmp_x, tmp_y, tmp_z, int_j1b
double precision :: wall0, wall1, sq_pi_3_2,sq_alpha
print*, ' providing int2_u_grad1u_x_j1b2_test ...'
sq_pi_3_2 = dacos(-1.D0)**(1.d0)
provide mu_erf final_grid_points j1b_pen
call wall_time(wall0)
int2_u_grad1u_x_j1b2_test = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, alpha_1s, dist, &
!$OMP alpha_1s_inv, centr_1s, expo_coef_1s, coef_tmp, &
!$OMP tmp_x, tmp_y, tmp_z,int_j1b,sq_alpha) &
!$OMP SHARED (n_points_final_grid, ao_num, List_comb_thr_b3_size, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_j_mu_1_erf, coef_gauss_j_mu_1_erf, &
!$OMP List_comb_thr_b3_coef, List_comb_thr_b3_expo, &
!$OMP List_comb_thr_b3_cent, int2_u_grad1u_x_j1b2_test,ao_abs_comb_b3_j1b,sq_pi_3_2)
!$OMP DO
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
tmp_x = 0.d0
tmp_y = 0.d0
tmp_z = 0.d0
do i_1s = 1, List_comb_thr_b3_size(j,i)
coef = List_comb_thr_b3_coef (i_1s,j,i)
beta = List_comb_thr_b3_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b3_j1b(i_1s,j,i)
if(dabs(coef)*dabs(int_j1b).lt.1.d-10)cycle
B_center(1) = List_comb_thr_b3_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b3_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b3_cent(3,i_1s,j,i)
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_1_erf(i_fit)
coef_fit = coef_gauss_j_mu_1_erf(i_fit)
dist = (B_center(1) - r(1)) * (B_center(1) - r(1)) &
+ (B_center(2) - r(2)) * (B_center(2) - r(2)) &
+ (B_center(3) - r(3)) * (B_center(3) - r(3))
alpha_1s = beta + expo_fit
alpha_1s_inv = 1.d0 / alpha_1s
centr_1s(1) = alpha_1s_inv * (beta * B_center(1) + expo_fit * r(1))
centr_1s(2) = alpha_1s_inv * (beta * B_center(2) + expo_fit * r(2))
centr_1s(3) = alpha_1s_inv * (beta * B_center(3) + expo_fit * r(3))
expo_coef_1s = beta * expo_fit * alpha_1s_inv * dist
coef_tmp = coef * coef_fit * dexp(-expo_coef_1s)
sq_alpha = alpha_1s_inv * dsqrt(alpha_1s_inv)
! if(dabs(coef_tmp*int_j1b) .lt. 1d-10) cycle ! old version
if(dabs(coef_tmp*int_j1b*sq_pi_3_2*sq_alpha) .lt. 1d-10) cycle
call NAI_pol_x_mult_erf_ao_with1s(i, j, alpha_1s, centr_1s, 1.d+9, r, int_fit)
tmp_x += coef_tmp * int_fit(1)
tmp_y += coef_tmp * int_fit(2)
tmp_z += coef_tmp * int_fit(3)
enddo
! ---
enddo
int2_u_grad1u_x_j1b2_test(j,i,ipoint,1) = tmp_x
int2_u_grad1u_x_j1b2_test(j,i,ipoint,2) = tmp_y
int2_u_grad1u_x_j1b2_test(j,i,ipoint,3) = tmp_z
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
int2_u_grad1u_x_j1b2_test(j,i,ipoint,1) = int2_u_grad1u_x_j1b2_test(i,j,ipoint,1)
int2_u_grad1u_x_j1b2_test(j,i,ipoint,2) = int2_u_grad1u_x_j1b2_test(i,j,ipoint,2)
int2_u_grad1u_x_j1b2_test(j,i,ipoint,3) = int2_u_grad1u_x_j1b2_test(i,j,ipoint,3)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_u_grad1u_x_j1b2_test', wall1 - wall0
END_PROVIDER
BEGIN_PROVIDER [ double precision, int2_u_grad1u_j1b2_test, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 u_12^mu [\grad_1 u_12^mu]
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit, expo_fit, coef_fit, coef_tmp
double precision :: coef, beta, B_center(3), dist
double precision :: alpha_1s, alpha_1s_inv, centr_1s(3), expo_coef_1s, tmp
double precision :: wall0, wall1
double precision, external :: NAI_pol_mult_erf_ao_with1s
double precision :: j12_mu_r12,int_j1b
double precision :: sigma_ij,dist_ij_ipoint,dsqpi_3_2
double precision :: beta_ij,center_ij_1s(3),factor_ij_1s
print*, ' providing int2_u_grad1u_j1b2_test ...'
dsqpi_3_2 = (dacos(-1.d0))**(1.5d0)
provide mu_erf final_grid_points j1b_pen ao_overlap_abs List_comb_thr_b3_cent
call wall_time(wall0)
int2_u_grad1u_j1b2_test = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp, alpha_1s, dist, &
!$OMP beta_ij,center_ij_1s,factor_ij_1s, &
!$OMP int_j1b,alpha_1s_inv, centr_1s, expo_coef_1s, coef_tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_comb_thr_b3_size, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_j_mu_1_erf, coef_gauss_j_mu_1_erf, &
!$OMP ao_prod_dist_grid, ao_prod_sigma, ao_overlap_abs_grid,ao_prod_center,dsqpi_3_2, &
!$OMP List_comb_thr_b3_coef, List_comb_thr_b3_expo, ao_abs_comb_b3_j1b, &
!$OMP List_comb_thr_b3_cent, int2_u_grad1u_j1b2_test)
!$OMP DO
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
if(dabs(ao_overlap_abs_grid(j,i)).lt.1.d-10) cycle
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
tmp = 0.d0
! --- --- ---
! i_1s = 1
! --- --- ---
int_j1b = ao_abs_comb_b3_j1b(1,j,i)
if(dabs(int_j1b).lt.1.d-10) cycle
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_1_erf(i_fit)
if(dabs(int_j1b)*dsqpi_3_2*expo_fit**(-1.5d0).lt.1.d-15) cycle
coef_fit = coef_gauss_j_mu_1_erf(i_fit)
int_fit = NAI_pol_mult_erf_ao_with1s(i, j, expo_fit, r, 1.d+9, r)
tmp += coef_fit * int_fit
enddo
! --- --- ---
! i_1s > 1
! --- --- ---
do i_1s = 2, List_comb_thr_b3_size(j,i)
coef = List_comb_thr_b3_coef (i_1s,j,i)
beta = List_comb_thr_b3_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b3_j1b(i_1s,j,i)
if(dabs(coef)*dabs(int_j1b).lt.1.d-10)cycle
B_center(1) = List_comb_thr_b3_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b3_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b3_cent(3,i_1s,j,i)
dist = (B_center(1) - r(1)) * (B_center(1) - r(1)) &
+ (B_center(2) - r(2)) * (B_center(2) - r(2)) &
+ (B_center(3) - r(3)) * (B_center(3) - r(3))
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_1_erf(i_fit)
call gaussian_product(expo_fit,r,beta,B_center,factor_ij_1s,beta_ij,center_ij_1s)
if(factor_ij_1s*dabs(coef*int_j1b)*dsqpi_3_2*beta_ij**(-1.5d0).lt.1.d-15)cycle
coef_fit = coef_gauss_j_mu_1_erf(i_fit)
alpha_1s = beta + expo_fit
alpha_1s_inv = 1.d0 / alpha_1s
centr_1s(1) = alpha_1s_inv * (beta * B_center(1) + expo_fit * r(1))
centr_1s(2) = alpha_1s_inv * (beta * B_center(2) + expo_fit * r(2))
centr_1s(3) = alpha_1s_inv * (beta * B_center(3) + expo_fit * r(3))
expo_coef_1s = beta * expo_fit * alpha_1s_inv * dist
if(expo_coef_1s .gt. 20.d0) cycle
coef_tmp = coef * coef_fit * dexp(-expo_coef_1s)
if(dabs(coef_tmp) .lt. 1d-08) cycle
int_fit = NAI_pol_mult_erf_ao_with1s(i, j, alpha_1s, centr_1s, 1.d+9, r)
tmp += coef_tmp * int_fit
enddo
enddo
int2_u_grad1u_j1b2_test(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
int2_u_grad1u_j1b2_test(j,i,ipoint) = int2_u_grad1u_j1b2_test(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_u_grad1u_j1b2_test', wall1 - wall0
END_PROVIDER
! ---

420
src/ao_many_one_e_ints/grad2_jmu_modif.irp.f Normal file
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@ -0,0 +1,420 @@
! ---
BEGIN_PROVIDER [ double precision, int2_grad1u2_grad2u2_j1b2, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! -\frac{1}{4} x int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 [1 - erf(mu r12)]^2
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit, expo_fit, coef_fit
double precision :: coef, beta, B_center(3)
double precision :: tmp
double precision :: wall0, wall1
double precision, external :: overlap_gauss_r12_ao
double precision, external :: overlap_gauss_r12_ao_with1s
print*, ' providing int2_grad1u2_grad2u2_j1b2 ...'
call wall_time(wall0)
provide mu_erf final_grid_points j1b_pen
int2_grad1u2_grad2u2_j1b2 = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_1_erf_x_2, coef_gauss_1_erf_x_2, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_grad1u2_grad2u2_j1b2)
!$OMP DO
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
tmp = 0.d0
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_1_erf_x_2(i_fit)
coef_fit = coef_gauss_1_erf_x_2(i_fit)
! ---
int_fit = overlap_gauss_r12_ao(r, expo_fit, i, j)
tmp += -0.25d0 * coef_fit * int_fit
! if(dabs(coef_fit*int_fit) .lt. 1d-12) cycle
! ---
do i_1s = 2, List_all_comb_b3_size
coef = List_all_comb_b3_coef (i_1s)
beta = List_all_comb_b3_expo (i_1s)
B_center(1) = List_all_comb_b3_cent(1,i_1s)
B_center(2) = List_all_comb_b3_cent(2,i_1s)
B_center(3) = List_all_comb_b3_cent(3,i_1s)
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
tmp += -0.25d0 * coef * coef_fit * int_fit
enddo
! ---
enddo
int2_grad1u2_grad2u2_j1b2(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
int2_grad1u2_grad2u2_j1b2(j,i,ipoint) = int2_grad1u2_grad2u2_j1b2(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_grad1u2_grad2u2_j1b2 =', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_u2_j1b2, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 [u_12^mu]^2
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit, expo_fit, coef_fit
double precision :: coef, beta, B_center(3), tmp
double precision :: wall0, wall1
double precision, external :: overlap_gauss_r12_ao
double precision, external :: overlap_gauss_r12_ao_with1s
print*, ' providing int2_u2_j1b2 ...'
call wall_time(wall0)
provide mu_erf final_grid_points j1b_pen
int2_u2_j1b2 = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_j_mu_x_2, coef_gauss_j_mu_x_2, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_u2_j1b2)
!$OMP DO
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
tmp = 0.d0
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_x_2(i_fit)
coef_fit = coef_gauss_j_mu_x_2(i_fit)
! ---
int_fit = overlap_gauss_r12_ao(r, expo_fit, i, j)
tmp += coef_fit * int_fit
! if(dabs(coef_fit*int_fit) .lt. 1d-12) cycle
! ---
do i_1s = 2, List_all_comb_b3_size
coef = List_all_comb_b3_coef (i_1s)
beta = List_all_comb_b3_expo (i_1s)
B_center(1) = List_all_comb_b3_cent(1,i_1s)
B_center(2) = List_all_comb_b3_cent(2,i_1s)
B_center(3) = List_all_comb_b3_cent(3,i_1s)
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
tmp += coef * coef_fit * int_fit
enddo
! ---
enddo
int2_u2_j1b2(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
int2_u2_j1b2(j,i,ipoint) = int2_u2_j1b2(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_u2_j1b2', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_u_grad1u_x_j1b2, (ao_num, ao_num, n_points_final_grid, 3)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 u_12^mu [\grad_1 u_12^mu] r2
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit(3), expo_fit, coef_fit
double precision :: coef, beta, B_center(3), dist
double precision :: alpha_1s, alpha_1s_inv, centr_1s(3), expo_coef_1s, coef_tmp
double precision :: tmp_x, tmp_y, tmp_z
double precision :: wall0, wall1
print*, ' providing int2_u_grad1u_x_j1b2 ...'
call wall_time(wall0)
provide mu_erf final_grid_points j1b_pen
int2_u_grad1u_x_j1b2 = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, alpha_1s, dist, &
!$OMP alpha_1s_inv, centr_1s, expo_coef_1s, coef_tmp, &
!$OMP tmp_x, tmp_y, tmp_z) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_j_mu_1_erf, coef_gauss_j_mu_1_erf, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_u_grad1u_x_j1b2)
!$OMP DO
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
tmp_x = 0.d0
tmp_y = 0.d0
tmp_z = 0.d0
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_1_erf(i_fit)
coef_fit = coef_gauss_j_mu_1_erf(i_fit)
! ---
call NAI_pol_x_mult_erf_ao_with1s(i, j, expo_fit, r, 1.d+9, r, int_fit)
tmp_x += coef_fit * int_fit(1)
tmp_y += coef_fit * int_fit(2)
tmp_z += coef_fit * int_fit(3)
! if( dabs(coef_fit)*(dabs(int_fit(1)) + dabs(int_fit(2)) + dabs(int_fit(3))) .lt. 3d-10 ) cycle
! ---
do i_1s = 2, List_all_comb_b3_size
coef = List_all_comb_b3_coef (i_1s)
beta = List_all_comb_b3_expo (i_1s)
B_center(1) = List_all_comb_b3_cent(1,i_1s)
B_center(2) = List_all_comb_b3_cent(2,i_1s)
B_center(3) = List_all_comb_b3_cent(3,i_1s)
dist = (B_center(1) - r(1)) * (B_center(1) - r(1)) &
+ (B_center(2) - r(2)) * (B_center(2) - r(2)) &
+ (B_center(3) - r(3)) * (B_center(3) - r(3))
alpha_1s = beta + expo_fit
alpha_1s_inv = 1.d0 / alpha_1s
centr_1s(1) = alpha_1s_inv * (beta * B_center(1) + expo_fit * r(1))
centr_1s(2) = alpha_1s_inv * (beta * B_center(2) + expo_fit * r(2))
centr_1s(3) = alpha_1s_inv * (beta * B_center(3) + expo_fit * r(3))
expo_coef_1s = beta * expo_fit * alpha_1s_inv * dist
coef_tmp = coef * coef_fit * dexp(-expo_coef_1s)
! if(dabs(coef_tmp) .lt. 1d-12) cycle
call NAI_pol_x_mult_erf_ao_with1s(i, j, alpha_1s, centr_1s, 1.d+9, r, int_fit)
tmp_x += coef_tmp * int_fit(1)
tmp_y += coef_tmp * int_fit(2)
tmp_z += coef_tmp * int_fit(3)
enddo
! ---
enddo
int2_u_grad1u_x_j1b2(j,i,ipoint,1) = tmp_x
int2_u_grad1u_x_j1b2(j,i,ipoint,2) = tmp_y
int2_u_grad1u_x_j1b2(j,i,ipoint,3) = tmp_z
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
int2_u_grad1u_x_j1b2(j,i,ipoint,1) = int2_u_grad1u_x_j1b2(i,j,ipoint,1)
int2_u_grad1u_x_j1b2(j,i,ipoint,2) = int2_u_grad1u_x_j1b2(i,j,ipoint,2)
int2_u_grad1u_x_j1b2(j,i,ipoint,3) = int2_u_grad1u_x_j1b2(i,j,ipoint,3)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_u_grad1u_x_j1b2 = ', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_u_grad1u_j1b2, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 u_12^mu [\grad_1 u_12^mu]
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit, expo_fit, coef_fit, coef_tmp
double precision :: coef, beta, B_center(3), dist
double precision :: alpha_1s, alpha_1s_inv, centr_1s(3), expo_coef_1s, tmp
double precision :: wall0, wall1
double precision, external :: NAI_pol_mult_erf_ao_with1s
print*, ' providing int2_u_grad1u_j1b2 ...'
call wall_time(wall0)
provide mu_erf final_grid_points j1b_pen
int2_u_grad1u_j1b2 = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp, alpha_1s, dist, &
!$OMP alpha_1s_inv, centr_1s, expo_coef_1s, coef_tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_j_mu_1_erf, coef_gauss_j_mu_1_erf, &
!$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
!$OMP List_all_comb_b3_cent, int2_u_grad1u_j1b2)
!$OMP DO
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = i, ao_num
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
tmp = 0.d0
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_1_erf(i_fit)
coef_fit = coef_gauss_j_mu_1_erf(i_fit)
! ---
int_fit = NAI_pol_mult_erf_ao_with1s(i, j, expo_fit, r, 1.d+9, r)
! if(dabs(coef_fit)*dabs(int_fit) .lt. 1d-12) cycle
tmp += coef_fit * int_fit
! ---
do i_1s = 2, List_all_comb_b3_size
coef = List_all_comb_b3_coef (i_1s)
beta = List_all_comb_b3_expo (i_1s)
B_center(1) = List_all_comb_b3_cent(1,i_1s)
B_center(2) = List_all_comb_b3_cent(2,i_1s)
B_center(3) = List_all_comb_b3_cent(3,i_1s)
dist = (B_center(1) - r(1)) * (B_center(1) - r(1)) &
+ (B_center(2) - r(2)) * (B_center(2) - r(2)) &
+ (B_center(3) - r(3)) * (B_center(3) - r(3))
alpha_1s = beta + expo_fit
alpha_1s_inv = 1.d0 / alpha_1s
centr_1s(1) = alpha_1s_inv * (beta * B_center(1) + expo_fit * r(1))
centr_1s(2) = alpha_1s_inv * (beta * B_center(2) + expo_fit * r(2))
centr_1s(3) = alpha_1s_inv * (beta * B_center(3) + expo_fit * r(3))
expo_coef_1s = beta * expo_fit * alpha_1s_inv * dist
if(expo_coef_1s .gt. 80.d0) cycle
coef_tmp = coef * coef_fit * dexp(-expo_coef_1s)
if(dabs(coef_tmp) .lt. 1d-12) cycle
int_fit = NAI_pol_mult_erf_ao_with1s(i, j, alpha_1s, centr_1s, 1.d+9, r)
tmp += coef_tmp * int_fit
enddo
! ---
enddo
int2_u_grad1u_j1b2(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
int2_u_grad1u_j1b2(j,i,ipoint) = int2_u_grad1u_j1b2(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for int2_u_grad1u_j1b2', wall1 - wall0
END_PROVIDER
! ---

453
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!
!! ---
!
!BEGIN_PROVIDER [ double precision, int2_grad1u2_grad2u2_j1b2, (ao_num, ao_num, n_points_final_grid)]
!
! BEGIN_DOC
! !
! ! -\frac{1}{4} int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 [1 - erf(mu r12)]^2
! !
! END_DOC
!
! implicit none
! integer :: i, j, ipoint, i_1s, i_fit
! integer :: i_mask_grid
! double precision :: r(3), expo_fit, coef_fit
! double precision :: coef, beta, B_center(3)
! double precision :: wall0, wall1
!
! integer, allocatable :: n_mask_grid(:)
! double precision, allocatable :: r_mask_grid(:,:)
! double precision, allocatable :: int_fit_v(:)
!
! print*, ' providing int2_grad1u2_grad2u2_j1b2'
!
! provide mu_erf final_grid_points_transp j1b_pen
! call wall_time(wall0)
!
! int2_grad1u2_grad2u2_j1b2(:,:,:) = 0.d0
!
! !$OMP PARALLEL DEFAULT (NONE) &
! !$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center,&
! !$OMP coef_fit, expo_fit, int_fit_v, n_mask_grid, &
! !$OMP i_mask_grid, r_mask_grid) &
! !$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size,&
! !$OMP final_grid_points_transp, n_max_fit_slat, &
! !$OMP expo_gauss_1_erf_x_2, coef_gauss_1_erf_x_2, &
! !$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
! !$OMP List_all_comb_b3_cent, int2_grad1u2_grad2u2_j1b2, &
! !$OMP ao_overlap_abs)
!
! allocate(int_fit_v(n_points_final_grid))
! allocate(n_mask_grid(n_points_final_grid))
! allocate(r_mask_grid(n_points_final_grid,3))
!
! !$OMP DO SCHEDULE(dynamic)
! do i = 1, ao_num
! do j = i, ao_num
!
! if(ao_overlap_abs(j,i) .lt. 1.d-12) then
! cycle
! endif
!
! do i_fit = 1, n_max_fit_slat
!
! expo_fit = expo_gauss_1_erf_x_2(i_fit)
! coef_fit = coef_gauss_1_erf_x_2(i_fit) * (-0.25d0)
!
! ! ---
!
! call overlap_gauss_r12_ao_v(final_grid_points_transp, n_points_final_grid, expo_fit, i, j, int_fit_v, n_points_final_grid, n_points_final_grid)
!
! i_mask_grid = 0 ! dim
! n_mask_grid = 0 ! ind
! r_mask_grid = 0.d0 ! val
! do ipoint = 1, n_points_final_grid
!
! int2_grad1u2_grad2u2_j1b2(j,i,ipoint) += coef_fit * int_fit_v(ipoint)
!
! if(dabs(int_fit_v(ipoint)) .gt. 1d-10) then
! i_mask_grid += 1
! n_mask_grid(i_mask_grid ) = ipoint
! r_mask_grid(i_mask_grid,1) = final_grid_points_transp(ipoint,1)
! r_mask_grid(i_mask_grid,2) = final_grid_points_transp(ipoint,2)
! r_mask_grid(i_mask_grid,3) = final_grid_points_transp(ipoint,3)
! endif
!
! enddo
!
! if(i_mask_grid .eq. 0) cycle
!
! ! ---
!
! do i_1s = 2, List_all_comb_b3_size
!
! coef = List_all_comb_b3_coef (i_1s) * coef_fit
! beta = List_all_comb_b3_expo (i_1s)
! B_center(1) = List_all_comb_b3_cent(1,i_1s)
! B_center(2) = List_all_comb_b3_cent(2,i_1s)
! B_center(3) = List_all_comb_b3_cent(3,i_1s)
!
! call overlap_gauss_r12_ao_with1s_v(B_center, beta, r_mask_grid, n_points_final_grid, expo_fit, i, j, int_fit_v, n_points_final_grid, i_mask_grid)
!
! do ipoint = 1, i_mask_grid
! int2_grad1u2_grad2u2_j1b2(j,i,n_mask_grid(ipoint)) += coef * int_fit_v(ipoint)
! enddo
!
! enddo
!
! ! ---
!
! enddo
! enddo
! enddo
! !$OMP END DO
!
! deallocate(n_mask_grid)
! deallocate(r_mask_grid)
! deallocate(int_fit_v)
!
! !$OMP END PARALLEL
!
! do ipoint = 1, n_points_final_grid
! do i = 2, ao_num
! do j = 1, i-1
! int2_grad1u2_grad2u2_j1b2(j,i,ipoint) = int2_grad1u2_grad2u2_j1b2(i,j,ipoint)
! enddo
! enddo
! enddo
!
! call wall_time(wall1)
! print*, ' wall time for int2_grad1u2_grad2u2_j1b2', wall1 - wall0
!
!END_PROVIDER
!
!! ---
!
!BEGIN_PROVIDER [ double precision, int2_u2_j1b2, (ao_num, ao_num, n_points_final_grid)]
!
! BEGIN_DOC
! !
! ! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 [u_12^mu]^2
! !
! END_DOC
!
! implicit none
! integer :: i, j, ipoint, i_1s, i_fit
! integer :: i_mask_grid
! double precision :: r(3), expo_fit, coef_fit
! double precision :: coef, beta, B_center(3), tmp
! double precision :: wall0, wall1
!
! integer, allocatable :: n_mask_grid(:)
! double precision, allocatable :: r_mask_grid(:,:)
! double precision, allocatable :: int_fit_v(:)
!
! print*, ' providing int2_u2_j1b2'
!
! provide mu_erf final_grid_points_transp j1b_pen
! call wall_time(wall0)
!
! int2_u2_j1b2(:,:,:) = 0.d0
!
! !$OMP PARALLEL DEFAULT (NONE) &
! !$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
! !$OMP coef_fit, expo_fit, int_fit_v, &
! !$OMP i_mask_grid, n_mask_grid, r_mask_grid ) &
! !$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
! !$OMP final_grid_points_transp, n_max_fit_slat, &
! !$OMP expo_gauss_j_mu_x_2, coef_gauss_j_mu_x_2, &
! !$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
! !$OMP List_all_comb_b3_cent, int2_u2_j1b2)
!
! allocate(n_mask_grid(n_points_final_grid))
! allocate(r_mask_grid(n_points_final_grid,3))
! allocate(int_fit_v(n_points_final_grid))
!
! !$OMP DO SCHEDULE(dynamic)
! do i = 1, ao_num
! do j = i, ao_num
!
! do i_fit = 1, n_max_fit_slat
!
! expo_fit = expo_gauss_j_mu_x_2(i_fit)
! coef_fit = coef_gauss_j_mu_x_2(i_fit)
!
! ! ---
!
! call overlap_gauss_r12_ao_v(final_grid_points_transp, n_points_final_grid, expo_fit, i, j, int_fit_v, n_points_final_grid, n_points_final_grid)
!
! i_mask_grid = 0 ! dim
! n_mask_grid = 0 ! ind
! r_mask_grid = 0.d0 ! val
!
! do ipoint = 1, n_points_final_grid
! int2_u2_j1b2(j,i,ipoint) += coef_fit * int_fit_v(ipoint)
!
! if(dabs(int_fit_v(ipoint)) .gt. 1d-10) then
! i_mask_grid += 1
! n_mask_grid(i_mask_grid ) = ipoint
! r_mask_grid(i_mask_grid,1) = final_grid_points_transp(ipoint,1)
! r_mask_grid(i_mask_grid,2) = final_grid_points_transp(ipoint,2)
! r_mask_grid(i_mask_grid,3) = final_grid_points_transp(ipoint,3)
! endif
! enddo
!
! if(i_mask_grid .eq. 0) cycle
!
! ! ---
!
! do i_1s = 2, List_all_comb_b3_size
!
! coef = List_all_comb_b3_coef (i_1s) * coef_fit
! beta = List_all_comb_b3_expo (i_1s)
! B_center(1) = List_all_comb_b3_cent(1,i_1s)
! B_center(2) = List_all_comb_b3_cent(2,i_1s)
! B_center(3) = List_all_comb_b3_cent(3,i_1s)
!
! call overlap_gauss_r12_ao_with1s_v(B_center, beta, r_mask_grid, n_points_final_grid, expo_fit, i, j, int_fit_v, n_points_final_grid, i_mask_grid)
!
! do ipoint = 1, i_mask_grid
! int2_u2_j1b2(j,i,n_mask_grid(ipoint)) += coef * int_fit_v(ipoint)
! enddo
!
! enddo
!
! ! ---
!
! enddo
! enddo
! enddo
! !$OMP END DO
!
! deallocate(n_mask_grid)
! deallocate(r_mask_grid)
! deallocate(int_fit_v)
!
! !$OMP END PARALLEL
!
! do ipoint = 1, n_points_final_grid
! do i = 2, ao_num
! do j = 1, i-1
! int2_u2_j1b2(j,i,ipoint) = int2_u2_j1b2(i,j,ipoint)
! enddo
! enddo
! enddo
!
! call wall_time(wall1)
! print*, ' wall time for int2_u2_j1b2', wall1 - wall0
!
!END_PROVIDER
!
!! ---
!
!BEGIN_PROVIDER [ double precision, int2_u_grad1u_x_j1b2, (ao_num, ao_num, n_points_final_grid, 3)]
!
! BEGIN_DOC
! !
! ! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2)^2 u_12^mu [\grad_1 u_12^mu] r2
! !
! END_DOC
!
! implicit none
!
! integer :: i, j, ipoint, i_1s, i_fit
! integer :: i_mask_grid1, i_mask_grid2, i_mask_grid3, i_mask_grid(3)
! double precision :: x, y, z, expo_fit, coef_fit
! double precision :: coef, beta, B_center(3)
! double precision :: alpha_1s, alpha_1s_inv, expo_coef_1s
! double precision :: wall0, wall1
!
! integer, allocatable :: n_mask_grid(:,:)
! double precision, allocatable :: r_mask_grid(:,:,:)
! double precision, allocatable :: int_fit_v(:,:), dist(:,:), centr_1s(:,:,:)
!
! print*, ' providing int2_u_grad1u_x_j1b2'
!
! provide mu_erf final_grid_points_transp j1b_pen
! call wall_time(wall0)
!
! int2_u_grad1u_x_j1b2(:,:,:,:) = 0.d0
!
! !$OMP PARALLEL DEFAULT (NONE) &
! !$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, x, y, z, coef, beta, &
! !$OMP coef_fit, expo_fit, int_fit_v, alpha_1s, dist, B_center,&
! !$OMP alpha_1s_inv, centr_1s, expo_coef_1s, &
! !$OMP i_mask_grid1, i_mask_grid2, i_mask_grid3, i_mask_grid, &
! !$OMP n_mask_grid, r_mask_grid) &
! !$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b3_size, &
! !$OMP final_grid_points_transp, n_max_fit_slat, &
! !$OMP expo_gauss_j_mu_1_erf, coef_gauss_j_mu_1_erf, &
! !$OMP List_all_comb_b3_coef, List_all_comb_b3_expo, &
! !$OMP List_all_comb_b3_cent, int2_u_grad1u_x_j1b2)
!
! allocate(dist(n_points_final_grid,3))
! allocate(centr_1s(n_points_final_grid,3,3))
! allocate(n_mask_grid(n_points_final_grid,3))
! allocate(r_mask_grid(n_points_final_grid,3,3))
! allocate(int_fit_v(n_points_final_grid,3))
!
! !$OMP DO SCHEDULE(dynamic)
! do i = 1, ao_num
! do j = i, ao_num
! do i_fit = 1, n_max_fit_slat
!
! expo_fit = expo_gauss_j_mu_1_erf(i_fit)
! coef_fit = coef_gauss_j_mu_1_erf(i_fit)
!
! ! ---
!
! call NAI_pol_x_mult_erf_ao_with1s_v0(i, j, expo_fit, final_grid_points_transp, n_points_final_grid, 1.d+9, final_grid_points_transp, n_points_final_grid, int_fit_v, n_points_final_grid, n_points_final_grid)
!
! i_mask_grid1 = 0 ! dim
! i_mask_grid2 = 0 ! dim
! i_mask_grid3 = 0 ! dim
! n_mask_grid = 0 ! ind
! r_mask_grid = 0.d0 ! val
! do ipoint = 1, n_points_final_grid
!
! ! ---
!
! int2_u_grad1u_x_j1b2(j,i,ipoint,1) += coef_fit * int_fit_v(ipoint,1)
!
! if(dabs(int_fit_v(ipoint,1)) .gt. 1d-10) then
! i_mask_grid1 += 1
! n_mask_grid(i_mask_grid1, 1) = ipoint
! r_mask_grid(i_mask_grid1,1,1) = final_grid_points_transp(ipoint,1)
! r_mask_grid(i_mask_grid1,2,1) = final_grid_points_transp(ipoint,2)
! r_mask_grid(i_mask_grid1,3,1) = final_grid_points_transp(ipoint,3)
! endif
!
! ! ---
!
! int2_u_grad1u_x_j1b2(j,i,ipoint,2) += coef_fit * int_fit_v(ipoint,2)
!
! if(dabs(int_fit_v(ipoint,2)) .gt. 1d-10) then
! i_mask_grid2 += 1
! n_mask_grid(i_mask_grid2, 2) = ipoint
! r_mask_grid(i_mask_grid2,1,2) = final_grid_points_transp(ipoint,1)
! r_mask_grid(i_mask_grid2,2,2) = final_grid_points_transp(ipoint,2)
! r_mask_grid(i_mask_grid2,3,2) = final_grid_points_transp(ipoint,3)
! endif
!
! ! ---
!
! int2_u_grad1u_x_j1b2(j,i,ipoint,3) += coef_fit * int_fit_v(ipoint,3)
!
! if(dabs(int_fit_v(ipoint,3)) .gt. 1d-10) then
! i_mask_grid3 += 1
! n_mask_grid(i_mask_grid3, 3) = ipoint
! r_mask_grid(i_mask_grid3,1,3) = final_grid_points_transp(ipoint,1)
! r_mask_grid(i_mask_grid3,2,3) = final_grid_points_transp(ipoint,2)
! r_mask_grid(i_mask_grid3,3,3) = final_grid_points_transp(ipoint,3)
! endif
!
! ! ---
!
! enddo
!
! if((i_mask_grid1+i_mask_grid2+i_mask_grid3) .eq. 0) cycle
!
! i_mask_grid(1) = i_mask_grid1
! i_mask_grid(2) = i_mask_grid2
! i_mask_grid(3) = i_mask_grid3
!
! ! ---
!
! do i_1s = 2, List_all_comb_b3_size
!
! coef = List_all_comb_b3_coef (i_1s) * coef_fit
! beta = List_all_comb_b3_expo (i_1s)
! B_center(1) = List_all_comb_b3_cent(1,i_1s)
! B_center(2) = List_all_comb_b3_cent(2,i_1s)
! B_center(3) = List_all_comb_b3_cent(3,i_1s)
!
! alpha_1s = beta + expo_fit
! alpha_1s_inv = 1.d0 / alpha_1s
! expo_coef_1s = beta * expo_fit * alpha_1s_inv
!
! do ipoint = 1, i_mask_grid1
!
! x = r_mask_grid(ipoint,1,1)
! y = r_mask_grid(ipoint,2,1)
! z = r_mask_grid(ipoint,3,1)
!
! centr_1s(ipoint,1,1) = alpha_1s_inv * (beta * B_center(1) + expo_fit * x)
! centr_1s(ipoint,2,1) = alpha_1s_inv * (beta * B_center(2) + expo_fit * y)
! centr_1s(ipoint,3,1) = alpha_1s_inv * (beta * B_center(3) + expo_fit * z)
!
! dist(ipoint,1) = (B_center(1) - x) * (B_center(1) - x) + (B_center(2) - y) * (B_center(2) - y) + (B_center(3) - z) * (B_center(3) - z)
! enddo
!
! do ipoint = 1, i_mask_grid2
!
! x = r_mask_grid(ipoint,1,2)
! y = r_mask_grid(ipoint,2,2)
! z = r_mask_grid(ipoint,3,2)
!
! centr_1s(ipoint,1,2) = alpha_1s_inv * (beta * B_center(1) + expo_fit * x)
! centr_1s(ipoint,2,2) = alpha_1s_inv * (beta * B_center(2) + expo_fit * y)
! centr_1s(ipoint,3,2) = alpha_1s_inv * (beta * B_center(3) + expo_fit * z)
!
! dist(ipoint,2) = (B_center(1) - x) * (B_center(1) - x) + (B_center(2) - y) * (B_center(2) - y) + (B_center(3) - z) * (B_center(3) - z)
! enddo
!
! do ipoint = 1, i_mask_grid3
!
! x = r_mask_grid(ipoint,1,3)
! y = r_mask_grid(ipoint,2,3)
! z = r_mask_grid(ipoint,3,3)
!
! centr_1s(ipoint,1,3) = alpha_1s_inv * (beta * B_center(1) + expo_fit * x)
! centr_1s(ipoint,2,3) = alpha_1s_inv * (beta * B_center(2) + expo_fit * y)
! centr_1s(ipoint,3,3) = alpha_1s_inv * (beta * B_center(3) + expo_fit * z)
!
! dist(ipoint,3) = (B_center(1) - x) * (B_center(1) - x) + (B_center(2) - y) * (B_center(2) - y) + (B_center(3) - z) * (B_center(3) - z)
! enddo
!
! call NAI_pol_x_mult_erf_ao_with1s_v(i, j, alpha_1s, centr_1s, n_points_final_grid, 1.d+9, r_mask_grid, n_points_final_grid, int_fit_v, n_points_final_grid, i_mask_grid)
!
! do ipoint = 1, i_mask_grid1
! int2_u_grad1u_x_j1b2(j,i,n_mask_grid(ipoint,1),1) += coef * dexp(-expo_coef_1s * dist(ipoint,1)) * int_fit_v(ipoint,1)
! enddo
!
! do ipoint = 1, i_mask_grid2
! int2_u_grad1u_x_j1b2(j,i,n_mask_grid(ipoint,2),2) += coef * dexp(-expo_coef_1s * dist(ipoint,2)) * int_fit_v(ipoint,2)
! enddo
!
! do ipoint = 1, i_mask_grid3
! int2_u_grad1u_x_j1b2(j,i,n_mask_grid(ipoint,3),3) += coef * dexp(-expo_coef_1s * dist(ipoint,3)) * int_fit_v(ipoint,3)
! enddo
!
! enddo
!
! ! ---
!
! enddo
! enddo
! enddo
! !$OMP END DO
!
! deallocate(dist)
! deallocate(centr_1s)
! deallocate(n_mask_grid)
! deallocate(r_mask_grid)
! deallocate(int_fit_v)
!
! !$OMP END PARALLEL
!
! do ipoint = 1, n_points_final_grid
! do i = 2, ao_num
! do j = 1, i-1
! int2_u_grad1u_x_j1b2(j,i,ipoint,1) = int2_u_grad1u_x_j1b2(i,j,ipoint,1)
! int2_u_grad1u_x_j1b2(j,i,ipoint,2) = int2_u_grad1u_x_j1b2(i,j,ipoint,2)
! int2_u_grad1u_x_j1b2(j,i,ipoint,3) = int2_u_grad1u_x_j1b2(i,j,ipoint,3)
! enddo
! enddo
! enddo
!
! call wall_time(wall1)
! print*, ' wall time for int2_u_grad1u_x_j1b2 =', wall1 - wall0
!
!END_PROVIDER
!

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! ---
BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu_j1b_test, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr phi_i(r) phi_j(r) 1s_j1b(r) (erf(mu(R) |r - R| - 1) / |r - R|
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s
double precision :: r(3), int_mu, int_coulomb
double precision :: coef, beta, B_center(3)
double precision :: tmp,int_j1b
double precision :: wall0, wall1
double precision, external :: NAI_pol_mult_erf_ao_with1s
double precision :: sigma_ij,dist_ij_ipoint,dsqpi_3_2
print*, ' providing v_ij_erf_rk_cst_mu_j1b_test ...'
dsqpi_3_2 = (dacos(-1.d0))**(1.5d0)
provide mu_erf final_grid_points j1b_pen
call wall_time(wall0)
v_ij_erf_rk_cst_mu_j1b_test = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, r, coef, beta, B_center, int_mu, int_coulomb, tmp, int_j1b)&
!$OMP SHARED (n_points_final_grid, ao_num, List_comb_thr_b2_size, final_grid_points, &
!$OMP List_comb_thr_b2_coef, List_comb_thr_b2_expo, List_comb_thr_b2_cent,ao_abs_comb_b2_j1b, &
!$OMP v_ij_erf_rk_cst_mu_j1b_test, mu_erf, &
!$OMP ao_overlap_abs_grid,ao_prod_center,ao_prod_sigma,dsqpi_3_2)
!$OMP DO
!do ipoint = 1, 10
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
if(dabs(ao_overlap_abs_grid(j,i)).lt.1.d-20)cycle
tmp = 0.d0
do i_1s = 1, List_comb_thr_b2_size(j,i)
coef = List_comb_thr_b2_coef (i_1s,j,i)
beta = List_comb_thr_b2_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b2_j1b(i_1s,j,i)
if(dabs(coef)*dabs(int_j1b).lt.1.d-10)cycle
B_center(1) = List_comb_thr_b2_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b2_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b2_cent(3,i_1s,j,i)
! TODO :: cycle on the 1 - erf(mur12)
int_mu = NAI_pol_mult_erf_ao_with1s(i, j, beta, B_center, mu_erf, r)
int_coulomb = NAI_pol_mult_erf_ao_with1s(i, j, beta, B_center, 1.d+9, r)
tmp += coef * (int_mu - int_coulomb)
enddo
v_ij_erf_rk_cst_mu_j1b_test(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
v_ij_erf_rk_cst_mu_j1b_test(j,i,ipoint) = v_ij_erf_rk_cst_mu_j1b_test(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for v_ij_erf_rk_cst_mu_j1b_test', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_j1b_test, (ao_num, ao_num, n_points_final_grid, 3)]
BEGIN_DOC
! int dr x phi_i(r) phi_j(r) 1s_j1b(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint, i_1s
double precision :: coef, beta, B_center(3), r(3), ints(3), ints_coulomb(3)
double precision :: tmp_x, tmp_y, tmp_z
double precision :: wall0, wall1
double precision :: sigma_ij,dist_ij_ipoint,dsqpi_3_2,int_j1b,factor_ij_1s,beta_ij,center_ij_1s
print*, ' providing x_v_ij_erf_rk_cst_mu_j1b_test ...'
dsqpi_3_2 = (dacos(-1.d0))**(1.5d0)
provide expo_erfc_mu_gauss ao_prod_sigma ao_prod_center
call wall_time(wall0)
x_v_ij_erf_rk_cst_mu_j1b_test = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, r, coef, beta, B_center, ints, ints_coulomb, &
!$OMP int_j1b, tmp_x, tmp_y, tmp_z,factor_ij_1s,beta_ij,center_ij_1s) &
!$OMP SHARED (n_points_final_grid, ao_num, List_comb_thr_b2_size, final_grid_points,&
!$OMP List_comb_thr_b2_coef, List_comb_thr_b2_expo, List_comb_thr_b2_cent, &
!$OMP x_v_ij_erf_rk_cst_mu_j1b_test, mu_erf,ao_abs_comb_b2_j1b, &
!$OMP ao_overlap_abs_grid,ao_prod_center,ao_prod_sigma)
! !$OMP ao_overlap_abs_grid,ao_prod_center,ao_prod_sigma,dsqpi_3_2,expo_erfc_mu_gauss)
!$OMP DO
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
if(dabs(ao_overlap_abs_grid(j,i)).lt.1.d-10)cycle
tmp_x = 0.d0
tmp_y = 0.d0
tmp_z = 0.d0
do i_1s = 1, List_comb_thr_b2_size(j,i)
coef = List_comb_thr_b2_coef (i_1s,j,i)
beta = List_comb_thr_b2_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b2_j1b(i_1s,j,i)
if(dabs(coef)*dabs(int_j1b).lt.1.d-10)cycle
B_center(1) = List_comb_thr_b2_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b2_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b2_cent(3,i_1s,j,i)
! if(ao_prod_center(1,j,i).ne.10000.d0)then
! ! approximate 1 - erf(mu r12) by a gaussian * 10
! !DIR$ FORCEINLINE
! call gaussian_product(expo_erfc_mu_gauss,r, &
! ao_prod_sigma(j,i),ao_prod_center(1,j,i), &
! factor_ij_1s,beta_ij,center_ij_1s)
! if(dabs(coef * factor_ij_1s*int_j1b*10.d0 * dsqpi_3_2 * beta_ij**(-1.5d0)).lt.1.d-10)cycle
! endif
call NAI_pol_x_mult_erf_ao_with1s(i, j, beta, B_center, mu_erf, r, ints )
call NAI_pol_x_mult_erf_ao_with1s(i, j, beta, B_center, 1.d+9, r, ints_coulomb)
tmp_x += coef * (ints(1) - ints_coulomb(1))
tmp_y += coef * (ints(2) - ints_coulomb(2))
tmp_z += coef * (ints(3) - ints_coulomb(3))
enddo
x_v_ij_erf_rk_cst_mu_j1b_test(j,i,ipoint,1) = tmp_x
x_v_ij_erf_rk_cst_mu_j1b_test(j,i,ipoint,2) = tmp_y
x_v_ij_erf_rk_cst_mu_j1b_test(j,i,ipoint,3) = tmp_z
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
x_v_ij_erf_rk_cst_mu_j1b_test(j,i,ipoint,1) = x_v_ij_erf_rk_cst_mu_j1b_test(i,j,ipoint,1)
x_v_ij_erf_rk_cst_mu_j1b_test(j,i,ipoint,2) = x_v_ij_erf_rk_cst_mu_j1b_test(i,j,ipoint,2)
x_v_ij_erf_rk_cst_mu_j1b_test(j,i,ipoint,3) = x_v_ij_erf_rk_cst_mu_j1b_test(i,j,ipoint,3)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for x_v_ij_erf_rk_cst_mu_j1b_test', wall1 - wall0
END_PROVIDER
! ---
! TODO analytically
BEGIN_PROVIDER [ double precision, v_ij_u_cst_mu_j1b_test, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2) u(mu, r12)
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit, expo_fit, coef_fit
double precision :: coef, beta, B_center(3)
double precision :: tmp
double precision :: wall0, wall1
double precision :: beta_ij_u, factor_ij_1s_u, center_ij_1s_u(3), coeftot
double precision :: sigma_ij, dist_ij_ipoint, dsqpi_3_2, int_j1b
double precision, external :: overlap_gauss_r12_ao
double precision, external :: overlap_gauss_r12_ao_with1s
print*, ' providing v_ij_u_cst_mu_j1b_test ...'
dsqpi_3_2 = (dacos(-1.d0))**(1.5d0)
provide mu_erf final_grid_points j1b_pen
call wall_time(wall0)
v_ij_u_cst_mu_j1b_test = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP beta_ij_u, factor_ij_1s_u, center_ij_1s_u, &
!$OMP coef_fit, expo_fit, int_fit, tmp,coeftot,int_j1b) &
!$OMP SHARED (n_points_final_grid, ao_num, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_j_mu_x, coef_gauss_j_mu_x, &
!$OMP List_comb_thr_b2_coef, List_comb_thr_b2_expo,List_comb_thr_b2_size, &
!$OMP List_comb_thr_b2_cent, v_ij_u_cst_mu_j1b_test,ao_abs_comb_b2_j1b, &
!$OMP ao_overlap_abs_grid,ao_prod_center,ao_prod_sigma,dsqpi_3_2)
!$OMP DO
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
if(dabs(ao_overlap_abs_grid(j,i)).lt.1.d-20)cycle
tmp = 0.d0
! --- --- ---
! i_1s = 1
! --- --- ---
int_j1b = ao_abs_comb_b2_j1b(1,j,i)
if(dabs(int_j1b).lt.1.d-10) cycle
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_x(i_fit)
coef_fit = coef_gauss_j_mu_x(i_fit)
if(ao_overlap_abs_grid(j,i).lt.1.d-15) cycle
int_fit = overlap_gauss_r12_ao(r, expo_fit, i, j)
tmp += coef_fit * int_fit
enddo
! --- --- ---
! i_1s > 1
! --- --- ---
do i_1s = 2, List_comb_thr_b2_size(j,i)
coef = List_comb_thr_b2_coef (i_1s,j,i)
beta = List_comb_thr_b2_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b2_j1b(i_1s,j,i)
if(dabs(coef)*dabs(int_j1b).lt.1.d-10)cycle
B_center(1) = List_comb_thr_b2_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b2_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b2_cent(3,i_1s,j,i)
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_x(i_fit)
coef_fit = coef_gauss_j_mu_x(i_fit)
coeftot = coef * coef_fit
if(dabs(coeftot).lt.1.d-15)cycle
call gaussian_product(beta,B_center,expo_fit,r,factor_ij_1s_u,beta_ij_u,center_ij_1s_u)
if(factor_ij_1s_u*ao_overlap_abs_grid(j,i).lt.1.d-15)cycle
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
tmp += coef * coef_fit * int_fit
enddo
enddo
v_ij_u_cst_mu_j1b_test(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
v_ij_u_cst_mu_j1b_test(j,i,ipoint) = v_ij_u_cst_mu_j1b_test(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for v_ij_u_cst_mu_j1b_test', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, v_ij_u_cst_mu_j1b_ng_1_test, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2) u(mu, r12) with u(mu,r12) \approx 1/2 mu e^{-2.5 * mu (r12)^2}
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s
double precision :: r(3), int_fit, expo_fit, coef_fit
double precision :: coef, beta, B_center(3)
double precision :: tmp
double precision :: wall0, wall1
double precision :: beta_ij_u, factor_ij_1s_u, center_ij_1s_u(3), coeftot
double precision :: sigma_ij, dist_ij_ipoint, dsqpi_3_2, int_j1b
double precision, external :: overlap_gauss_r12_ao
double precision, external :: overlap_gauss_r12_ao_with1s
dsqpi_3_2 = (dacos(-1.d0))**(1.5d0)
provide mu_erf final_grid_points j1b_pen
call wall_time(wall0)
v_ij_u_cst_mu_j1b_ng_1_test = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, r, coef, beta, B_center, &
!$OMP beta_ij_u, factor_ij_1s_u, center_ij_1s_u, &
!$OMP coef_fit, expo_fit, int_fit, tmp,coeftot,int_j1b) &
!$OMP SHARED (n_points_final_grid, ao_num, &
!$OMP final_grid_points, expo_good_j_mu_1gauss,coef_good_j_mu_1gauss, &
!$OMP expo_gauss_j_mu_x, coef_gauss_j_mu_x, &
!$OMP List_comb_thr_b2_coef, List_comb_thr_b2_expo,List_comb_thr_b2_size, &
!$OMP List_comb_thr_b2_cent, v_ij_u_cst_mu_j1b_ng_1_test,ao_abs_comb_b2_j1b, &
!$OMP ao_overlap_abs_grid,ao_prod_center,ao_prod_sigma,dsqpi_3_2)
!$OMP DO
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
if(dabs(ao_overlap_abs_grid(j,i)).lt.1.d-20)cycle
tmp = 0.d0
! --- --- ---
! i_1s = 1
! --- --- ---
int_j1b = ao_abs_comb_b2_j1b(1,j,i)
if(dabs(int_j1b).lt.1.d-10) cycle
expo_fit = expo_good_j_mu_1gauss
int_fit = overlap_gauss_r12_ao(r, expo_fit, i, j)
tmp += int_fit
! --- --- ---
! i_1s > 1
! --- --- ---
do i_1s = 2, List_comb_thr_b2_size(j,i)
coef = List_comb_thr_b2_coef (i_1s,j,i)
beta = List_comb_thr_b2_expo (i_1s,j,i)
int_j1b = ao_abs_comb_b2_j1b(i_1s,j,i)
if(dabs(coef)*dabs(int_j1b).lt.1.d-10)cycle
B_center(1) = List_comb_thr_b2_cent(1,i_1s,j,i)
B_center(2) = List_comb_thr_b2_cent(2,i_1s,j,i)
B_center(3) = List_comb_thr_b2_cent(3,i_1s,j,i)
! do i_fit = 1, ng_fit_jast
expo_fit = expo_good_j_mu_1gauss
coef_fit = 1.d0
coeftot = coef * coef_fit
if(dabs(coeftot).lt.1.d-15)cycle
call gaussian_product(beta,B_center,expo_fit,r,factor_ij_1s_u,beta_ij_u,center_ij_1s_u)
if(factor_ij_1s_u*ao_overlap_abs_grid(j,i).lt.1.d-15)cycle
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
tmp += coef * coef_fit * int_fit
! enddo
enddo
v_ij_u_cst_mu_j1b_ng_1_test(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
v_ij_u_cst_mu_j1b_ng_1_test(j,i,ipoint) = v_ij_u_cst_mu_j1b_ng_1_test(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for v_ij_u_cst_mu_j1b_ng_1_test', wall1 - wall0
END_PROVIDER
! ---

300
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! ---
BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu_j1b, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr phi_i(r) phi_j(r) 1s_j1b(r) (erf(mu(R) |r - R| - 1) / |r - R|
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s
double precision :: r(3), int_mu, int_coulomb
double precision :: coef, beta, B_center(3)
double precision :: tmp
double precision :: wall0, wall1
double precision, external :: NAI_pol_mult_erf_ao_with1s
print *, ' providing v_ij_erf_rk_cst_mu_j1b ...'
call wall_time(wall0)
provide mu_erf final_grid_points j1b_pen
v_ij_erf_rk_cst_mu_j1b = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, r, coef, beta, B_center, int_mu, int_coulomb, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b2_size, final_grid_points, &
!$OMP List_all_comb_b2_coef, List_all_comb_b2_expo, List_all_comb_b2_cent, &
!$OMP v_ij_erf_rk_cst_mu_j1b, mu_erf)
!$OMP DO
!do ipoint = 1, 10
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
tmp = 0.d0
! ---
coef = List_all_comb_b2_coef (1)
beta = List_all_comb_b2_expo (1)
B_center(1) = List_all_comb_b2_cent(1,1)
B_center(2) = List_all_comb_b2_cent(2,1)
B_center(3) = List_all_comb_b2_cent(3,1)
int_mu = NAI_pol_mult_erf_ao_with1s(i, j, beta, B_center, mu_erf, r)
int_coulomb = NAI_pol_mult_erf_ao_with1s(i, j, beta, B_center, 1.d+9, r)
! if(dabs(coef)*dabs(int_mu - int_coulomb) .lt. 1d-12) cycle
tmp += coef * (int_mu - int_coulomb)
! ---
do i_1s = 2, List_all_comb_b2_size
coef = List_all_comb_b2_coef (i_1s)
beta = List_all_comb_b2_expo (i_1s)
B_center(1) = List_all_comb_b2_cent(1,i_1s)
B_center(2) = List_all_comb_b2_cent(2,i_1s)
B_center(3) = List_all_comb_b2_cent(3,i_1s)
int_mu = NAI_pol_mult_erf_ao_with1s(i, j, beta, B_center, mu_erf, r)
int_coulomb = NAI_pol_mult_erf_ao_with1s(i, j, beta, B_center, 1.d+9, r)
tmp += coef * (int_mu - int_coulomb)
enddo
! ---
v_ij_erf_rk_cst_mu_j1b(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
v_ij_erf_rk_cst_mu_j1b(j,i,ipoint) = v_ij_erf_rk_cst_mu_j1b(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for v_ij_erf_rk_cst_mu_j1b', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, x_v_ij_erf_rk_cst_mu_j1b, (ao_num, ao_num, n_points_final_grid, 3)]
BEGIN_DOC
! int dr x phi_i(r) phi_j(r) 1s_j1b(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint, i_1s
double precision :: coef, beta, B_center(3), r(3), ints(3), ints_coulomb(3)
double precision :: tmp_x, tmp_y, tmp_z
double precision :: wall0, wall1
print*, ' providing x_v_ij_erf_rk_cst_mu_j1b ...'
call wall_time(wall0)
x_v_ij_erf_rk_cst_mu_j1b = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, r, coef, beta, B_center, ints, ints_coulomb, &
!$OMP tmp_x, tmp_y, tmp_z) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b2_size, final_grid_points,&
!$OMP List_all_comb_b2_coef, List_all_comb_b2_expo, List_all_comb_b2_cent, &
!$OMP x_v_ij_erf_rk_cst_mu_j1b, mu_erf)
!$OMP DO
!do ipoint = 1, 10
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
tmp_x = 0.d0
tmp_y = 0.d0
tmp_z = 0.d0
! ---
coef = List_all_comb_b2_coef (1)
beta = List_all_comb_b2_expo (1)
B_center(1) = List_all_comb_b2_cent(1,1)
B_center(2) = List_all_comb_b2_cent(2,1)
B_center(3) = List_all_comb_b2_cent(3,1)
call NAI_pol_x_mult_erf_ao_with1s(i, j, beta, B_center, mu_erf, r, ints )
call NAI_pol_x_mult_erf_ao_with1s(i, j, beta, B_center, 1.d+9, r, ints_coulomb)
! if( dabs(coef)*(dabs(ints(1)-ints_coulomb(1)) + dabs(ints(2)-ints_coulomb(2)) + dabs(ints(3)-ints_coulomb(3))) .lt. 3d-10) cycle
tmp_x += coef * (ints(1) - ints_coulomb(1))
tmp_y += coef * (ints(2) - ints_coulomb(2))
tmp_z += coef * (ints(3) - ints_coulomb(3))
! ---
do i_1s = 2, List_all_comb_b2_size
coef = List_all_comb_b2_coef (i_1s)
beta = List_all_comb_b2_expo (i_1s)
B_center(1) = List_all_comb_b2_cent(1,i_1s)
B_center(2) = List_all_comb_b2_cent(2,i_1s)
B_center(3) = List_all_comb_b2_cent(3,i_1s)
call NAI_pol_x_mult_erf_ao_with1s(i, j, beta, B_center, mu_erf, r, ints )
call NAI_pol_x_mult_erf_ao_with1s(i, j, beta, B_center, 1.d+9, r, ints_coulomb)
tmp_x += coef * (ints(1) - ints_coulomb(1))
tmp_y += coef * (ints(2) - ints_coulomb(2))
tmp_z += coef * (ints(3) - ints_coulomb(3))
enddo
! ---
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,1) = tmp_x
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,2) = tmp_y
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,3) = tmp_z
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,1) = x_v_ij_erf_rk_cst_mu_j1b(i,j,ipoint,1)
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,2) = x_v_ij_erf_rk_cst_mu_j1b(i,j,ipoint,2)
x_v_ij_erf_rk_cst_mu_j1b(j,i,ipoint,3) = x_v_ij_erf_rk_cst_mu_j1b(i,j,ipoint,3)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for x_v_ij_erf_rk_cst_mu_j1b =', wall1 - wall0
END_PROVIDER
! ---
! TODO analytically
BEGIN_PROVIDER [ double precision, v_ij_u_cst_mu_j1b, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr2 phi_i(r2) phi_j(r2) 1s_j1b(r2) u(mu, r12)
!
END_DOC
implicit none
integer :: i, j, ipoint, i_1s, i_fit
double precision :: r(3), int_fit, expo_fit, coef_fit
double precision :: coef, beta, B_center(3)
double precision :: tmp
double precision :: wall0, wall1
double precision, external :: overlap_gauss_r12_ao_with1s
print*, ' providing v_ij_u_cst_mu_j1b ...'
call wall_time(wall0)
provide mu_erf final_grid_points j1b_pen
v_ij_u_cst_mu_j1b = 0.d0
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, i_1s, i_fit, r, coef, beta, B_center, &
!$OMP coef_fit, expo_fit, int_fit, tmp) &
!$OMP SHARED (n_points_final_grid, ao_num, List_all_comb_b2_size, &
!$OMP final_grid_points, ng_fit_jast, &
!$OMP expo_gauss_j_mu_x, coef_gauss_j_mu_x, &
!$OMP List_all_comb_b2_coef, List_all_comb_b2_expo, &
!$OMP List_all_comb_b2_cent, v_ij_u_cst_mu_j1b)
!$OMP DO
!do ipoint = 1, 10
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
tmp = 0.d0
do i_fit = 1, ng_fit_jast
expo_fit = expo_gauss_j_mu_x(i_fit)
coef_fit = coef_gauss_j_mu_x(i_fit)
! ---
coef = List_all_comb_b2_coef (1)
beta = List_all_comb_b2_expo (1)
B_center(1) = List_all_comb_b2_cent(1,1)
B_center(2) = List_all_comb_b2_cent(2,1)
B_center(3) = List_all_comb_b2_cent(3,1)
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
! if(dabs(int_fit*coef) .lt. 1d-12) cycle
tmp += coef * coef_fit * int_fit
! ---
do i_1s = 2, List_all_comb_b2_size
coef = List_all_comb_b2_coef (i_1s)
beta = List_all_comb_b2_expo (i_1s)
B_center(1) = List_all_comb_b2_cent(1,i_1s)
B_center(2) = List_all_comb_b2_cent(2,i_1s)
B_center(3) = List_all_comb_b2_cent(3,i_1s)
int_fit = overlap_gauss_r12_ao_with1s(B_center, beta, r, expo_fit, i, j)
tmp += coef * coef_fit * int_fit
enddo
! ---
enddo
v_ij_u_cst_mu_j1b(j,i,ipoint) = tmp
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
v_ij_u_cst_mu_j1b(j,i,ipoint) = v_ij_u_cst_mu_j1b(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for v_ij_u_cst_mu_j1b', wall1 - wall0
END_PROVIDER
! ---

437
src/ao_many_one_e_ints/grad_related_ints.irp.f Normal file
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! ---
BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu, (ao_num, ao_num, n_points_final_grid)]
BEGIN_DOC
!
! int dr phi_i(r) phi_j(r) (erf(mu(R) |r - R| - 1) / |r - R|
!
END_DOC
implicit none
integer :: i, j, ipoint
double precision :: r(3)
double precision :: int_mu, int_coulomb
double precision :: wall0, wall1
double precision :: NAI_pol_mult_erf_ao
print*, ' providing v_ij_erf_rk_cst_mu ...'
provide mu_erf final_grid_points
call wall_time(wall0)
v_ij_erf_rk_cst_mu = 0.d0
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i, j, ipoint, r, int_mu, int_coulomb) &
!$OMP SHARED (ao_num, n_points_final_grid, v_ij_erf_rk_cst_mu, final_grid_points, mu_erf)
!$OMP DO SCHEDULE (dynamic)
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
int_mu = NAI_pol_mult_erf_ao(i, j, mu_erf, r)
int_coulomb = NAI_pol_mult_erf_ao(i, j, 1.d+9, r)
v_ij_erf_rk_cst_mu(j,i,ipoint) = int_mu - int_coulomb
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
v_ij_erf_rk_cst_mu(j,i,ipoint) = v_ij_erf_rk_cst_mu(i,j,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print*, ' wall time for v_ij_erf_rk_cst_mu = ', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, v_ij_erf_rk_cst_mu_transp, (n_points_final_grid, ao_num, ao_num)]
BEGIN_DOC
! int dr phi_i(r) phi_j(r) (erf(mu(R) |r - R| - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint
double precision :: r(3)
double precision :: int_mu, int_coulomb
double precision :: wall0, wall1
double precision :: NAI_pol_mult_erf_ao
print *, ' providing v_ij_erf_rk_cst_mu_transp ...'
provide mu_erf final_grid_points
call wall_time(wall0)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,ipoint,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 ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
int_mu = NAI_pol_mult_erf_ao(i, j, mu_erf, 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 = 2, 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)]
BEGIN_DOC
! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint
double precision :: r(3), ints(3), ints_coulomb(3)
double precision :: wall0, wall1
print*, ' providing x_v_ij_erf_rk_cst_mu_tmp ...'
call wall_time(wall0)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,ipoint,r,ints,ints_coulomb) &
!$OMP SHARED (ao_num,n_points_final_grid,x_v_ij_erf_rk_cst_mu_tmp,final_grid_points,mu_erf)
!$OMP DO SCHEDULE (dynamic)
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = i, ao_num
call NAI_pol_x_mult_erf_ao(i, j, mu_erf, r, ints )
call NAI_pol_x_mult_erf_ao(i, j, 1.d+9 , r, ints_coulomb)
x_v_ij_erf_rk_cst_mu_tmp(1,j,i,ipoint) = ints(1) - ints_coulomb(1)
x_v_ij_erf_rk_cst_mu_tmp(2,j,i,ipoint) = ints(2) - ints_coulomb(2)
x_v_ij_erf_rk_cst_mu_tmp(3,j,i,ipoint) = ints(3) - ints_coulomb(3)
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do ipoint = 1, n_points_final_grid
do i = 2, ao_num
do j = 1, i-1
x_v_ij_erf_rk_cst_mu_tmp(1,j,i,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(1,i,j,ipoint)
x_v_ij_erf_rk_cst_mu_tmp(2,j,i,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(2,i,j,ipoint)
x_v_ij_erf_rk_cst_mu_tmp(3,j,i,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(3,i,j,ipoint)
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)]
BEGIN_DOC
! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint
double precision :: wall0, wall1
print *, ' providing x_v_ij_erf_rk_cst_mu ...'
call wall_time(wall0)
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, ao_num
x_v_ij_erf_rk_cst_mu(j,i,ipoint,1) = x_v_ij_erf_rk_cst_mu_tmp(1,j,i,ipoint)
x_v_ij_erf_rk_cst_mu(j,i,ipoint,2) = x_v_ij_erf_rk_cst_mu_tmp(2,j,i,ipoint)
x_v_ij_erf_rk_cst_mu(j,i,ipoint,3) = x_v_ij_erf_rk_cst_mu_tmp(3,j,i,ipoint)
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)]
BEGIN_DOC
! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint
double precision :: wall0, wall1
print *, ' providing x_v_ij_erf_rk_cst_mu_transp ...'
call wall_time(wall0)
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, ao_num
x_v_ij_erf_rk_cst_mu_transp(j,i,1,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(1,j,i,ipoint)
x_v_ij_erf_rk_cst_mu_transp(j,i,2,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(2,j,i,ipoint)
x_v_ij_erf_rk_cst_mu_transp(j,i,3,ipoint) = x_v_ij_erf_rk_cst_mu_tmp(3,j,i,ipoint)
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)]
BEGIN_DOC
! int dr x * phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/|r - R|
END_DOC
implicit none
integer :: i, j, ipoint
double precision :: wall0, wall1
print *, ' providing x_v_ij_erf_rk_cst_mu_transp_bis ...'
call wall_time(wall0)
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,1) = x_v_ij_erf_rk_cst_mu_tmp(1,j,i,ipoint)
x_v_ij_erf_rk_cst_mu_transp_bis(ipoint,j,i,2) = x_v_ij_erf_rk_cst_mu_tmp(2,j,i,ipoint)
x_v_ij_erf_rk_cst_mu_transp_bis(ipoint,j,i,3) = x_v_ij_erf_rk_cst_mu_tmp(3,j,i,ipoint)
enddo
enddo
enddo
call wall_time(wall1)
print *, ' wall time for x_v_ij_erf_rk_cst_mu_transp_bis = ', 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)]
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
implicit none
integer :: i, j, ipoint
double precision :: r(3), ints(3), ints_coulomb(3)
double precision :: wall0, wall1
print *, ' providing d_dx_v_ij_erf_rk_cst_mu_tmp ...'
call wall_time(wall0)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,ipoint,r,ints,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 ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = 1, ao_num
call phi_j_erf_mu_r_dxyz_phi(j, i, mu_erf, r, ints)
call phi_j_erf_mu_r_dxyz_phi(j, i, 1.d+9, r, ints_coulomb)
d_dx_v_ij_erf_rk_cst_mu_tmp(1,ipoint,j,i) = ints(1) - ints_coulomb(1)
d_dx_v_ij_erf_rk_cst_mu_tmp(2,ipoint,j,i) = ints(2) - ints_coulomb(2)
d_dx_v_ij_erf_rk_cst_mu_tmp(3,ipoint,j,i) = ints(3) - ints_coulomb(3)
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)]
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
implicit none
integer :: i, j, ipoint
double precision :: wall0, wall1
print *, ' providing d_dx_v_ij_erf_rk_cst_mu ...'
call wall_time(wall0)
do i = 1, ao_num
do j = 1, ao_num
do ipoint = 1, n_points_final_grid
d_dx_v_ij_erf_rk_cst_mu(ipoint,j,i,1) = d_dx_v_ij_erf_rk_cst_mu_tmp(1,ipoint,j,i)
d_dx_v_ij_erf_rk_cst_mu(ipoint,j,i,2) = d_dx_v_ij_erf_rk_cst_mu_tmp(2,ipoint,j,i)
d_dx_v_ij_erf_rk_cst_mu(ipoint,j,i,3) = d_dx_v_ij_erf_rk_cst_mu_tmp(3,ipoint,j,i)
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)]
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
implicit none
integer :: i, j, ipoint
double precision :: r(3), ints(3), ints_coulomb(3)
double precision :: wall0, wall1
print *, ' providing x_d_dx_v_ij_erf_rk_cst_mu_tmp ...'
call wall_time(wall0)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,ipoint,r,ints,ints_coulomb) &
!$OMP SHARED (ao_num,n_points_final_grid,x_d_dx_v_ij_erf_rk_cst_mu_tmp,final_grid_points,mu_erf)
!$OMP DO SCHEDULE (dynamic)
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
do i = 1, ao_num
do j = 1, ao_num
call phi_j_erf_mu_r_xyz_dxyz_phi(j, i, mu_erf, r, ints)
call phi_j_erf_mu_r_xyz_dxyz_phi(j, i, 1.d+9, r, ints_coulomb)
x_d_dx_v_ij_erf_rk_cst_mu_tmp(1,ipoint,j,i) = ints(1) - ints_coulomb(1)
x_d_dx_v_ij_erf_rk_cst_mu_tmp(2,ipoint,j,i) = ints(2) - ints_coulomb(2)
x_d_dx_v_ij_erf_rk_cst_mu_tmp(3,ipoint,j,i) = ints(3) - ints_coulomb(3)
enddo
enddo
enddo
!$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)]
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
implicit none
integer :: i, j, ipoint
double precision :: wall0, wall1
print *, ' providing x_d_dx_v_ij_erf_rk_cst_mu ...'
call wall_time(wall0)
do i = 1, ao_num
do j = 1, ao_num
do ipoint = 1, n_points_final_grid
x_d_dx_v_ij_erf_rk_cst_mu(ipoint,j,i,1) = x_d_dx_v_ij_erf_rk_cst_mu_tmp(1,ipoint,j,i)
x_d_dx_v_ij_erf_rk_cst_mu(ipoint,j,i,2) = x_d_dx_v_ij_erf_rk_cst_mu_tmp(2,ipoint,j,i)
x_d_dx_v_ij_erf_rk_cst_mu(ipoint,j,i,3) = x_d_dx_v_ij_erf_rk_cst_mu_tmp(3,ipoint,j,i)
enddo
enddo
enddo
call wall_time(wall1)
print *, ' wall time for x_d_dx_v_ij_erf_rk_cst_mu = ', wall1 - wall0
END_PROVIDER
! ---

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BEGIN_PROVIDER [ integer, n_pts_grid_ao_prod, (ao_num, ao_num)]
&BEGIN_PROVIDER [ integer, max_n_pts_grid_ao_prod]
implicit none
integer :: i,j,ipoint
double precision :: overlap, r(3),thr, overlap_abs_gauss_r12_ao,overlap_gauss_r12_ao
double precision :: sigma,dist,center_ij(3),fact_gauss, alpha, center(3)
n_pts_grid_ao_prod = 0
thr = 1.d-11
print*,' expo_good_j_mu_1gauss = ',expo_good_j_mu_1gauss
!$OMP PARALLEL DEFAULT (NONE) &
!$OMP PRIVATE (ipoint, i, j, r, overlap, fact_gauss, alpha, center,dist,sigma,center_ij) &
!$OMP SHARED (n_points_final_grid, ao_num, thr, ao_overlap_abs_grid,n_pts_grid_ao_prod,expo_good_j_mu_1gauss,&
!$OMP final_grid_points,ao_prod_center,ao_prod_sigma,ao_nucl)
!$OMP DO
do i = 1, ao_num
! do i = 3,3
do j = 1, ao_num
! do i = 22,22
! do j = 9,9
center_ij(1:3) = ao_prod_center(1:3,j,i)
sigma = ao_prod_sigma(j,i)
sigma *= sigma
sigma = 0.5d0 /sigma
! if(dabs(ao_overlap_abs_grid(j,i)).lt.1.d-10)cycle
do ipoint = 1, n_points_final_grid
r(1) = final_grid_points(1,ipoint)
r(2) = final_grid_points(2,ipoint)
r(3) = final_grid_points(3,ipoint)
dist = (center_ij(1) - r(1))*(center_ij(1) - r(1))
dist += (center_ij(2) - r(2))*(center_ij(2) - r(2))
dist += (center_ij(3) - r(3))*(center_ij(3) - r(3))
dist = dsqrt(dist)
call gaussian_product(sigma, center_ij, expo_good_j_mu_1gauss, r, fact_gauss, alpha, center)
! print*,''
! print*,j,i,ao_overlap_abs_grid(j,i),ao_overlap_abs(j,i)
! print*,r
! print*,dist,sigma
! print*,fact_gauss
if( fact_gauss*ao_overlap_abs_grid(j,i).lt.1.d-11)cycle
if(ao_nucl(i) == ao_nucl(j))then
overlap = overlap_abs_gauss_r12_ao(r, expo_good_j_mu_1gauss, i, j)
else
overlap = overlap_gauss_r12_ao(r, expo_good_j_mu_1gauss, i, j)
endif
! print*,overlap
if(dabs(overlap).lt.thr)cycle
n_pts_grid_ao_prod(j,i) += 1
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
integer :: list(ao_num)
do i = 1, ao_num
list(i) = maxval(n_pts_grid_ao_prod(:,i))
enddo
max_n_pts_grid_ao_prod = maxval(list)
END_PROVIDER

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! ---
BEGIN_PROVIDER [ integer, List_all_comb_b2_size]
implicit none
List_all_comb_b2_size = 2**nucl_num
END_PROVIDER
! ---
BEGIN_PROVIDER [ integer, List_all_comb_b2, (nucl_num, List_all_comb_b2_size)]
implicit none
integer :: i, j
if(nucl_num .gt. 32) then
print *, ' nucl_num = ', nucl_num, '> 32'
stop
endif
List_all_comb_b2 = 0
do i = 0, List_all_comb_b2_size-1
do j = 0, nucl_num-1
if (btest(i,j)) then
List_all_comb_b2(j+1,i+1) = 1
endif
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, List_all_comb_b2_coef, ( List_all_comb_b2_size)]
&BEGIN_PROVIDER [ double precision, List_all_comb_b2_expo, ( List_all_comb_b2_size)]
&BEGIN_PROVIDER [ double precision, List_all_comb_b2_cent, (3, List_all_comb_b2_size)]
implicit none
integer :: i, j, k, phase
double precision :: tmp_alphaj, tmp_alphak
double precision :: tmp_cent_x, tmp_cent_y, tmp_cent_z
provide j1b_pen
List_all_comb_b2_coef = 0.d0
List_all_comb_b2_expo = 0.d0
List_all_comb_b2_cent = 0.d0
do i = 1, List_all_comb_b2_size
tmp_cent_x = 0.d0
tmp_cent_y = 0.d0
tmp_cent_z = 0.d0
do j = 1, nucl_num
tmp_alphaj = dble(List_all_comb_b2(j,i)) * j1b_pen(j)
List_all_comb_b2_expo(i) += tmp_alphaj
tmp_cent_x += tmp_alphaj * nucl_coord(j,1)
tmp_cent_y += tmp_alphaj * nucl_coord(j,2)
tmp_cent_z += tmp_alphaj * nucl_coord(j,3)
enddo
if(List_all_comb_b2_expo(i) .lt. 1d-10) cycle
List_all_comb_b2_cent(1,i) = tmp_cent_x / List_all_comb_b2_expo(i)
List_all_comb_b2_cent(2,i) = tmp_cent_y / List_all_comb_b2_expo(i)
List_all_comb_b2_cent(3,i) = tmp_cent_z / List_all_comb_b2_expo(i)
enddo
! ---
do i = 1, List_all_comb_b2_size
do j = 2, nucl_num, 1
tmp_alphaj = dble(List_all_comb_b2(j,i)) * j1b_pen(j)
do k = 1, j-1, 1
tmp_alphak = dble(List_all_comb_b2(k,i)) * j1b_pen(k)
List_all_comb_b2_coef(i) += tmp_alphaj * tmp_alphak * ( (nucl_coord(j,1) - nucl_coord(k,1)) * (nucl_coord(j,1) - nucl_coord(k,1)) &
+ (nucl_coord(j,2) - nucl_coord(k,2)) * (nucl_coord(j,2) - nucl_coord(k,2)) &
+ (nucl_coord(j,3) - nucl_coord(k,3)) * (nucl_coord(j,3) - nucl_coord(k,3)) )
enddo
enddo
if(List_all_comb_b2_expo(i) .lt. 1d-10) cycle
List_all_comb_b2_coef(i) = List_all_comb_b2_coef(i) / List_all_comb_b2_expo(i)
enddo
! ---
do i = 1, List_all_comb_b2_size
phase = 0
do j = 1, nucl_num
phase += List_all_comb_b2(j,i)
enddo
List_all_comb_b2_coef(i) = (-1.d0)**dble(phase) * dexp(-List_all_comb_b2_coef(i))
enddo
!print *, ' coeff, expo & cent of list b2'
!do i = 1, List_all_comb_b2_size
! print*, i, List_all_comb_b2_coef(i), List_all_comb_b2_expo(i)
! print*, List_all_comb_b2_cent(1,i), List_all_comb_b2_cent(2,i), List_all_comb_b2_cent(3,i)
!enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ integer, List_all_comb_b3_size]
implicit none
List_all_comb_b3_size = 3**nucl_num
END_PROVIDER
! ---
BEGIN_PROVIDER [ integer, List_all_comb_b3, (nucl_num, List_all_comb_b3_size)]
implicit none
integer :: i, j, ii, jj
integer, allocatable :: M(:,:), p(:)
if(nucl_num .gt. 32) then
print *, ' nucl_num = ', nucl_num, '> 32'
stop
endif
List_all_comb_b3(:,:) = 0
List_all_comb_b3(:,List_all_comb_b3_size) = 2
allocate(p(nucl_num))
p = 0
do i = 2, List_all_comb_b3_size-1
do j = 1, nucl_num
ii = 0
do jj = 1, j-1, 1
ii = ii + p(jj) * 3**(jj-1)
enddo
p(j) = modulo(i-1-ii, 3**j) / 3**(j-1)
List_all_comb_b3(j,i) = p(j)
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, List_all_comb_b3_coef, ( List_all_comb_b3_size)]
&BEGIN_PROVIDER [ double precision, List_all_comb_b3_expo, ( List_all_comb_b3_size)]
&BEGIN_PROVIDER [ double precision, List_all_comb_b3_cent, (3, List_all_comb_b3_size)]
implicit none
integer :: i, j, k, phase
double precision :: tmp_alphaj, tmp_alphak, facto
provide j1b_pen
List_all_comb_b3_coef = 0.d0
List_all_comb_b3_expo = 0.d0
List_all_comb_b3_cent = 0.d0
do i = 1, List_all_comb_b3_size
do j = 1, nucl_num
tmp_alphaj = dble(List_all_comb_b3(j,i)) * j1b_pen(j)
List_all_comb_b3_expo(i) += tmp_alphaj
List_all_comb_b3_cent(1,i) += tmp_alphaj * nucl_coord(j,1)
List_all_comb_b3_cent(2,i) += tmp_alphaj * nucl_coord(j,2)
List_all_comb_b3_cent(3,i) += tmp_alphaj * nucl_coord(j,3)
enddo
if(List_all_comb_b3_expo(i) .lt. 1d-10) cycle
ASSERT(List_all_comb_b3_expo(i) .gt. 0d0)
List_all_comb_b3_cent(1,i) = List_all_comb_b3_cent(1,i) / List_all_comb_b3_expo(i)
List_all_comb_b3_cent(2,i) = List_all_comb_b3_cent(2,i) / List_all_comb_b3_expo(i)
List_all_comb_b3_cent(3,i) = List_all_comb_b3_cent(3,i) / List_all_comb_b3_expo(i)
enddo
! ---
do i = 1, List_all_comb_b3_size
do j = 2, nucl_num, 1
tmp_alphaj = dble(List_all_comb_b3(j,i)) * j1b_pen(j)
do k = 1, j-1, 1
tmp_alphak = dble(List_all_comb_b3(k,i)) * j1b_pen(k)
List_all_comb_b3_coef(i) += tmp_alphaj * tmp_alphak * ( (nucl_coord(j,1) - nucl_coord(k,1)) * (nucl_coord(j,1) - nucl_coord(k,1)) &
+ (nucl_coord(j,2) - nucl_coord(k,2)) * (nucl_coord(j,2) - nucl_coord(k,2)) &
+ (nucl_coord(j,3) - nucl_coord(k,3)) * (nucl_coord(j,3) - nucl_coord(k,3)) )
enddo
enddo
if(List_all_comb_b3_expo(i) .lt. 1d-10) cycle
List_all_comb_b3_coef(i) = List_all_comb_b3_coef(i) / List_all_comb_b3_expo(i)
enddo
! ---
do i = 1, List_all_comb_b3_size
facto = 1.d0
phase = 0
do j = 1, nucl_num
tmp_alphaj = dble(List_all_comb_b3(j,i))
facto *= 2.d0 / (gamma(tmp_alphaj+1.d0) * gamma(3.d0-tmp_alphaj))
phase += List_all_comb_b3(j,i)
enddo
List_all_comb_b3_coef(i) = (-1.d0)**dble(phase) * facto * dexp(-List_all_comb_b3_coef(i))
enddo
!print *, ' coeff, expo & cent of list b3'
!do i = 1, List_all_comb_b3_size
! print*, i, List_all_comb_b3_coef(i), List_all_comb_b3_expo(i)
! print*, List_all_comb_b3_cent(1,i), List_all_comb_b3_cent(2,i), List_all_comb_b3_cent(3,i)
!enddo
END_PROVIDER
! ---

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BEGIN_PROVIDER [ integer, List_comb_thr_b2_size, (ao_num, ao_num)]
&BEGIN_PROVIDER [ integer, max_List_comb_thr_b2_size]
implicit none
integer :: i_1s,i,j,ipoint
double precision :: coef,beta,center(3),int_j1b,thr
double precision :: r(3),weight,dist
thr = 1.d-15
List_comb_thr_b2_size = 0
do i = 1, ao_num
do j = i, ao_num
do i_1s = 1, List_all_comb_b2_size
coef = List_all_comb_b2_coef (i_1s)
if(dabs(coef).lt.1.d-15)cycle
beta = List_all_comb_b2_expo (i_1s)
beta = max(beta,1.d-12)
center(1:3) = List_all_comb_b2_cent(1:3,i_1s)
int_j1b = 0.d0
do ipoint = 1, n_points_extra_final_grid
r(1:3) = final_grid_points_extra(1:3,ipoint)
weight = final_weight_at_r_vector_extra(ipoint)
dist = ( center(1) - r(1) )*( center(1) - r(1) )
dist += ( center(2) - r(2) )*( center(2) - r(2) )
dist += ( center(3) - r(3) )*( center(3) - r(3) )
int_j1b += dabs(aos_in_r_array_extra_transp(ipoint,i) * aos_in_r_array_extra_transp(ipoint,j))*dexp(-beta*dist) * weight
enddo
if(dabs(coef)*dabs(int_j1b).gt.thr)then
List_comb_thr_b2_size(j,i) += 1
endif
enddo
enddo
enddo
do i = 1, ao_num
do j = 1, i-1
List_comb_thr_b2_size(j,i) = List_comb_thr_b2_size(i,j)
enddo
enddo
integer :: list(ao_num)
do i = 1, ao_num
list(i) = maxval(List_comb_thr_b2_size(:,i))
enddo
max_List_comb_thr_b2_size = maxval(list)
END_PROVIDER
BEGIN_PROVIDER [ double precision, List_comb_thr_b2_coef, ( max_List_comb_thr_b2_size,ao_num, ao_num )]
&BEGIN_PROVIDER [ double precision, List_comb_thr_b2_expo, ( max_List_comb_thr_b2_size,ao_num, ao_num )]
&BEGIN_PROVIDER [ double precision, List_comb_thr_b2_cent, (3, max_List_comb_thr_b2_size,ao_num, ao_num )]
&BEGIN_PROVIDER [ double precision, ao_abs_comb_b2_j1b, ( max_List_comb_thr_b2_size ,ao_num, ao_num)]
implicit none
integer :: i_1s,i,j,ipoint,icount
double precision :: coef,beta,center(3),int_j1b,thr
double precision :: r(3),weight,dist
thr = 1.d-15
ao_abs_comb_b2_j1b = 10000000.d0
do i = 1, ao_num
do j = i, ao_num
icount = 0
do i_1s = 1, List_all_comb_b2_size
coef = List_all_comb_b2_coef (i_1s)
if(dabs(coef).lt.1.d-12)cycle
beta = List_all_comb_b2_expo (i_1s)
center(1:3) = List_all_comb_b2_cent(1:3,i_1s)
int_j1b = 0.d0
do ipoint = 1, n_points_extra_final_grid
r(1:3) = final_grid_points_extra(1:3,ipoint)
weight = final_weight_at_r_vector_extra(ipoint)
dist = ( center(1) - r(1) )*( center(1) - r(1) )
dist += ( center(2) - r(2) )*( center(2) - r(2) )
dist += ( center(3) - r(3) )*( center(3) - r(3) )
int_j1b += dabs(aos_in_r_array_extra_transp(ipoint,i) * aos_in_r_array_extra_transp(ipoint,j))*dexp(-beta*dist) * weight
enddo
if(dabs(coef)*dabs(int_j1b).gt.thr)then
icount += 1
List_comb_thr_b2_coef(icount,j,i) = coef
List_comb_thr_b2_expo(icount,j,i) = beta
List_comb_thr_b2_cent(1:3,icount,j,i) = center(1:3)
ao_abs_comb_b2_j1b(icount,j,i) = int_j1b
endif
enddo
enddo
enddo
do i = 1, ao_num
do j = 1, i-1
do icount = 1, List_comb_thr_b2_size(j,i)
List_comb_thr_b2_coef(icount,j,i) = List_comb_thr_b2_coef(icount,i,j)
List_comb_thr_b2_expo(icount,j,i) = List_comb_thr_b2_expo(icount,i,j)
List_comb_thr_b2_cent(1:3,icount,j,i) = List_comb_thr_b2_cent(1:3,icount,i,j)
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [ integer, List_comb_thr_b3_size, (ao_num, ao_num)]
&BEGIN_PROVIDER [ integer, max_List_comb_thr_b3_size]
implicit none
integer :: i_1s,i,j,ipoint
double precision :: coef,beta,center(3),int_j1b,thr
double precision :: r(3),weight,dist
thr = 1.d-15
List_comb_thr_b3_size = 0
do i = 1, ao_num
do j = 1, ao_num
do i_1s = 1, List_all_comb_b3_size
coef = List_all_comb_b3_coef (i_1s)
beta = List_all_comb_b3_expo (i_1s)
center(1:3) = List_all_comb_b3_cent(1:3,i_1s)
if(dabs(coef).lt.thr)cycle
int_j1b = 0.d0
do ipoint = 1, n_points_extra_final_grid
r(1:3) = final_grid_points_extra(1:3,ipoint)
weight = final_weight_at_r_vector_extra(ipoint)
dist = ( center(1) - r(1) )*( center(1) - r(1) )
dist += ( center(2) - r(2) )*( center(2) - r(2) )
dist += ( center(3) - r(3) )*( center(3) - r(3) )
int_j1b += dabs(aos_in_r_array_extra_transp(ipoint,i) * aos_in_r_array_extra_transp(ipoint,j))*dexp(-beta*dist) * weight
enddo
if(dabs(coef)*dabs(int_j1b).gt.thr)then
List_comb_thr_b3_size(j,i) += 1
endif
enddo
enddo
enddo
! do i = 1, ao_num
! do j = 1, i-1
! List_comb_thr_b3_size(j,i) = List_comb_thr_b3_size(i,j)
! enddo
! enddo
integer :: list(ao_num)
do i = 1, ao_num
list(i) = maxval(List_comb_thr_b3_size(:,i))
enddo
max_List_comb_thr_b3_size = maxval(list)
print*,'max_List_comb_thr_b3_size = ',max_List_comb_thr_b3_size
END_PROVIDER
BEGIN_PROVIDER [ double precision, List_comb_thr_b3_coef, ( max_List_comb_thr_b3_size,ao_num, ao_num )]
&BEGIN_PROVIDER [ double precision, List_comb_thr_b3_expo, ( max_List_comb_thr_b3_size,ao_num, ao_num )]
&BEGIN_PROVIDER [ double precision, List_comb_thr_b3_cent, (3, max_List_comb_thr_b3_size,ao_num, ao_num )]
&BEGIN_PROVIDER [ double precision, ao_abs_comb_b3_j1b, ( max_List_comb_thr_b3_size ,ao_num, ao_num)]
implicit none
integer :: i_1s,i,j,ipoint,icount
double precision :: coef,beta,center(3),int_j1b,thr
double precision :: r(3),weight,dist
thr = 1.d-15
ao_abs_comb_b3_j1b = 10000000.d0
do i = 1, ao_num
do j = 1, ao_num
icount = 0
do i_1s = 1, List_all_comb_b3_size
coef = List_all_comb_b3_coef (i_1s)
beta = List_all_comb_b3_expo (i_1s)
beta = max(beta,1.d-12)
center(1:3) = List_all_comb_b3_cent(1:3,i_1s)
if(dabs(coef).lt.thr)cycle
int_j1b = 0.d0
do ipoint = 1, n_points_extra_final_grid
r(1:3) = final_grid_points_extra(1:3,ipoint)
weight = final_weight_at_r_vector_extra(ipoint)
dist = ( center(1) - r(1) )*( center(1) - r(1) )
dist += ( center(2) - r(2) )*( center(2) - r(2) )
dist += ( center(3) - r(3) )*( center(3) - r(3) )
int_j1b += dabs(aos_in_r_array_extra_transp(ipoint,i) * aos_in_r_array_extra_transp(ipoint,j))*dexp(-beta*dist) * weight
enddo
if(dabs(coef)*dabs(int_j1b).gt.thr)then
icount += 1
List_comb_thr_b3_coef(icount,j,i) = coef
List_comb_thr_b3_expo(icount,j,i) = beta
List_comb_thr_b3_cent(1:3,icount,j,i) = center(1:3)
ao_abs_comb_b3_j1b(icount,j,i) = int_j1b
endif
enddo
enddo
enddo
! do i = 1, ao_num
! do j = 1, i-1
! do icount = 1, List_comb_thr_b3_size(j,i)
! List_comb_thr_b3_coef(icount,j,i) = List_comb_thr_b3_coef(icount,i,j)
! List_comb_thr_b3_expo(icount,j,i) = List_comb_thr_b3_expo(icount,i,j)
! List_comb_thr_b3_cent(1:3,icount,j,i) = List_comb_thr_b3_cent(1:3,icount,i,j)
! enddo
! enddo
! enddo
END_PROVIDER

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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

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! ---
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
include 'constants.include.F'
implicit none
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
overlap_gauss_r12 = 0.d0
! 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)
if(fact_a_new.lt.thr)return
! 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)*fact_a_new
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 = accu
end
!---
double precision function overlap_abs_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,dx,lower_exp_val
integer :: d(3),i,lx,ly,lz,iorder_tmp(3),dim1
dim1=50
lower_exp_val = 40.d0
thr = 1.d-12
d(:) = 0 ! order of the polynom for the gaussian exp(-delta (r - D)^2 ) == 0
overlap_abs_gauss_r12 = 0.d0
! 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)
if(fact_a_new.lt.thr)return
! 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)*fact_a_new
! 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_x_abs(A_center_new(1),B_center(1),alpha_new,beta,iorder_tmp(1),power_B(1),overlap_x,lower_exp_val,dx,dim1)
call overlap_x_abs(A_center_new(2),B_center(2),alpha_new,beta,iorder_tmp(2),power_B(2),overlap_y,lower_exp_val,dx,dim1)
call overlap_x_abs(A_center_new(3),B_center(3),alpha_new,beta,iorder_tmp(3),power_B(3),overlap_z,lower_exp_val,dx,dim1)
accu += dabs(coefxyz * overlap_x * overlap_y * overlap_z)
enddo
enddo
enddo
overlap_abs_gauss_r12= accu
end
!---
! TODO apply Gaussian product three times first
subroutine overlap_gauss_r12_v(D_center, LD_D, delta, A_center, B_center, power_A, power_B, alpha, beta, rvec, LD_rvec, n_points)
BEGIN_DOC
!
! Computes the following integral :
!
! \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)
! using an array of D_centers
!
! n_points: nb of integrals
!
END_DOC
implicit none
include 'constants.include.F'
integer, intent(in) :: LD_D, LD_rvec, n_points
integer, intent(in) :: power_A(3), power_B(3)
double precision, intent(in) :: D_center(LD_D,3), delta
double precision, intent(in) :: A_center(3), B_center(3), alpha, beta
double precision, intent(out) :: rvec(LD_rvec)
integer :: maxab
integer :: d(3), i, lx, ly, lz, iorder_tmp(3), ipoint
double precision :: overlap_x, overlap_y, overlap_z
double precision :: alpha_new
double precision :: accu, thr, coefxy
integer, allocatable :: iorder_a_new(:)
double precision, allocatable :: overlap(:)
double precision, allocatable :: A_new(:,:,:), A_center_new(:,:)
double precision, allocatable :: fact_a_new(:)
thr = 1.d-10
d(:) = 0
maxab = maxval(power_A(1:3))
allocate(A_new(n_points,0:maxab,3), A_center_new(n_points,3), fact_a_new(n_points), iorder_a_new(3), overlap(n_points))
call give_explicit_poly_and_gaussian_v(A_new, maxab, A_center_new, alpha_new, fact_a_new, iorder_a_new, delta, alpha, d, power_A, D_center, LD_D, A_center, n_points)
rvec(:) = 0.d0
do lx = 0, iorder_a_new(1)
iorder_tmp(1) = lx
do ly = 0, iorder_a_new(2)
iorder_tmp(2) = ly
do lz = 0, iorder_a_new(3)
iorder_tmp(3) = lz
call overlap_gaussian_xyz_v(A_center_new, B_center, alpha_new, beta, iorder_tmp, power_B, overlap, n_points)
do ipoint = 1, n_points
rvec(ipoint) = rvec(ipoint) + A_new(ipoint,lx,1) * A_new(ipoint,ly,2) * A_new(ipoint,lz,3) * overlap(ipoint)
enddo
enddo
enddo
enddo
do ipoint = 1, n_points
rvec(ipoint) = rvec(ipoint) * fact_a_new(ipoint)
enddo
deallocate(A_new, A_center_new, fact_a_new, iorder_a_new, overlap)
end subroutine overlap_gauss_r12_v
!---
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

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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

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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

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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

627
src/ao_one_e_ints/pot_ao_erf_ints.irp.f
View File

@ -46,142 +46,327 @@ double precision function NAI_pol_mult_erf_ao(i_ao,j_ao,mu_in,C_center)
end
double precision function NAI_pol_mult_erf(A_center, B_center, power_A, power_B, alpha, beta, C_center, n_pt_in, mu_in)
double precision function NAI_pol_mult_erf(A_center,B_center,power_A,power_B,alpha,beta,C_center,n_pt_in,mu_in)
BEGIN_DOC
!
! Computes the following integral :
!
! .. 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 | }$.
! \frac{\erf(\mu |r - R_C |)}{| r - R_C |}$.
!
END_DOC
include 'utils/constants.include.F'
implicit none
integer, intent(in) :: n_pt_in
integer, intent(in) :: power_A(3), power_B(3)
double precision, intent(in) :: C_center(3), A_center(3), B_center(3), alpha, beta, mu_in
integer :: i, n_pt, n_pt_out
double precision :: P_center(3)
double precision :: d(0:n_pt_in), coeff, dist, const, factor
double precision :: const_factor, dist_integral
double precision :: accu, p_inv, p, rho, p_inv_2
double precision :: p_new
double precision :: rint
p = alpha + beta
p_inv = 1.d0 / p
p_inv_2 = 0.5d0 * p_inv
rho = alpha * beta * p_inv
dist = 0.d0
dist_integral = 0.d0
do i = 1, 3
P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
dist += (A_center(i) - B_center(i)) * (A_center(i) - B_center(i))
dist_integral += (P_center(i) - C_center(i)) * (P_center(i) - C_center(i))
enddo
const_factor = dist * rho
if(const_factor > 80.d0) then
NAI_pol_mult_erf = 0.d0
return
endif
p_new = mu_in / dsqrt(p + mu_in * mu_in)
factor = dexp(-const_factor)
coeff = dtwo_pi * factor * p_inv * p_new
n_pt = 2 * ( (power_A(1) + power_B(1)) + (power_A(2) + power_B(2)) + (power_A(3) + power_B(3)) )
const = p * dist_integral * p_new * p_new
if(n_pt == 0) then
NAI_pol_mult_erf = coeff * rint(0, const)
return
endif
do i = 0, n_pt_in
d(i) = 0.d0
enddo
! call give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in)
p_new = p_new * p_new
call give_polynomial_mult_center_one_e_erf_opt(A_center, B_center, power_A, power_B, C_center, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
if(n_pt_out < 0) then
NAI_pol_mult_erf = 0.d0
return
endif
! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
accu = 0.d0
do i = 0, n_pt_out, 2
accu += d(i) * rint(i/2, const)
enddo
NAI_pol_mult_erf = accu * coeff
end function NAI_pol_mult_erf
! ---
double precision function NAI_pol_mult_erf_ao_with1s(i_ao, j_ao, beta, B_center, mu_in, C_center)
BEGIN_DOC
!
! Computes the following integral :
! $\int_{-\infty}^{infty} dr \chi_i(r) \chi_j(r) e^{-\beta (r - B_center)^2} \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
!
END_DOC
implicit none
integer, intent(in) :: n_pt_in
double precision,intent(in) :: C_center(3),A_center(3),B_center(3),alpha,beta,mu_in
integer, intent(in) :: power_A(3),power_B(3)
integer :: i,j,k,l,n_pt
double precision :: P_center(3)
integer, intent(in) :: i_ao, j_ao
double precision, intent(in) :: beta, B_center(3)
double precision, intent(in) :: mu_in, C_center(3)
integer :: i, j, power_A1(3), power_A2(3), n_pt_in
double precision :: A1_center(3), A2_center(3), alpha1, alpha2, coef12, coef1, integral
double precision, external :: NAI_pol_mult_erf_with1s, NAI_pol_mult_erf_ao
ASSERT(beta .ge. 0.d0)
if(beta .lt. 1d-10) then
NAI_pol_mult_erf_ao_with1s = NAI_pol_mult_erf_ao(i_ao, j_ao, mu_in, C_center)
return
endif
power_A1(1:3) = ao_power(i_ao,1:3)
power_A2(1:3) = ao_power(j_ao,1:3)
A1_center(1:3) = nucl_coord(ao_nucl(i_ao),1:3)
A2_center(1:3) = nucl_coord(ao_nucl(j_ao),1:3)
n_pt_in = n_pt_max_integrals
NAI_pol_mult_erf_ao_with1s = 0.d0
do i = 1, ao_prim_num(i_ao)
alpha1 = ao_expo_ordered_transp (i,i_ao)
coef1 = ao_coef_normalized_ordered_transp(i,i_ao)
do j = 1, ao_prim_num(j_ao)
alpha2 = ao_expo_ordered_transp(j,j_ao)
coef12 = coef1 * ao_coef_normalized_ordered_transp(j,j_ao)
if(dabs(coef12) .lt. 1d-14) cycle
integral = NAI_pol_mult_erf_with1s( A1_center, A2_center, power_A1, power_A2, alpha1, alpha2 &
, beta, B_center, C_center, n_pt_in, mu_in )
NAI_pol_mult_erf_ao_with1s += integral * coef12
enddo
enddo
end function NAI_pol_mult_erf_ao_with1s
subroutine NAI_pol_mult_erf_with1s_v(A1_center, A2_center, power_A1, power_A2, alpha1, alpha2, beta, B_center, LD_B, C_center, LD_C, n_pt_in, mu_in, res_v, LD_resv, n_points)
BEGIN_DOC
!
! Computes the following integral :
!
! .. math ::
!
! \int dx (x - A1_x)^a_1 (x - B1_x)^a_2 \exp(-\alpha_1 (x - A1_x)^2 - \alpha_2 (x - A2_x)^2)
! \int dy (y - A1_y)^b_1 (y - B1_y)^b_2 \exp(-\alpha_1 (y - A1_y)^2 - \alpha_2 (y - A2_y)^2)
! \int dz (x - A1_z)^c_1 (z - B1_z)^c_2 \exp(-\alpha_1 (z - A1_z)^2 - \alpha_2 (z - A2_z)^2)
! \exp(-\beta (r - B)^2)
! \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
!
END_DOC
double precision :: d(0:n_pt_in),pouet,coeff,dist,const,pouet_2,factor
double precision :: I_n_special_exact,integrate_bourrin,I_n_bibi
double precision :: V_e_n,const_factor,dist_integral,tmp
double precision :: accu,rint,p_inv,p,rho,p_inv_2
integer :: n_pt_out,lmax
include 'utils/constants.include.F'
p = alpha + beta
p_inv = 1.d0/p
p_inv_2 = 0.5d0 * p_inv
rho = alpha * beta * p_inv
dist = 0.d0
dist_integral = 0.d0
do i = 1, 3
P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
dist += (A_center(i) - B_center(i))*(A_center(i) - B_center(i))
dist_integral += (P_center(i) - C_center(i))*(P_center(i) - C_center(i))
enddo
const_factor = dist*rho
if(const_factor > 80.d0)then
NAI_pol_mult_erf = 0.d0
return
endif
double precision :: p_new
p_new = mu_in/dsqrt(p+ mu_in * mu_in)
factor = dexp(-const_factor)
coeff = dtwo_pi * factor * p_inv * p_new
lmax = 20
implicit none
integer, intent(in) :: n_pt_in, LD_B, LD_C, LD_resv, n_points
integer, intent(in) :: power_A1(3), power_A2(3)
double precision, intent(in) :: A1_center(3), A2_center(3)
double precision, intent(in) :: C_center(LD_C,3), B_center(LD_B,3)
double precision, intent(in) :: alpha1, alpha2, beta, mu_in
double precision, intent(out) :: res_v(LD_resv)
! print*, "b"
do i = 0, n_pt_in
d(i) = 0.d0
enddo
n_pt = 2 * ( (power_A(1) + power_B(1)) +(power_A(2) + power_B(2)) +(power_A(3) + power_B(3)) )
const = p * dist_integral * p_new * p_new
if (n_pt == 0) then
pouet = rint(0,const)
NAI_pol_mult_erf = coeff * pouet
integer :: i, n_pt, n_pt_out, ipoint
double precision :: alpha12, alpha12_inv, alpha12_inv_2, rho12, A12_center(3), dist12, const_factor12
double precision :: p, p_inv, p_inv_2, rho, P_center(3), dist, const_factor
double precision :: dist_integral
double precision :: d(0:n_pt_in), coeff, const, factor
double precision :: accu
double precision :: p_new, p_new2, coef_tmp, cons_tmp
double precision :: rint
res_V(1:LD_resv) = 0.d0
! e^{-alpha1 (r - A1)^2} e^{-alpha2 (r - A2)^2} = e^{-K12} e^{-alpha12 (r - A12)^2}
alpha12 = alpha1 + alpha2
alpha12_inv = 1.d0 / alpha12
alpha12_inv_2 = 0.5d0 * alpha12_inv
rho12 = alpha1 * alpha2 * alpha12_inv
A12_center(1) = (alpha1 * A1_center(1) + alpha2 * A2_center(1)) * alpha12_inv
A12_center(2) = (alpha1 * A1_center(2) + alpha2 * A2_center(2)) * alpha12_inv
A12_center(3) = (alpha1 * A1_center(3) + alpha2 * A2_center(3)) * alpha12_inv
dist12 = (A1_center(1) - A2_center(1)) * (A1_center(1) - A2_center(1))&
+ (A1_center(2) - A2_center(2)) * (A1_center(2) - A2_center(2))&
+ (A1_center(3) - A2_center(3)) * (A1_center(3) - A2_center(3))
const_factor12 = dist12 * rho12
if(const_factor12 > 80.d0) then
return
endif
! call give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in)
p_new = p_new * p_new
call give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in,p,p_inv,p_inv_2,p_new,P_center)
! e^{-K12} e^{-alpha12 (r - A12)^2} e^{-beta (r - B)^2} = e^{-K} e^{-p (r - P)^2}
p = alpha12 + beta
p_inv = 1.d0 / p
p_inv_2 = 0.5d0 * p_inv
rho = alpha12 * beta * p_inv
p_new = mu_in / dsqrt(p + mu_in * mu_in)
p_new2 = p_new * p_new
coef_tmp = dtwo_pi * p_inv * p_new
cons_tmp = p * p_new2
n_pt = 2 * (power_A1(1) + power_A2(1) + power_A1(2) + power_A2(2) + power_A1(3) + power_A2(3) )
if(n_pt == 0) then
do ipoint = 1, n_points
dist = (A12_center(1) - B_center(ipoint,1)) * (A12_center(1) - B_center(ipoint,1))&
+ (A12_center(2) - B_center(ipoint,2)) * (A12_center(2) - B_center(ipoint,2))&
+ (A12_center(3) - B_center(ipoint,3)) * (A12_center(3) - B_center(ipoint,3))
const_factor = const_factor12 + dist * rho
if(const_factor > 80.d0) cycle
coeff = coef_tmp * dexp(-const_factor)
P_center(1) = (alpha12 * A12_center(1) + beta * B_center(ipoint,1)) * p_inv
P_center(2) = (alpha12 * A12_center(2) + beta * B_center(ipoint,2)) * p_inv
P_center(3) = (alpha12 * A12_center(3) + beta * B_center(ipoint,3)) * p_inv
dist_integral = (P_center(1) - C_center(ipoint,1)) * (P_center(1) - C_center(ipoint,1))&
+ (P_center(2) - C_center(ipoint,2)) * (P_center(2) - C_center(ipoint,2))&
+ (P_center(3) - C_center(ipoint,3)) * (P_center(3) - C_center(ipoint,3))
const = cons_tmp * dist_integral
res_v(ipoint) = coeff * rint(0, const)
enddo
else
do ipoint = 1, n_points
dist = (A12_center(1) - B_center(ipoint,1)) * (A12_center(1) - B_center(ipoint,1))&
+ (A12_center(2) - B_center(ipoint,2)) * (A12_center(2) - B_center(ipoint,2))&
+ (A12_center(3) - B_center(ipoint,3)) * (A12_center(3) - B_center(ipoint,3))
const_factor = const_factor12 + dist * rho
if(const_factor > 80.d0) cycle
coeff = coef_tmp * dexp(-const_factor)
P_center(1) = (alpha12 * A12_center(1) + beta * B_center(ipoint,1)) * p_inv
P_center(2) = (alpha12 * A12_center(2) + beta * B_center(ipoint,2)) * p_inv
P_center(3) = (alpha12 * A12_center(3) + beta * B_center(ipoint,3)) * p_inv
dist_integral = (P_center(1) - C_center(ipoint,1)) * (P_center(1) - C_center(ipoint,1))&
+ (P_center(2) - C_center(ipoint,2)) * (P_center(2) - C_center(ipoint,2))&
+ (P_center(3) - C_center(ipoint,3)) * (P_center(3) - C_center(ipoint,3))
const = cons_tmp * dist_integral
do i = 0, n_pt_in
d(i) = 0.d0
enddo
!TODO: VECTORIZE HERE
call give_polynomial_mult_center_one_e_erf_opt(A1_center, A2_center, power_A1, power_A2, C_center(ipoint,1:3), n_pt_in, d, n_pt_out, p_inv_2, p_new2, P_center)
if(n_pt_out < 0) then
cycle
endif
! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
accu = 0.d0
do i = 0, n_pt_out, 2
accu += d(i) * rint(i/2, const)
enddo
res_v(ipoint) = accu * coeff
enddo
if(n_pt_out<0)then
NAI_pol_mult_erf = 0.d0
return
endif
accu = 0.d0
! 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)
enddo
NAI_pol_mult_erf = accu * coeff
end subroutine NAI_pol_mult_erf_with1s_v
end
! ---
subroutine give_polynomial_mult_center_one_e_erf_opt(A_center, B_center, power_A, power_B, C_center, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,beta,&
power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in,p,p_inv,p_inv_2,p_new,P_center)
BEGIN_DOC
! Returns the explicit polynomial in terms of the $t$ variable of the
! following polynomial:
!
! $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$.
END_DOC
implicit none
integer, intent(in) :: n_pt_in
integer,intent(out) :: n_pt_out
double precision, intent(in) :: A_center(3), B_center(3),C_center(3),p,p_inv,p_inv_2,p_new,P_center(3)
double precision, intent(in) :: alpha,beta,mu_in
integer, intent(in) :: power_A(3), power_B(3)
integer :: a_x,b_x,a_y,b_y,a_z,b_z
double precision :: d(0:n_pt_in)
double precision :: d1(0:n_pt_in)
double precision :: d2(0:n_pt_in)
double precision :: d3(0:n_pt_in)
double precision :: accu
integer, intent(in) :: n_pt_in
integer, intent(in) :: power_A(3), power_B(3)
double precision, intent(in) :: A_center(3), B_center(3), C_center(3), p_inv_2, p_new, P_center(3)
integer, intent(out) :: n_pt_out
double precision, intent(out) :: d(0:n_pt_in)
integer :: a_x, b_x, a_y, b_y, a_z, b_z
integer :: n_pt1, n_pt2, n_pt3, dim, i
integer :: n_pt_tmp
double precision :: d1(0:n_pt_in)
double precision :: d2(0:n_pt_in)
double precision :: d3(0:n_pt_in)
double precision :: accu
double precision :: R1x(0:2), B01(0:2), R1xp(0:2), R2x(0:2)
accu = 0.d0
ASSERT (n_pt_in > 1)
double precision :: R1x(0:2), B01(0:2), R1xp(0:2),R2x(0:2)
R1x(0) = (P_center(1) - A_center(1))
R1x(1) = 0.d0
R1x(2) = -(P_center(1) - C_center(1))* p_new
R1x(0) = (P_center(1) - A_center(1))
R1x(1) = 0.d0
R1x(2) = -(P_center(1) - C_center(1))* p_new
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
R1xp(0) = (P_center(1) - B_center(1))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(1) - C_center(1))* p_new
R1xp(0) = (P_center(1) - B_center(1))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(1) - C_center(1))* p_new
!R1xp = (P_x - B_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
R2x(0) = p_inv_2
R2x(1) = 0.d0
R2x(2) = -p_inv_2* p_new
R2x(0) = p_inv_2
R2x(1) = 0.d0
R2x(2) = -p_inv_2 * p_new
!R2x = 0.5 / p - 0.5/p ( t * mu/sqrt(p+mu^2) )^2
do i = 0,n_pt_in
d(i) = 0.d0
enddo
do i = 0,n_pt_in
do i = 0, n_pt_in
d (i) = 0.d0
d1(i) = 0.d0
enddo
do i = 0,n_pt_in
d2(i) = 0.d0
enddo
do i = 0,n_pt_in
d3(i) = 0.d0
enddo
integer :: n_pt1,n_pt2,n_pt3,dim,i
n_pt1 = n_pt_in
n_pt2 = n_pt_in
n_pt3 = n_pt_in
a_x = power_A(1)
b_x = power_B(1)
call I_x1_pol_mult_one_e(a_x,b_x,R1x,R1xp,R2x,d1,n_pt1,n_pt_in)
call I_x1_pol_mult_one_e(a_x, b_x, R1x, R1xp, R2x, d1, n_pt1, n_pt_in)
if(n_pt1<0)then
n_pt_out = -1
do i = 0,n_pt_in
@ -190,17 +375,17 @@ subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,bet
return
endif
R1x(0) = (P_center(2) - A_center(2))
R1x(1) = 0.d0
R1x(2) = -(P_center(2) - C_center(2))* p_new
R1x(0) = (P_center(2) - A_center(2))
R1x(1) = 0.d0
R1x(2) = -(P_center(2) - C_center(2))* p_new
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
R1xp(0) = (P_center(2) - B_center(2))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(2) - C_center(2))* p_new
R1xp(0) = (P_center(2) - B_center(2))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(2) - C_center(2))* p_new
!R1xp = (P_x - B_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
a_y = power_A(2)
b_y = power_B(2)
call I_x1_pol_mult_one_e(a_y,b_y,R1x,R1xp,R2x,d2,n_pt2,n_pt_in)
call I_x1_pol_mult_one_e(a_y, b_y, R1x, R1xp, R2x, d2, n_pt2, n_pt_in)
if(n_pt2<0)then
n_pt_out = -1
do i = 0,n_pt_in
@ -209,51 +394,151 @@ subroutine give_polynomial_mult_center_one_e_erf_opt(A_center,B_center,alpha,bet
return
endif
R1x(0) = (P_center(3) - A_center(3))
R1x(1) = 0.d0
R1x(2) = -(P_center(3) - C_center(3))* p_new
R1x(0) = (P_center(3) - A_center(3))
R1x(1) = 0.d0
R1x(2) = -(P_center(3) - C_center(3)) * p_new
! R1x = (P_x - A_x) - (P_x - C_x) ( t * mu/sqrt(p+mu^2) )^2
R1xp(0) = (P_center(3) - B_center(3))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(3) - C_center(3))* p_new
R1xp(0) = (P_center(3) - B_center(3))
R1xp(1) = 0.d0
R1xp(2) =-(P_center(3) - C_center(3)) * p_new
!R2x = 0.5 / p - 0.5/p ( t * mu/sqrt(p+mu^2) )^2
a_z = power_A(3)
b_z = power_B(3)
call I_x1_pol_mult_one_e(a_z,b_z,R1x,R1xp,R2x,d3,n_pt3,n_pt_in)
if(n_pt3<0)then
call I_x1_pol_mult_one_e(a_z, b_z, R1x, R1xp, R2x, d3, n_pt3, n_pt_in)
if(n_pt3 < 0) then
n_pt_out = -1
do i = 0,n_pt_in
d(i) = 0.d0
enddo
return
endif
integer :: n_pt_tmp
n_pt_tmp = 0
call multiply_poly(d1,n_pt1,d2,n_pt2,d,n_pt_tmp)
do i = 0,n_pt_tmp
call multiply_poly(d1, n_pt1, d2, n_pt2, d, n_pt_tmp)
do i = 0, n_pt_tmp
d1(i) = 0.d0
enddo
n_pt_out = 0
call multiply_poly(d ,n_pt_tmp ,d3,n_pt3,d1,n_pt_out)
call multiply_poly(d, n_pt_tmp, d3, n_pt3, d1, n_pt_out)
do i = 0, n_pt_out
d(i) = d1(i)
enddo
end
end subroutine give_polynomial_mult_center_one_e_erf_opt
! ---
subroutine NAI_pol_mult_erf_v(A_center, B_center, power_A, power_B, alpha, beta, C_center, LD_C, n_pt_in, mu_in, res_v, LD_resv, n_points)
subroutine give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,&
power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in)
BEGIN_DOC
! Returns the explicit polynomial in terms of the $t$ variable of the
!
! Computes the following integral :
!
! .. 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 |}$.
!
END_DOC
include 'utils/constants.include.F'
implicit none
integer, intent(in) :: n_pt_in, n_points, LD_C, LD_resv
integer, intent(in) :: power_A(3), power_B(3)
double precision, intent(in) :: A_center(3), B_center(3), alpha, beta, mu_in
double precision, intent(in) :: C_center(LD_C,3)
double precision, intent(out) :: res_v(LD_resv)
integer :: i, n_pt, n_pt_out, ipoint
double precision :: P_center(3)
double precision :: d(0:n_pt_in), coeff, dist, const, factor
double precision :: const_factor, dist_integral
double precision :: accu, p_inv, p, rho, p_inv_2
double precision :: p_new, p_new2, coef_tmp
double precision :: rint
res_V(1:LD_resv) = 0.d0
p = alpha + beta
p_inv = 1.d0 / p
p_inv_2 = 0.5d0 * p_inv
rho = alpha * beta * p_inv
p_new = mu_in / dsqrt(p + mu_in * mu_in)
p_new2 = p_new * p_new
coef_tmp = p * p_new2
dist = 0.d0
do i = 1, 3
P_center(i) = (alpha * A_center(i) + beta * B_center(i)) * p_inv
dist += (A_center(i) - B_center(i)) * (A_center(i) - B_center(i))
enddo
const_factor = dist * rho
if(const_factor > 80.d0) then
return
endif
factor = dexp(-const_factor)
coeff = dtwo_pi * factor * p_inv * p_new
n_pt = 2 * ( power_A(1) + power_B(1) + power_A(2) + power_B(2) + power_A(3) + power_B(3) )
if(n_pt == 0) then
do ipoint = 1, n_points
dist_integral = 0.d0
do i = 1, 3
dist_integral += (P_center(i) - C_center(ipoint,i)) * (P_center(i) - C_center(ipoint,i))
enddo
const = coef_tmp * dist_integral
res_v(ipoint) = coeff * rint(0, const)
enddo
else
do ipoint = 1, n_points
dist_integral = 0.d0
do i = 1, 3
dist_integral += (P_center(i) - C_center(ipoint,i)) * (P_center(i) - C_center(ipoint,i))
enddo
const = coef_tmp * dist_integral
do i = 0, n_pt_in
d(i) = 0.d0
enddo
call give_polynomial_mult_center_one_e_erf_opt(A_center, B_center, power_A, power_B, C_center(ipoint,1:3), n_pt_in, d, n_pt_out, p_inv_2, p_new2, P_center)
if(n_pt_out < 0) then
res_v(ipoint) = 0.d0
cycle
endif
! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
accu = 0.d0
do i = 0, n_pt_out, 2
accu += d(i) * rint(i/2, const)
enddo
res_v(ipoint) = accu * coeff
enddo
endif
end subroutine NAI_pol_mult_erf_v
subroutine give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,power_A,power_B,C_center,n_pt_in,d,n_pt_out,mu_in)
BEGIN_DOC
! Returns the explicit polynomial in terms of the $t$ variable of the
! following polynomial:
!
! $I_{x1}(a_x, d_x,p,q) \times I_{x1}(a_y, d_y,p,q) \times I_{x1}(a_z, d_z,p,q)$.
END_DOC
implicit none
integer, intent(in) :: n_pt_in
integer,intent(out) :: n_pt_out
@ -374,3 +659,113 @@ subroutine give_polynomial_mult_center_one_e_erf(A_center,B_center,alpha,beta,&
end
double precision function NAI_pol_mult_erf_with1s( A1_center, A2_center, power_A1, power_A2, alpha1, alpha2 &
, beta, B_center, C_center, n_pt_in, mu_in )
BEGIN_DOC
!
! Computes the following integral :
!
! .. math::
!
! \int dx (x - A1_x)^a_1 (x - B1_x)^a_2 \exp(-\alpha_1 (x - A1_x)^2 - \alpha_2 (x - A2_x)^2)
! \int dy (y - A1_y)^b_1 (y - B1_y)^b_2 \exp(-\alpha_1 (y - A1_y)^2 - \alpha_2 (y - A2_y)^2)
! \int dz (x - A1_z)^c_1 (z - B1_z)^c_2 \exp(-\alpha_1 (z - A1_z)^2 - \alpha_2 (z - A2_z)^2)
! \exp(-\beta (r - B)^2)
! \frac{\erf(\mu |r - R_C|)}{|r - R_C|}$.
!
END_DOC
include 'utils/constants.include.F'
implicit none
integer, intent(in) :: n_pt_in
integer, intent(in) :: power_A1(3), power_A2(3)
double precision, intent(in) :: C_center(3), A1_center(3), A2_center(3), B_center(3)
double precision, intent(in) :: alpha1, alpha2, beta, mu_in
integer :: i, n_pt, n_pt_out
double precision :: alpha12, alpha12_inv, alpha12_inv_2, rho12, A12_center(3), dist12, const_factor12
double precision :: p, p_inv, p_inv_2, rho, P_center(3), dist, const_factor
double precision :: dist_integral
double precision :: d(0:n_pt_in), coeff, const, factor
double precision :: accu
double precision :: p_new
double precision :: rint
! e^{-alpha1 (r - A1)^2} e^{-alpha2 (r - A2)^2} = e^{-K12} e^{-alpha12 (r - A12)^2}
alpha12 = alpha1 + alpha2
alpha12_inv = 1.d0 / alpha12
alpha12_inv_2 = 0.5d0 * alpha12_inv
rho12 = alpha1 * alpha2 * alpha12_inv
A12_center(1) = (alpha1 * A1_center(1) + alpha2 * A2_center(1)) * alpha12_inv
A12_center(2) = (alpha1 * A1_center(2) + alpha2 * A2_center(2)) * alpha12_inv
A12_center(3) = (alpha1 * A1_center(3) + alpha2 * A2_center(3)) * alpha12_inv
dist12 = (A1_center(1) - A2_center(1)) * (A1_center(1) - A2_center(1)) &
+ (A1_center(2) - A2_center(2)) * (A1_center(2) - A2_center(2)) &
+ (A1_center(3) - A2_center(3)) * (A1_center(3) - A2_center(3))
const_factor12 = dist12 * rho12
if(const_factor12 > 80.d0) then
NAI_pol_mult_erf_with1s = 0.d0
return
endif
! ---
! e^{-K12} e^{-alpha12 (r - A12)^2} e^{-beta (r - B)^2} = e^{-K} e^{-p (r - P)^2}
p = alpha12 + beta
p_inv = 1.d0 / p
p_inv_2 = 0.5d0 * p_inv
rho = alpha12 * beta * p_inv
P_center(1) = (alpha12 * A12_center(1) + beta * B_center(1)) * p_inv
P_center(2) = (alpha12 * A12_center(2) + beta * B_center(2)) * p_inv
P_center(3) = (alpha12 * A12_center(3) + beta * B_center(3)) * p_inv
dist = (A12_center(1) - B_center(1)) * (A12_center(1) - B_center(1)) &
+ (A12_center(2) - B_center(2)) * (A12_center(2) - B_center(2)) &
+ (A12_center(3) - B_center(3)) * (A12_center(3) - B_center(3))
const_factor = const_factor12 + dist * rho
if(const_factor > 80.d0) then
NAI_pol_mult_erf_with1s = 0.d0
return
endif
dist_integral = (P_center(1) - C_center(1)) * (P_center(1) - C_center(1)) &
+ (P_center(2) - C_center(2)) * (P_center(2) - C_center(2)) &
+ (P_center(3) - C_center(3)) * (P_center(3) - C_center(3))
! ---
p_new = mu_in / dsqrt(p + mu_in * mu_in)
factor = dexp(-const_factor)
coeff = dtwo_pi * factor * p_inv * p_new
n_pt = 2 * ( (power_A1(1) + power_A2(1)) + (power_A1(2) + power_A2(2)) + (power_A1(3) + power_A2(3)) )
const = p * dist_integral * p_new * p_new
if(n_pt == 0) then
NAI_pol_mult_erf_with1s = coeff * rint(0, const)
return
endif
do i = 0, n_pt_in
d(i) = 0.d0
enddo
p_new = p_new * p_new
call give_polynomial_mult_center_one_e_erf_opt( A1_center, A2_center, power_A1, power_A2, C_center, n_pt_in, d, n_pt_out, p_inv_2, p_new, P_center)
if(n_pt_out < 0) then
NAI_pol_mult_erf_with1s = 0.d0
return
endif
! sum of integrals of type : int {t,[0,1]} exp-(rho.(P-Q)^2 * t^2) * t^i
accu = 0.d0
do i = 0, n_pt_out, 2
accu += d(i) * rint(i/2, const)
enddo
NAI_pol_mult_erf_with1s = accu * coeff
end function NAI_pol_mult_erf_with1s

4
src/ao_one_e_ints/pot_ao_ints.irp.f
View File

@ -80,6 +80,10 @@ BEGIN_PROVIDER [ double precision, ao_integrals_n_e, (ao_num,ao_num)]
IF (DO_PSEUDO) THEN
ao_integrals_n_e += ao_pseudo_integrals
ENDIF
IF(point_charges) THEN
ao_integrals_n_e += ao_integrals_pt_chrg
ENDIF
endif

108
src/ao_one_e_ints/pot_pt_charges.irp.f Normal file
View File

@ -0,0 +1,108 @@
BEGIN_PROVIDER [ double precision, ao_integrals_pt_chrg, (ao_num,ao_num)]
BEGIN_DOC
! Point charge-electron interaction, in the |AO| basis set.
!
! :math:`\langle \chi_i | -\sum_charge charge * \frac{1}{|r-R_charge|} | \chi_j \rangle`
!
! Notice the minus sign convention as it is supposed to be for electrons.
END_DOC
implicit none
integer :: num_A, num_B, power_A(3), power_B(3)
integer :: i, j, k, l, n_pt_in, m
double precision :: alpha, beta
double precision :: A_center(3),B_center(3),C_center(3)
double precision :: overlap_x,overlap_y,overlap_z,overlap,dx,NAI_pol_mult
ao_integrals_pt_chrg = 0.d0
! if (read_ao_integrals_pt_chrg) then
!
! call ezfio_get_ao_one_e_ints_ao_integrals_pt_chrg(ao_integrals_pt_chrg)
! print *, 'AO N-e integrals read from disk'
!
! else
! if(use_cosgtos) then
! !print *, " use_cosgtos for ao_integrals_pt_chrg ?", use_cosgtos
!
! do j = 1, ao_num
! do i = 1, ao_num
! ao_integrals_pt_chrg(i,j) = ao_integrals_pt_chrg_cosgtos(i,j)
! enddo
! enddo
!
! else
!$OMP PARALLEL &
!$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,c1,n_pt_in) &
!$OMP SHARED (ao_num,ao_prim_num,ao_expo_ordered_transp,ao_power,ao_nucl,pts_charge_coord,ao_coef_normalized_ordered_transp,nucl_coord,&
!$OMP n_pt_max_integrals,ao_integrals_pt_chrg,n_pts_charge,pts_charge_z)
n_pt_in = n_pt_max_integrals
!$OMP DO SCHEDULE (dynamic)
do j = 1, ao_num
num_A = ao_nucl(j)
power_A(1:3)= ao_power(j,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
do i = 1, ao_num
num_B = ao_nucl(i)
power_B(1:3)= ao_power(i,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
do l=1,ao_prim_num(j)
alpha = ao_expo_ordered_transp(l,j)
do m=1,ao_prim_num(i)
beta = ao_expo_ordered_transp(m,i)
double precision :: c, c1
c = 0.d0
do k = 1, n_pts_charge
double precision :: Z
Z = pts_charge_z(k)
C_center(1:3) = pts_charge_coord(k,1:3)
c1 = NAI_pol_mult( A_center, B_center, power_A, power_B &
, alpha, beta, C_center, n_pt_in )
c = c - Z * c1
enddo
ao_integrals_pt_chrg(i,j) = ao_integrals_pt_chrg(i,j) &
+ ao_coef_normalized_ordered_transp(l,j) &
* ao_coef_normalized_ordered_transp(m,i) * c
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
! endif
! IF(do_pseudo) THEN
! ao_integrals_pt_chrg += ao_pseudo_integrals
! ENDIF
! endif
! if (write_ao_integrals_pt_chrg) then
! call ezfio_set_ao_one_e_ints_ao_integrals_pt_chrg(ao_integrals_pt_chrg)
! print *, 'AO N-e integrals written to disk'
! endif
END_PROVIDER

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ao_two_e_erf_ints
mo_one_e_ints
ao_many_one_e_ints
dft_utils_in_r
tc_keywords

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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.

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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
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_2e_j1, j1b_gauss_2e_j2
PROVIDE j1b_type
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_type .eq. 1 ) then
!print *, ' j1b type 1 is added'
integral = integral + j1b_gauss_2e_j1(i, k, j, l)
elseif( j1b_type .eq. 2 ) then
!print *, ' j1b type 2 is added'
integral = integral + j1b_gauss_2e_j2(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

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BEGIN_PROVIDER [ double precision, expo_j_xmu_1gauss ]
&BEGIN_PROVIDER [ double precision, coef_j_xmu_1gauss ]
implicit none
BEGIN_DOC
! Upper bound long range fit of F(x) = x * (1 - erf(x)) - 1/sqrt(pi) * exp(-x**2)
!
! with a single gaussian.
!
! Such a function can be used to screen integrals with F(x).
END_DOC
expo_j_xmu_1gauss = 0.5d0
coef_j_xmu_1gauss = 1.d0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, expo_erfc_gauss ]
implicit none
expo_erfc_gauss = 1.41211d0
END_PROVIDER
BEGIN_PROVIDER [ double precision, expo_erfc_mu_gauss ]
implicit none
expo_erfc_mu_gauss = expo_erfc_gauss * mu_erf * mu_erf
END_PROVIDER
BEGIN_PROVIDER [ double precision, expo_good_j_mu_1gauss ]
&BEGIN_PROVIDER [ double precision, coef_good_j_mu_1gauss ]
implicit none
BEGIN_DOC
! exponent of Gaussian in order to obtain an upper bound of J(r12,mu)
!
! Can be used to scree integrals with J(r12,mu)
END_DOC
expo_good_j_mu_1gauss = 2.D0 * mu_erf * expo_j_xmu_1gauss
coef_good_j_mu_1gauss = 0.5d0/mu_erf * coef_j_xmu_1gauss
END_PROVIDER
BEGIN_PROVIDER [ double precision, expo_j_xmu, (n_fit_1_erf_x) ]
implicit none
BEGIN_DOC
! F(x) = x * (1 - erf(x)) - 1/sqrt(pi) * exp(-x**2) is fitted with a gaussian and a Slater
!
! \approx - 1/sqrt(pi) * exp(-alpha * x ) exp(-beta * x**2)
!
! where alpha = expo_j_xmu(1) and beta = expo_j_xmu(2)
END_DOC
expo_j_xmu(1) = 1.7477d0
expo_j_xmu(2) = 0.668662d0
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, expo_gauss_j_mu_x, (ng_fit_jast)]
&BEGIN_PROVIDER [double precision, coef_gauss_j_mu_x, (ng_fit_jast)]
BEGIN_DOC
!
! J(mu,r12) = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2) is expressed as
!
! J(mu,r12) = 0.5/mu * F(r12*mu) where F(x) = x * (1 - erf(x)) - 1/sqrt(pi) * exp(-x**2)
!
! F(x) is fitted by - 1/sqrt(pi) * exp(-alpha * x) exp(-beta * x^2) (see expo_j_xmu)
!
! The slater function exp(-alpha * x) is fitted with n_max_fit_slat gaussians
!
! See Appendix 2 of JCP 154, 084119 (2021)
!
END_DOC
implicit none
integer :: i
double precision :: tmp
double precision :: expos(ng_fit_jast), alpha, beta
if(ng_fit_jast .eq. 1) then
coef_gauss_j_mu_x = (/ -0.47947881d0 /)
expo_gauss_j_mu_x = (/ 3.4987848d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x(i) = tmp * expo_gauss_j_mu_x(i)
enddo
elseif(ng_fit_jast .eq. 2) then
coef_gauss_j_mu_x = (/ -0.18390742d0, -0.35512656d0 /)
expo_gauss_j_mu_x = (/ 31.9279947d0 , 2.11428789d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x(i) = tmp * expo_gauss_j_mu_x(i)
enddo
elseif(ng_fit_jast .eq. 3) then
coef_gauss_j_mu_x = (/ -0.07501725d0, -0.28499012d0, -0.1953932d0 /)
expo_gauss_j_mu_x = (/ 206.74058566d0, 1.72974157d0, 11.18735164d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x(i) = tmp * expo_gauss_j_mu_x(i)
enddo
elseif(ng_fit_jast .eq. 5) then
coef_gauss_j_mu_x = (/ -0.01832955d0 , -0.10188952d0 , -0.20710858d0 , -0.18975032d0 , -0.04641657d0 /)
expo_gauss_j_mu_x = (/ 4.33116687d+03, 2.61292842d+01, 1.43447161d+00, 4.92767426d+00, 2.10654699d+02 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x(i) = tmp * expo_gauss_j_mu_x(i)
enddo
elseif(ng_fit_jast .eq. 6) then
coef_gauss_j_mu_x = (/ -0.08783664d0 , -0.16088711d0 , -0.18464486d0 , -0.0368509d0 , -0.08130028d0 , -0.0126972d0 /)
expo_gauss_j_mu_x = (/ 4.09729729d+01, 7.11620618d+00, 2.03692338d+00, 4.10831731d+02, 1.12480198d+00, 1.00000000d+04 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x(i) = tmp * expo_gauss_j_mu_x(i)
enddo
elseif(ng_fit_jast .eq. 7) then
coef_gauss_j_mu_x = (/ -0.01756495d0 , -0.01023623d0 , -0.06548959d0 , -0.03539446d0 , -0.17150646d0 , -0.15071096d0 , -0.11326834d0 /)
expo_gauss_j_mu_x = (/ 9.88572565d+02, 1.21363371d+04, 3.69794870d+01, 1.67364529d+02, 3.03962934d+00, 1.27854005d+00, 9.76383343d+00 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x(i) = tmp * expo_gauss_j_mu_x(i)
enddo
elseif(ng_fit_jast .eq. 8) then
coef_gauss_j_mu_x = (/ -0.11489205d0 , -0.16008968d0 , -0.12892456d0 , -0.04250838d0 , -0.0718451d0 , -0.02394051d0 , -0.00913353d0 , -0.01285182d0 /)
expo_gauss_j_mu_x = (/ 6.97632442d+00, 2.56010878d+00, 1.22760977d+00, 7.47697124d+01, 2.16104215d+01, 2.96549728d+02, 1.40773328d+04, 1.43335159d+03 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x(i) = tmp * expo_gauss_j_mu_x(i)
enddo
!elseif(ng_fit_jast .eq. 9) then
! coef_gauss_j_mu_x = (/ /)
! expo_gauss_j_mu_x = (/ /)
! tmp = mu_erf * mu_erf
! do i = 1, ng_fit_jast
! expo_gauss_j_mu_x(i) = tmp * expo_gauss_j_mu_x(i)
! enddo
elseif(ng_fit_jast .eq. 20) then
ASSERT(n_max_fit_slat == 20)
alpha = expo_j_xmu(1) * mu_erf
call expo_fit_slater_gam(alpha, expos)
beta = expo_j_xmu(2) * mu_erf * mu_erf
tmp = -1.0d0 / sqrt(dacos(-1.d0))
do i = 1, ng_fit_jast
expo_gauss_j_mu_x(i) = expos(i) + beta
coef_gauss_j_mu_x(i) = tmp * coef_fit_slat_gauss(i)
enddo
else
print *, ' not implemented yet'
stop
endif
tmp = 0.5d0 / mu_erf
do i = 1, ng_fit_jast
coef_gauss_j_mu_x(i) = tmp * coef_gauss_j_mu_x(i)
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, expo_gauss_j_mu_x_2, (ng_fit_jast)]
&BEGIN_PROVIDER [double precision, coef_gauss_j_mu_x_2, (ng_fit_jast)]
BEGIN_DOC
!
! J(mu,r12)^2 = 0.25/mu^2 F(r12*mu)^2
!
! F(x)^2 = 1/pi * exp(-2 * alpha * x) exp(-2 * beta * x^2)
!
! The slater function exp(-2 * alpha * x) is fitted with n_max_fit_slat gaussians
!
! See Appendix 2 of JCP 154, 084119 (2021)
!
END_DOC
implicit none
integer :: i
double precision :: tmp
double precision :: expos(ng_fit_jast), alpha, beta
double precision :: alpha_opt, beta_opt
if(ng_fit_jast .eq. 1) then
coef_gauss_j_mu_x_2 = (/ 0.26699573d0 /)
expo_gauss_j_mu_x_2 = (/ 11.71029824d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x_2(i) = tmp * expo_gauss_j_mu_x_2(i)
enddo
elseif(ng_fit_jast .eq. 2) then
coef_gauss_j_mu_x_2 = (/ 0.11627934d0 , 0.18708824d0 /)
expo_gauss_j_mu_x_2 = (/ 102.41386863d0, 6.36239771d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x_2(i) = tmp * expo_gauss_j_mu_x_2(i)
enddo
elseif(ng_fit_jast .eq. 3) then
coef_gauss_j_mu_x_2 = (/ 0.04947216d0 , 0.14116238d0, 0.12276501d0 /)
expo_gauss_j_mu_x_2 = (/ 635.29701766d0, 4.87696954d0, 33.36745891d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x_2(i) = tmp * expo_gauss_j_mu_x_2(i)
enddo
elseif(ng_fit_jast .eq. 5) then
coef_gauss_j_mu_x_2 = (/ 0.01461527d0 , 0.03257147d0 , 0.08831354d0 , 0.11411794d0 , 0.06858783d0 /)
expo_gauss_j_mu_x_2 = (/ 8.76554470d+03, 4.90224577d+02, 3.68267125d+00, 1.29663940d+01, 6.58240931d+01 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x_2(i) = tmp * expo_gauss_j_mu_x_2(i)
enddo
elseif(ng_fit_jast .eq. 6) then
coef_gauss_j_mu_x_2 = (/ 0.01347632d0 , 0.03929124d0 , 0.06289468d0 , 0.10702493d0 , 0.06999865d0 , 0.02558191d0 /)
expo_gauss_j_mu_x_2 = (/ 1.00000000d+04, 1.20900717d+02, 3.20346191d+00, 8.92157196d+00, 3.28119120d+01, 6.49045808d+02 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x_2(i) = tmp * expo_gauss_j_mu_x_2(i)
enddo
elseif(ng_fit_jast .eq. 7) then
coef_gauss_j_mu_x_2 = (/ 0.05202849d0 , 0.01031081d0 , 0.04699157d0 , 0.01451002d0 , 0.07442576d0 , 0.02692033d0 , 0.09311842d0 /)
expo_gauss_j_mu_x_2 = (/ 3.04469415d+00, 1.40682034d+04, 7.45960945d+01, 1.43067466d+03, 2.16815661d+01, 2.95750306d+02, 7.23471236d+00 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x_2(i) = tmp * expo_gauss_j_mu_x_2(i)
enddo
elseif(ng_fit_jast .eq. 8) then
coef_gauss_j_mu_x_2 = (/ 0.00942115d0 , 0.07332421d0 , 0.0508308d0 , 0.08204949d0 , 0.0404099d0 , 0.03201288d0 , 0.01911313d0 , 0.01114732d0 /)
expo_gauss_j_mu_x_2 = (/ 1.56957321d+04, 1.52867810d+01, 4.36016903d+01, 5.96818956d+00, 2.85535269d+00, 1.36064008d+02, 4.71968910d+02, 1.92022350d+03 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_x_2(i) = tmp * expo_gauss_j_mu_x_2(i)
enddo
!elseif(ng_fit_jast .eq. 9) then
! coef_gauss_j_mu_x_2 = (/ /)
! expo_gauss_j_mu_x_2 = (/ /)
!
! tmp = mu_erf * mu_erf
! do i = 1, ng_fit_jast
! expo_gauss_j_mu_x_2(i) = tmp * expo_gauss_j_mu_x_2(i)
! enddo
elseif(ng_fit_jast .eq. 20) then
ASSERT(n_max_fit_slat == 20)
!alpha_opt = 2.d0 * expo_j_xmu(1)
!beta_opt = 2.d0 * expo_j_xmu(2)
! direct opt
alpha_opt = 3.52751759d0
beta_opt = 1.26214809d0
alpha = alpha_opt * mu_erf
call expo_fit_slater_gam(alpha, expos)
beta = beta_opt * mu_erf * mu_erf
tmp = 1.d0 / dacos(-1.d0)
do i = 1, ng_fit_jast
expo_gauss_j_mu_x_2(i) = expos(i) + beta
coef_gauss_j_mu_x_2(i) = tmp * coef_fit_slat_gauss(i)
enddo
else
print *, ' not implemented yet'
stop
endif
tmp = 0.25d0 / (mu_erf * mu_erf)
do i = 1, ng_fit_jast
coef_gauss_j_mu_x_2(i) = tmp * coef_gauss_j_mu_x_2(i)
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, expo_gauss_j_mu_1_erf, (ng_fit_jast)]
&BEGIN_PROVIDER [double precision, coef_gauss_j_mu_1_erf, (ng_fit_jast)]
BEGIN_DOC
!
! J(mu,r12) x \frac{1 - erf(mu * r12)}{2} =
!
! - \frac{1}{4 \sqrt{\pi} \mu} \exp(-(alpha1 + alpha2) * mu * r12 - (beta1 + beta2) * mu^2 * r12^2)
!
END_DOC
implicit none
integer :: i
double precision :: tmp
double precision :: expos(ng_fit_jast), alpha, beta
double precision :: alpha_opt, beta_opt
if(ng_fit_jast .eq. 1) then
coef_gauss_j_mu_1_erf = (/ -0.47742461d0 /)
expo_gauss_j_mu_1_erf = (/ 8.72255696d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_1_erf(i) = tmp * expo_gauss_j_mu_1_erf(i)
enddo
elseif(ng_fit_jast .eq. 2) then
coef_gauss_j_mu_1_erf = (/ -0.19342649d0, -0.34563835d0 /)
expo_gauss_j_mu_1_erf = (/ 78.66099999d0, 5.04324363d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_1_erf(i) = tmp * expo_gauss_j_mu_1_erf(i)
enddo
elseif(ng_fit_jast .eq. 3) then
coef_gauss_j_mu_1_erf = (/ -0.0802541d0 , -0.27019258d0, -0.20546681d0 /)
expo_gauss_j_mu_1_erf = (/ 504.53350764d0, 4.01408169d0, 26.5758329d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_1_erf(i) = tmp * expo_gauss_j_mu_1_erf(i)
enddo
elseif(ng_fit_jast .eq. 5) then
coef_gauss_j_mu_1_erf = (/ -0.02330531d0 , -0.11888176d0 , -0.16476192d0 , -0.19874713d0 , -0.05889174d0 /)
expo_gauss_j_mu_1_erf = (/ 1.00000000d+04, 4.66067922d+01, 3.04359857d+00, 9.54726649d+00, 3.59796835d+02 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_1_erf(i) = tmp * expo_gauss_j_mu_1_erf(i)
enddo
elseif(ng_fit_jast .eq. 6) then
coef_gauss_j_mu_1_erf = (/ -0.01865654d0 , -0.18319251d0 , -0.06543196d0 , -0.11522778d0 , -0.14825793d0 , -0.03327101d0 /)
expo_gauss_j_mu_1_erf = (/ 1.00000000d+04, 8.05593848d+00, 1.27986190d+02, 2.92674319d+01, 2.93583623d+00, 7.65609148d+02 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_1_erf(i) = tmp * expo_gauss_j_mu_1_erf(i)
enddo
elseif(ng_fit_jast .eq. 7) then
coef_gauss_j_mu_1_erf = (/ -0.11853067d0 , -0.01522824d0 , -0.07419098d0 , -0.022202d0 , -0.12242283d0 , -0.04177571d0 , -0.16983107d0 /)
expo_gauss_j_mu_1_erf = (/ 2.74057056d+00, 1.37626591d+04, 6.65578663d+01, 1.34693031d+03, 1.90547699d+01, 2.69445390d+02, 6.31845879d+00/)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_1_erf(i) = tmp * expo_gauss_j_mu_1_erf(i)
enddo
elseif(ng_fit_jast .eq. 8) then
coef_gauss_j_mu_1_erf = (/ -0.12263328d0 , -0.04965255d0 , -0.15463564d0 , -0.09675781d0 , -0.0807023d0 , -0.02923298d0 , -0.01381381d0 , -0.01675923d0 /)
expo_gauss_j_mu_1_erf = (/ 1.36101994d+01, 1.24908367d+02, 5.29061388d+00, 2.60692516d+00, 3.93396935d+01, 4.43071610d+02, 1.54902240d+04, 1.85170446d+03 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_j_mu_1_erf(i) = tmp * expo_gauss_j_mu_1_erf(i)
enddo
!elseif(ng_fit_jast .eq. 9) then
! coef_gauss_j_mu_1_erf = (/ /)
! expo_gauss_j_mu_1_erf = (/ /)
! tmp = mu_erf * mu_erf
! do i = 1, ng_fit_jast
! expo_gauss_j_mu_1_erf(i) = tmp * expo_gauss_j_mu_1_erf(i)
! enddo
elseif(ng_fit_jast .eq. 20) then
ASSERT(n_max_fit_slat == 20)
!alpha_opt = expo_j_xmu(1) + expo_gauss_1_erf_x(1)
!beta_opt = expo_j_xmu(2) + expo_gauss_1_erf_x(2)
! direct opt
alpha_opt = 2.87875632d0
beta_opt = 1.34801003d0
alpha = alpha_opt * mu_erf
call expo_fit_slater_gam(alpha, expos)
beta = beta_opt * mu_erf * mu_erf
tmp = -1.d0 / dsqrt(dacos(-1.d0))
do i = 1, ng_fit_jast
expo_gauss_j_mu_1_erf(i) = expos(i) + beta
coef_gauss_j_mu_1_erf(i) = tmp * coef_fit_slat_gauss(i)
enddo
else
print *, ' not implemented yet'
stop
endif
tmp = 0.25d0 / mu_erf
do i = 1, ng_fit_jast
coef_gauss_j_mu_1_erf(i) = tmp * coef_gauss_j_mu_1_erf(i)
enddo
END_PROVIDER
! ---
double precision function F_x_j(x)
implicit none
BEGIN_DOC
! F_x_j(x) = dimension-less correlation factor = x (1 - erf(x)) - 1/sqrt(pi) exp(-x^2)
END_DOC
double precision, intent(in) :: x
F_x_j = x * (1.d0 - derf(x)) - 1/dsqrt(dacos(-1.d0)) * dexp(-x**2)
end
double precision function j_mu_F_x_j(x)
implicit none
BEGIN_DOC
! j_mu_F_x_j(x) = correlation factor = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2)
!
! = 1/(2*mu) * F_x_j(mu*x)
END_DOC
double precision :: F_x_j
double precision, intent(in) :: x
j_mu_F_x_j = 0.5d0/mu_erf * F_x_j(x*mu_erf)
end
double precision function j_mu(x)
implicit none
double precision, intent(in) :: x
BEGIN_DOC
! j_mu(x) = correlation factor = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2)
END_DOC
j_mu = 0.5d0* x * (1.d0 - derf(mu_erf*x)) - 0.5d0/( dsqrt(dacos(-1.d0))*mu_erf) * dexp(-(mu_erf*x)*(mu_erf*x))
end
double precision function j_mu_fit_gauss(x)
implicit none
BEGIN_DOC
! j_mu_fit_gauss(x) = correlation factor = 1/2 r12 * (1 - erf(mu*r12)) - 1/(2 sqrt(pi)*mu) exp(-(mu*r12)^2)
!
! but fitted with gaussians
END_DOC
double precision, intent(in) :: x
integer :: i
double precision :: alpha,coef
j_mu_fit_gauss = 0.d0
do i = 1, n_max_fit_slat
alpha = expo_gauss_j_mu_x(i)
coef = coef_gauss_j_mu_x(i)
j_mu_fit_gauss += coef * dexp(-alpha*x*x)
enddo
end
! ---

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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

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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
integer :: i,j,k,l,ii
integer(key_kind) :: idx
real(integral_kind) :: integral
PROVIDE ao_tc_sym_two_e_pot_in_map
!$OMP PARALLEL DO PRIVATE (i,j,k,l,idx,ii,integral)
do l = ao_tc_sym_two_e_pot_cache_min, ao_tc_sym_two_e_pot_cache_max
do k = ao_tc_sym_two_e_pot_cache_min, ao_tc_sym_two_e_pot_cache_max
do j = ao_tc_sym_two_e_pot_cache_min, ao_tc_sym_two_e_pot_cache_max
do i = ao_tc_sym_two_e_pot_cache_min, ao_tc_sym_two_e_pot_cache_max
!DIR$ 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
!$OMP END PARALLEL DO
END_PROVIDER
! ---
subroutine insert_into_ao_tc_sym_two_e_pot_map(n_integrals, buffer_i, buffer_values)
use map_module
implicit none
BEGIN_DOC
! Create new entry into |AO| map
END_DOC
integer, intent(in) :: n_integrals
integer(key_kind), intent(inout) :: buffer_i(n_integrals)
real(integral_kind), intent(inout) :: buffer_values(n_integrals)
call map_append(ao_tc_sym_two_e_pot_map, buffer_i, buffer_values, n_integrals)
end
! ---
double precision function get_ao_tc_sym_two_e_pot(i, j, k, l, map) result(result)
use map_module
implicit none
BEGIN_DOC
! Gets one |AO| two-electron integral from the |AO| map
END_DOC
integer, intent(in) :: i,j,k,l
integer(key_kind) :: idx
type(map_type), intent(inout) :: map
integer :: ii
real(integral_kind) :: tmp
logical, external :: ao_two_e_integral_zero
PROVIDE ao_tc_sym_two_e_pot_in_map ao_tc_sym_two_e_pot_cache ao_tc_sym_two_e_pot_cache_min
!DIR$ 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

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! ---
BEGIN_PROVIDER [ double precision, j1b_gauss_hermII, (ao_num,ao_num)]
BEGIN_DOC
!
! :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, coef1, coef2
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_type j1b_pen j1b_coeff
! --------------------------------------------------------------------------------
! -- 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
if(j1b_type .eq. 1) then
! \tau_1b = \sum_iA -[1 - exp(-alpha_A r_iA^2)]
!$OMP PARALLEL &
!$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, &
!$OMP nucl_num, j1b_pen, j1b_gauss_hermII)
!$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_pen(k1)
C_center1(1:3) = nucl_coord(k1,1:3)
do k2 = 1, nucl_num
gama2 = j1b_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
elseif(j1b_type .eq. 2) then
! \tau_1b = \sum_iA [c_A exp(-alpha_A r_iA^2)]
!$OMP PARALLEL &
!$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 coef1, coef2) &
!$OMP SHARED (ao_num, ao_prim_num, ao_expo_ordered_transp, &
!$OMP ao_power, ao_nucl, nucl_coord, &
!$OMP ao_coef_normalized_ordered_transp, &
!$OMP nucl_num, j1b_pen, j1b_gauss_hermII, &
!$OMP j1b_coeff)
!$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_pen (k1)
coef1 = j1b_coeff(k1)
C_center1(1:3) = nucl_coord(k1,1:3)
do k2 = 1, nucl_num
gama2 = j1b_pen (k2)
coef2 = j1b_coeff(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 * coef1 * coef2 * 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
endif
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
!_____________________________________________________________________________________________________________
!_____________________________________________________________________________________________________________

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! ---
BEGIN_PROVIDER [ double precision, j1b_gauss_hermI, (ao_num,ao_num)]
BEGIN_DOC
!
! :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, coef
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_type j1b_pen j1b_coeff
! --------------------------------------------------------------------------------
! -- 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
if(j1b_type .eq. 1) then
! \tau_1b = \sum_iA -[1 - exp(-alpha_A r_iA^2)]
!$OMP PARALLEL &
!$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, &
!$OMP nucl_num, j1b_pen, j1b_gauss_hermI)
!$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_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
elseif(j1b_type .eq. 2) then
! \tau_1b = \sum_iA [c_A exp(-alpha_A r_iA^2)]
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i, j, k, l, m, alpha, beta, gama, coef, &
!$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, &
!$OMP nucl_num, j1b_pen, j1b_gauss_hermI, &
!$OMP j1b_coeff)
!$OMP DO SCHEDULE (dynamic)
do j = 1, ao_num
num_A = ao_nucl(j)
power_A(1:3) = ao_power(j,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
do i = 1, ao_num
num_B = ao_nucl(i)
power_B(1:3) = ao_power(i,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
do l = 1, ao_prim_num(j)
alpha = ao_expo_ordered_transp(l,j)
do m = 1, ao_prim_num(i)
beta = ao_expo_ordered_transp(m,i)
c = 0.d0
do k = 1, nucl_num
gama = j1b_pen (k)
coef = j1b_coeff(k)
C_center(1:3) = nucl_coord(k,1:3)
! < XA | exp[-gama r_C^2] | XB >
c1 = int_gauss_r0( A_center, B_center, C_center &
, power_A, power_B, alpha, beta, gama )
! < XA | r_A^2 exp[-gama r_C^2] | XB >
c2 = int_gauss_r2( A_center, B_center, C_center &
, power_A, power_B, alpha, beta, gama )
c = c + 3.d0 * gama * coef * c1 - 2.d0 * gama * gama * coef * c2
enddo
j1b_gauss_hermI(i,j) = j1b_gauss_hermI(i,j) &
+ ao_coef_normalized_ordered_transp(l,j) &
* ao_coef_normalized_ordered_transp(m,i) * c
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
endif
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
!_____________________________________________________________________________________________________________
!_____________________________________________________________________________________________________________

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! ---
BEGIN_PROVIDER [ double precision, j1b_gauss_nonherm, (ao_num,ao_num)]
BEGIN_DOC
!
! j1b_gauss_nonherm(i,j) = \langle \chi_j | - grad \tau_{1b} \cdot grad | \chi_i \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, coef
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_type j1b_pen j1b_coeff
! --------------------------------------------------------------------------------
! -- 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
if(j1b_type .eq. 1) then
! \tau_1b = \sum_iA -[1 - exp(-alpha_A r_iA^2)]
!$OMP PARALLEL &
!$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, &
!$OMP nucl_num, j1b_pen, j1b_gauss_nonherm)
!$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_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
elseif(j1b_type .eq. 2) then
! \tau_1b = \sum_iA [c_A exp(-alpha_A r_iA^2)]
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i, j, k, l, m, alpha, beta, gama, coef, &
!$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, &
!$OMP nucl_num, j1b_pen, j1b_gauss_nonherm, &
!$OMP j1b_coeff)
!$OMP DO SCHEDULE (dynamic)
do j = 1, ao_num
num_A = ao_nucl(j)
power_A(1:3) = ao_power(j,1:3)
A_center(1:3) = nucl_coord(num_A,1:3)
do i = 1, ao_num
num_B = ao_nucl(i)
power_B(1:3) = ao_power(i,1:3)
B_center(1:3) = nucl_coord(num_B,1:3)
do l = 1, ao_prim_num(j)
alpha = ao_expo_ordered_transp(l,j)
do m = 1, ao_prim_num(i)
beta = ao_expo_ordered_transp(m,i)
c = 0.d0
do k = 1, nucl_num
gama = j1b_pen (k)
coef = j1b_coeff(k)
C_center(1:3) = nucl_coord(k,1:3)
! \langle \chi_A | exp[-gama r_C^2] r_C \cdot grad | \chi_B \rangle
c1 = int_gauss_deriv( A_center, B_center, C_center &
, power_A, power_B, alpha, beta, gama )
c = c + 2.d0 * gama * coef * c1
enddo
j1b_gauss_nonherm(i,j) = j1b_gauss_nonherm(i,j) &
+ ao_coef_normalized_ordered_transp(l,j) &
* ao_coef_normalized_ordered_transp(m,i) * c
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
endif
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
!_____________________________________________________________________________________________________________
!_____________________________________________________________________________________________________________

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! ---
BEGIN_PROVIDER [integer, n_gauss_eff_pot]
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
implicit none
n_gauss_eff_pot = ng_fit_jast + 1
END_PROVIDER
! ---
BEGIN_PROVIDER [integer, n_gauss_eff_pot_deriv]
BEGIN_DOC
! V(r12) = -(1 - erf(mu*r12))^2 is expanded in Gaussians as Eqs A11-A20 in JCP 154, 084119 (2021)
END_DOC
implicit none
n_gauss_eff_pot_deriv = ng_fit_jast
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)]
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'
implicit none
integer :: i
! fit of the -0.25 * (1 - erf(mu*x))^2 with n_max_fit_slat gaussians
do i = 1, ng_fit_jast
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(ng_fit_jast+1) = mu_erf * mu_erf
coef_gauss_eff_pot(ng_fit_jast+1) = 1.d0 * mu_erf * inv_sq_pi
END_PROVIDER
! ---
double precision function eff_pot_gauss(x, mu)
BEGIN_DOC
! V(mu,r12) = -0.25 * (1 - erf(mu*r12))^2 + 1/(\sqrt(pi)mu) * exp(-(mu*r12)^2)
END_DOC
implicit none
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)]
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
implicit none
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 * mu_erf
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)
BEGIN_DOC
! fit_1_erf_x(x) = \sum_i c_i exp (-alpha_i x^2) \approx (1 - erf(mu*x))
END_DOC
implicit none
integer :: i
double precision, intent(in) :: x
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, (ng_fit_jast)]
&BEGIN_PROVIDER [double precision, coef_gauss_1_erf_x_2, (ng_fit_jast)]
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
implicit none
integer :: i
double precision :: expos(ng_fit_jast), alpha, beta, tmp
if(ng_fit_jast .eq. 1) then
coef_gauss_1_erf_x_2 = (/ 0.85345277d0 /)
expo_gauss_1_erf_x_2 = (/ 6.23519457d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_1_erf_x_2(i) = tmp * expo_gauss_1_erf_x_2(i)
enddo
elseif(ng_fit_jast .eq. 2) then
coef_gauss_1_erf_x_2 = (/ 0.31030624d0 , 0.64364964d0 /)
expo_gauss_1_erf_x_2 = (/ 55.39184787d0, 3.92151407d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_1_erf_x_2(i) = tmp * expo_gauss_1_erf_x_2(i)
enddo
elseif(ng_fit_jast .eq. 3) then
coef_gauss_1_erf_x_2 = (/ 0.33206082d0 , 0.52347449d0, 0.12605012d0 /)
expo_gauss_1_erf_x_2 = (/ 19.90272209d0, 3.2671671d0 , 336.47320445d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_1_erf_x_2(i) = tmp * expo_gauss_1_erf_x_2(i)
enddo
elseif(ng_fit_jast .eq. 5) then
coef_gauss_1_erf_x_2 = (/ 0.02956716d0, 0.17025555d0, 0.32774114d0, 0.39034764d0, 0.07822781d0 /)
expo_gauss_1_erf_x_2 = (/ 6467.28126d0, 46.9071990d0, 9.09617721d0, 2.76883328d0, 360.367093d0 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_1_erf_x_2(i) = tmp * expo_gauss_1_erf_x_2(i)
enddo
elseif(ng_fit_jast .eq. 6) then
coef_gauss_1_erf_x_2 = (/ 0.18331042d0 , 0.10971118d0 , 0.29949169d0 , 0.34853132d0 , 0.0394275d0 , 0.01874444d0 /)
expo_gauss_1_erf_x_2 = (/ 2.54293498d+01, 1.40317872d+02, 7.14630801d+00, 2.65517675d+00, 1.45142619d+03, 1.00000000d+04 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_1_erf_x_2(i) = tmp * expo_gauss_1_erf_x_2(i)
enddo
elseif(ng_fit_jast .eq. 7) then
coef_gauss_1_erf_x_2 = (/ 0.0213619d0 , 0.03221511d0 , 0.29966689d0 , 0.19178934d0 , 0.06154732d0 , 0.28214555d0 , 0.11125985d0 /)
expo_gauss_1_erf_x_2 = (/ 1.34727067d+04, 1.27166613d+03, 5.52584567d+00, 1.67753218d+01, 2.46145691d+02, 2.47971820d+00, 5.95141293d+01 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_1_erf_x_2(i) = tmp * expo_gauss_1_erf_x_2(i)
enddo
elseif(ng_fit_jast .eq. 8) then
coef_gauss_1_erf_x_2 = (/ 0.28189124d0 , 0.19518669d0 , 0.12161735d0 , 0.24257438d0 , 0.07309656d0 , 0.042435d0 , 0.01926109d0 , 0.02393415d0 /)
expo_gauss_1_erf_x_2 = (/ 4.69795903d+00, 1.21379451d+01, 3.55527053d+01, 2.39227172d+00, 1.14827721d+02, 4.16320213d+02, 1.52813587d+04, 1.78516557d+03 /)
tmp = mu_erf * mu_erf
do i = 1, ng_fit_jast
expo_gauss_1_erf_x_2(i) = tmp * expo_gauss_1_erf_x_2(i)
enddo
!elseif(ng_fit_jast .eq. 9) then
! coef_gauss_1_erf_x_2 = (/ /)
! expo_gauss_1_erf_x_2 = (/ /)
! tmp = mu_erf * mu_erf
! do i = 1, ng_fit_jast
! expo_gauss_1_erf_x_2(i) = tmp * expo_gauss_1_erf_x_2(i)
! enddo
elseif(ng_fit_jast .eq. 20) then
ASSERT(n_max_fit_slat == 20)
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 * mu_erf
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
else
print *, ' not implemented yet'
stop
endif
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

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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

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! ---
double precision function j1b_gauss_2e_j1(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_2e_j1_schwartz
if( ao_prim_num(i) * ao_prim_num(j) * ao_prim_num(k) * ao_prim_num(l) > 1024 ) then
j1b_gauss_2e_j1 = j1b_gauss_2e_j1_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_2e_j1 = 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_j1( 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_2e_j1 = j1b_gauss_2e_j1 + coef4 * ( cx + cy + cz )
enddo ! s
enddo ! r
enddo ! q
enddo ! p
return
end function j1b_gauss_2e_j1
! ---
double precision function j1b_gauss_2e_j1_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_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_j1( 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_2e_j1_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_j1( 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_j1( 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_2e_j1_schwartz = j1b_gauss_2e_j1_schwartz + coef4 * ( cx + cy + cz )
enddo ! s
enddo ! r
enddo ! q
enddo ! p
deallocate( schwartz_kl )
return
end function j1b_gauss_2e_j1_schwartz
! ---
subroutine get_cxcycz_j1( 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
PROVIDE j1b_pen
cx = 0.d0
cy = 0.d0
cz = 0.d0
do ii = 1, nucl_num
expoii = j1b_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_j1
! ---

729
src/ao_tc_eff_map/two_e_1bgauss_j2.irp.f Normal file
View File

@ -0,0 +1,729 @@
! ---
double precision function j1b_gauss_2e_j2(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 c_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
! = [ (1 - erf(mu r12) / r12 ] \sum_A a_A c_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_2e_j2_schwartz
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_2e_j2 = j1b_gauss_2e_j2_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_2e_j2 = 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_j2( 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_2e_j2 = j1b_gauss_2e_j2 + coef4 * ( cx + cy + cz )
enddo ! s
enddo ! r
enddo ! q
enddo ! p
return
end function j1b_gauss_2e_j2
! ---
double precision function j1b_gauss_2e_j2_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 c_A) [ r1A exp(-aA r1A^2) - r2A exp(-aA r2A^2) ]
! = [ (1 - erf(mu r12) / r12 ] \sum_A a_A c_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(:,:)
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_j2( 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_2e_j2_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_j2( 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_j2( 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_2e_j2_schwartz = j1b_gauss_2e_j2_schwartz + coef4 * ( cx + cy + cz )
enddo ! s
enddo ! r
enddo ! q
enddo ! p
deallocate( schwartz_kl )
return
end function j1b_gauss_2e_j2_schwartz
! ---
subroutine get_cxcycz_j2( 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 :: coefii, 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
PROVIDE j1b_pen j1b_coeff
cx = 0.d0
cy = 0.d0
cz = 0.d0
do ii = 1, nucl_num
expoii = j1b_pen (ii)
coefii = j1b_coeff(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 c_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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 c_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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 c_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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 c_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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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 * coefii * 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_j2
! ---

327
src/ao_tc_eff_map/two_e_ints_gauss.irp.f Normal file
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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
!do i = 1, n_gauss_eff_pot-1
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

364
src/ao_tc_eff_map/useful_sub.irp.f Normal file
View File

@ -0,0 +1,364 @@
! ---
!______________________________________________________________________________________________________________________
!______________________________________________________________________________________________________________________
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
!______________________________________________________________________________________________________________________
!______________________________________________________________________________________________________________________
!______________________________________________________________________________________________________________________
!______________________________________________________________________________________________________________________
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
!______________________________________________________________________________________________________________________
!______________________________________________________________________________________________________________________

23
src/ao_two_e_ints/map_integrals.irp.f
View File

@ -142,7 +142,7 @@ subroutine ao_idx2_sq(i,j,ij)
ij=i*i
endif
end
subroutine idx2_tri_int(i,j,ij)
implicit none
integer, intent(in) :: i,j
@ -152,7 +152,7 @@ subroutine idx2_tri_int(i,j,ij)
q = min(i,j)
ij = q+ishft(p*p-p,-1)
end
subroutine ao_idx2_tri_key(i,j,ij)
use map_module
implicit none
@ -163,8 +163,8 @@ subroutine ao_idx2_tri_key(i,j,ij)
q = min(i,j)
ij = q+ishft(p*p-p,-1)
end
subroutine two_e_integrals_index_2fold(i,j,k,l,i1)
subroutine two_e_integrals_index_2fold(i,j,k,l,i1)
use map_module
implicit none
integer, intent(in) :: i,j,k,l
@ -176,7 +176,7 @@ subroutine two_e_integrals_index_2fold(i,j,k,l,i1)
call ao_idx2_tri_key(ik,jl,i1)
end
subroutine ao_idx2_sq_rev(i,k,ik)
subroutine ao_idx2_sq_rev(i,k,ik)
BEGIN_DOC
! reverse square compound index
END_DOC
@ -321,14 +321,15 @@ BEGIN_PROVIDER [ double precision, ao_integrals_cache, (0:64*64*64*64) ]
!$OMP END PARALLEL DO
END_PROVIDER
! ---
double precision function get_ao_two_e_integral(i,j,k,l,map) result(result)
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
@ -398,7 +399,7 @@ BEGIN_PROVIDER [ complex*16, ao_integrals_cache_periodic, (0:64*64*64*64) ]
tmp_im = 0.d0
integral = dcmplx(tmp_re,tmp_im)
endif
ii = l-ao_integrals_cache_min
ii = ior( shiftl(ii,6), k-ao_integrals_cache_min)
ii = ior( shiftl(ii,6), j-ao_integrals_cache_min)
@ -473,7 +474,7 @@ subroutine get_ao_two_e_integrals(j,k,l,sze,out_val)
BEGIN_DOC
! Gets multiple AO bi-electronic integral from the AO map .
! All i are retrieved for j,k,l fixed.
! physicist convention : <ij|kl>
! physicist convention : <ij|kl>
END_DOC
implicit none
integer, intent(in) :: j,k,l, sze
@ -502,7 +503,7 @@ subroutine get_ao_two_e_integrals_periodic(j,k,l,sze,out_val)
BEGIN_DOC
! Gets multiple AO bi-electronic integral from the AO map .
! All i are retrieved for j,k,l fixed.
! physicist convention : <ij|kl>
! physicist convention : <ij|kl>
END_DOC
implicit none
integer, intent(in) :: j,k,l, sze

1
src/ao_two_e_ints/two_e_integrals.irp.f
View File

@ -101,6 +101,7 @@ double precision function ao_two_e_integral(i,j,k,l)
endif
endif
end
double precision function ao_two_e_integral_schwartz_accel(i,j,k,l)

3
src/basis_correction/TODO
View File

@ -1 +1,4 @@
change all correlation functionals with the pbe_on_top general
factor 2 in two-rdm involved in:
on-top, mu(r), pbe-on-top, sc_basis_corr and so on
casscf : state_av_act_2_rdm_spin_trace_mo

14
src/basis_correction/pbe_on_top.irp.f
View File

@ -41,13 +41,13 @@
if(mu_of_r_potential == "cas_ful")then
! You take the on-top of the CAS wave function which is computed with mu(r)
on_top = on_top_cas_mu_r(ipoint,istate)
on_top = on_top_cas_mu_r(ipoint,istate)
else
! You take the on-top of the CAS wave function computed separately
on_top = total_cas_on_top_density(ipoint,istate)
endif
! We take the extrapolated on-top pair density * 2 because of normalization
on_top_extrap = 2.d0 * mu_correction_of_on_top(mu,on_top)
! We take the extrapolated on-top pair density
on_top_extrap = mu_correction_of_on_top(mu,on_top)
call ec_md_pbe_on_top_general(mu,rho_a,rho_b,grad_rho_a,grad_rho_b,on_top_extrap,eps_c_md_on_top_PBE)
@ -108,8 +108,8 @@
! You take the on-top of the CAS wave function computed separately
on_top = total_cas_on_top_density(ipoint,istate)
endif
! We take the extrapolated on-top pair density * 2 because of normalization
on_top_extrap = 2.d0 * mu_correction_of_on_top(mu,on_top)
! We take the extrapolated on-top pair density
on_top_extrap = mu_correction_of_on_top(mu,on_top)
call ec_md_pbe_on_top_general(mu,rho_a,rho_b,grad_rho_a,grad_rho_b,on_top_extrap,eps_c_md_on_top_PBE)
@ -170,8 +170,8 @@
! You take the on-top of the CAS wave function computed separately
on_top = total_cas_on_top_density(ipoint,istate)
endif
! We DO NOT take the extrapolated on-top pair density, but there is * 2 because of normalization
on_top_extrap = 2.d0 * on_top
! We DO NOT take the extrapolated on-top pair density
on_top_extrap = on_top
call ec_md_pbe_on_top_general(mu,rho_a,rho_b,grad_rho_a,grad_rho_b,on_top_extrap,eps_c_md_on_top_PBE)

6
src/basis_correction/print_routine.irp.f
View File

@ -18,7 +18,7 @@ subroutine print_basis_correction
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*, ' Journal of Chemical Physics 152, 174104 (2020) '
print*, '****************************************'
print*, '****************************************'
print*, 'mu_of_r_potential = ',mu_of_r_potential
@ -56,14 +56,14 @@ subroutine print_basis_correction
print*,''
print*,'********************************************'
print*,'********************************************'
print*,'+) PBE-on-top Ecmd functional : (??????? REF-SCF ??????????)'
print*,'+) PBE-on-top Ecmd functional : JCP, 152, 174104 (2020) '
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-on-top no spin polarization Ecmd functional : JCP, 152, 174104 (2020)'
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)

4
src/bi_ort_ints/NEED Normal file
View File

@ -0,0 +1,4 @@
non_h_ints_mu
ao_tc_eff_map
bi_ortho_mos
tc_keywords

25
src/bi_ort_ints/README.rst Normal file
View File

@ -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

44
src/bi_ort_ints/bi_ort_ints.irp.f Normal file
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@ -0,0 +1,44 @@
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 = 10
my_n_pt_a_grid = 14
touch my_grid_becke my_n_pt_r_grid my_n_pt_a_grid
call test_3e
end
subroutine test_3e
implicit none
integer :: i,k,j,l,m,n,ipoint
double precision :: accu, contrib,new,ref
i = 1
k = 1
accu = 0.d0
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do l = 1, mo_num
do m = 1, mo_num
do n = 1, mo_num
call give_integrals_3_body_bi_ort(n, l, k, m, j, i, new)
call give_integrals_3_body_bi_ort_old(n, l, k, m, j, i, ref)
contrib = dabs(new - ref)
accu += contrib
if(contrib .gt. 1.d-10)then
print*,'pb !!'
print*,i,k,j,l,m,n
print*,ref,new,contrib
endif
enddo
enddo
enddo
enddo
enddo
enddo
print*,'accu = ',accu/dble(mo_num)**6
end

153
src/bi_ort_ints/biorthog_mo_for_h.irp.f Normal file
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@ -0,0 +1,153 @@
! ---
double precision function bi_ortho_mo_coul_ints(l, k, j, i)
BEGIN_DOC
!
! < mo^L_k mo^L_l | 1/r12 | mo^R_i mo^R_j >
!
END_DOC
implicit none
integer, intent(in) :: i, j, k, l
integer :: m, n, p, q
bi_ortho_mo_coul_ints = 0.d0
do m = 1, ao_num
do p = 1, ao_num
do n = 1, ao_num
do q = 1, ao_num
! p1h1p2h2 l1 l2 r1 r2
bi_ortho_mo_coul_ints += ao_two_e_coul(n,q,m,p) * mo_l_coef(m,l) * mo_l_coef(n,k) * mo_r_coef(p,j) * mo_r_coef(q,i)
enddo
enddo
enddo
enddo
end function bi_ortho_mo_coul_ints
! ---
! TODO :: transform into DEGEMM
BEGIN_PROVIDER [double precision, mo_bi_ortho_coul_e_chemist, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! mo_bi_ortho_coul_e_chemist(k,i,l,j) = < k l | 1/r12 | i j > where i,j are right MOs and k,l are left MOs
!
END_DOC
implicit none
integer :: i, j, k, l, m, n, p, q
double precision, allocatable :: mo_tmp_1(:,:,:,:), mo_tmp_2(:,:,:,:)
allocate(mo_tmp_1(mo_num,ao_num,ao_num,ao_num))
mo_tmp_1 = 0.d0
do m = 1, ao_num
do p = 1, ao_num
do n = 1, ao_num
do q = 1, ao_num
do k = 1, mo_num
! (k n|p m) = sum_q c_qk * (q n|p m)
mo_tmp_1(k,n,p,m) += mo_l_coef_transp(k,q) * ao_two_e_coul(q,n,p,m)
enddo
enddo
enddo
enddo
enddo
allocate(mo_tmp_2(mo_num,mo_num,ao_num,ao_num))
mo_tmp_2 = 0.d0
do m = 1, ao_num
do p = 1, ao_num
do n = 1, ao_num
do i = 1, mo_num
do k = 1, mo_num
! (k i|p m) = sum_n c_ni * (k n|p m)
mo_tmp_2(k,i,p,m) += mo_r_coef_transp(i,n) * mo_tmp_1(k,n,p,m)
enddo
enddo
enddo
enddo
enddo
deallocate(mo_tmp_1)
allocate(mo_tmp_1(mo_num,mo_num,mo_num,ao_num))
mo_tmp_1 = 0.d0
do m = 1, ao_num
do p = 1, ao_num
do l = 1, mo_num
do i = 1, mo_num
do k = 1, mo_num
mo_tmp_1(k,i,l,m) += mo_l_coef_transp(l,p) * mo_tmp_2(k,i,p,m)
enddo
enddo
enddo
enddo
enddo
deallocate(mo_tmp_2)
mo_bi_ortho_coul_e_chemist = 0.d0
do m = 1, ao_num
do j = 1, mo_num
do l = 1, mo_num
do i = 1, mo_num
do k = 1, mo_num
mo_bi_ortho_coul_e_chemist(k,i,l,j) += mo_r_coef_transp(j,m) * mo_tmp_1(k,i,l,m)
enddo
enddo
enddo
enddo
enddo
deallocate(mo_tmp_1)
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, mo_bi_ortho_coul_e, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! mo_bi_ortho_coul_e(k,l,i,j) = < k l | 1/r12 | i j > where i,j are right MOs and k,l are left MOs
!
END_DOC
implicit none
integer :: i, j, k, l
do j = 1, mo_num
do i = 1, mo_num
do l = 1, mo_num
do k = 1, mo_num
! < k l | V12 | i j > (k i|l j)
mo_bi_ortho_coul_e(k,l,i,j) = mo_bi_ortho_coul_e_chemist(k,i,l,j)
enddo
enddo
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, mo_bi_ortho_one_e, (mo_num, mo_num)]
BEGIN_DOC
!
! mo_bi_ortho_one_e(k,i) = < MO^L_k | h_c | MO^R_i >
!
END_DOC
implicit none
call ao_to_mo_bi_ortho(ao_one_e_integrals, ao_num, mo_bi_ortho_one_e , mo_num)
END_PROVIDER
! ---

75
src/bi_ort_ints/one_e_bi_ort.irp.f Normal file
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@ -0,0 +1,75 @@
! ---
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_type
if( (j1b_type .eq. 1) .or. (j1b_type .eq. 2) ) 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)]
BEGIN_DOC
!
! mo_bi_ortho_tc_one_e(k,i) = <MO^L_k | h_c | MO^R_i>
!
END_DOC
implicit none
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 Left MO_i * x Right MO_j
! array of the integrals of Left MO_i * y Right MO_j
! array of the integrals of Left MO_i * z Right 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

318
src/bi_ort_ints/semi_num_ints_mo.irp.f Normal file
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@ -0,0 +1,318 @@
! ---
! TODO :: optimization : transform into a DGEMM
BEGIN_PROVIDER [ double precision, mo_v_ki_bi_ortho_erf_rk_cst_mu, (mo_num, mo_num, n_points_final_grid)]
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
implicit none
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)
!$OMP DO SCHEDULE (dynamic)
do ipoint = 1, n_points_final_grid
call ao_to_mo_bi_ortho( v_ij_erf_rk_cst_mu (1,1,ipoint), size(v_ij_erf_rk_cst_mu, 1) &
, mo_v_ki_bi_ortho_erf_rk_cst_mu(1,1,ipoint), size(mo_v_ki_bi_ortho_erf_rk_cst_mu, 1) )
enddo
!$OMP END DO
!$OMP END PARALLEL
mo_v_ki_bi_ortho_erf_rk_cst_mu = mo_v_ki_bi_ortho_erf_rk_cst_mu * 0.5d0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, mo_v_ki_bi_ortho_erf_rk_cst_mu_transp, (n_points_final_grid, mo_num, mo_num)]
BEGIN_DOC
!
! int dr phi_i(r) phi_j(r) (erf(mu(R) |r - R|) - 1)/(2|r - R|) on the BI-ORTHO MO basis
!
END_DOC
implicit none
integer :: ipoint, i, j
do i = 1, mo_num
do j = 1, mo_num
do ipoint = 1, n_points_final_grid
mo_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,j,i) = mo_v_ki_bi_ortho_erf_rk_cst_mu(j,i,ipoint)
enddo
enddo
enddo
! FREE mo_v_ki_bi_ortho_erf_rk_cst_mu
END_PROVIDER
! ---
! TODO :: optimization : transform into a DGEMM
BEGIN_PROVIDER [ double precision, mo_x_v_ki_bi_ortho_erf_rk_cst_mu, (mo_num, mo_num, 3, n_points_final_grid)]
BEGIN_DOC
!
! mo_x_v_ki_bi_ortho_erf_rk_cst_mu(k,i,m,ip) = int dr x(m) * chi_k(r) phi_i(r) (erf(mu |r - R_ip|) - 1)/2|r - R_ip| on the BI-ORTHO MO basis
!
! where chi_k(r)/phi_i(r) are left/right MOs, m=1 => x(m) = x, m=2 => x(m) = y, m=3 => x(m) = z,
!
! R_ip = the "ip"-th point of the DFT Grid
!
END_DOC
implicit none
integer :: ipoint
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (ipoint) &
!$OMP SHARED (n_points_final_grid,x_v_ij_erf_rk_cst_mu_transp,mo_x_v_ki_bi_ortho_erf_rk_cst_mu)
!$OMP DO SCHEDULE (dynamic)
do ipoint = 1, n_points_final_grid
call ao_to_mo_bi_ortho( x_v_ij_erf_rk_cst_mu_transp (1,1,1,ipoint), size(x_v_ij_erf_rk_cst_mu_transp, 1) &
, mo_x_v_ki_bi_ortho_erf_rk_cst_mu(1,1,1,ipoint), size(mo_x_v_ki_bi_ortho_erf_rk_cst_mu, 1) )
call ao_to_mo_bi_ortho( x_v_ij_erf_rk_cst_mu_transp (1,1,2,ipoint), size(x_v_ij_erf_rk_cst_mu_transp, 1) &
, mo_x_v_ki_bi_ortho_erf_rk_cst_mu(1,1,2,ipoint), size(mo_x_v_ki_bi_ortho_erf_rk_cst_mu, 1) )
call ao_to_mo_bi_ortho( x_v_ij_erf_rk_cst_mu_transp (1,1,3,ipoint), size(x_v_ij_erf_rk_cst_mu_transp, 1) &
, mo_x_v_ki_bi_ortho_erf_rk_cst_mu(1,1,3,ipoint), size(mo_x_v_ki_bi_ortho_erf_rk_cst_mu, 1) )
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, int2_grad1_u12_ao_transp, (ao_num, ao_num, 3, n_points_final_grid)]
implicit none
integer :: i, j, ipoint
double precision :: wall0, wall1
print *, ' providing int2_grad1_u12_ao_transp ...'
call wall_time(wall0)
if(test_cycle_tc)then
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, ao_num
int2_grad1_u12_ao_transp(j,i,1,ipoint) = int2_grad1_u12_ao_test(j,i,ipoint,1)
int2_grad1_u12_ao_transp(j,i,2,ipoint) = int2_grad1_u12_ao_test(j,i,ipoint,2)
int2_grad1_u12_ao_transp(j,i,3,ipoint) = int2_grad1_u12_ao_test(j,i,ipoint,3)
enddo
enddo
enddo
else
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, ao_num
int2_grad1_u12_ao_transp(j,i,1,ipoint) = int2_grad1_u12_ao(j,i,ipoint,1)
int2_grad1_u12_ao_transp(j,i,2,ipoint) = int2_grad1_u12_ao(j,i,ipoint,2)
int2_grad1_u12_ao_transp(j,i,3,ipoint) = int2_grad1_u12_ao(j,i,ipoint,3)
enddo
enddo
enddo
endif
call wall_time(wall1)
print *, ' wall time for int2_grad1_u12_ao_transp ', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_grad1_u12_bimo_transp, (mo_num, mo_num, 3, n_points_final_grid)]
implicit none
integer :: ipoint
double precision :: wall0, wall1
!print *, ' providing int2_grad1_u12_bimo_transp'
call wall_time(wall0)
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (ipoint) &
!$OMP SHARED (n_points_final_grid,int2_grad1_u12_ao_transp,int2_grad1_u12_bimo_transp)
!$OMP DO SCHEDULE (dynamic)
do ipoint = 1, n_points_final_grid
call ao_to_mo_bi_ortho( int2_grad1_u12_ao_transp (1,1,1,ipoint), size(int2_grad1_u12_ao_transp , 1) &
, int2_grad1_u12_bimo_transp(1,1,1,ipoint), size(int2_grad1_u12_bimo_transp, 1) )
call ao_to_mo_bi_ortho( int2_grad1_u12_ao_transp (1,1,2,ipoint), size(int2_grad1_u12_ao_transp , 1) &
, int2_grad1_u12_bimo_transp(1,1,2,ipoint), size(int2_grad1_u12_bimo_transp, 1) )
call ao_to_mo_bi_ortho( int2_grad1_u12_ao_transp (1,1,3,ipoint), size(int2_grad1_u12_ao_transp , 1) &
, int2_grad1_u12_bimo_transp(1,1,3,ipoint), size(int2_grad1_u12_bimo_transp, 1) )
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
!print *, ' Wall time for providing int2_grad1_u12_bimo_transp',wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_grad1_u12_bimo_t, (n_points_final_grid,3, mo_num, mo_num )]
implicit none
integer :: i, j, ipoint
do ipoint = 1, n_points_final_grid
do i = 1, mo_num
do j = 1, mo_num
int2_grad1_u12_bimo_t(ipoint,1,j,i) = int2_grad1_u12_bimo_transp(j,i,1,ipoint)
int2_grad1_u12_bimo_t(ipoint,2,j,i) = int2_grad1_u12_bimo_transp(j,i,2,ipoint)
int2_grad1_u12_bimo_t(ipoint,3,j,i) = int2_grad1_u12_bimo_transp(j,i,3,ipoint)
enddo
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, int2_grad1_u12_ao_t, (n_points_final_grid, 3, ao_num, ao_num)]
implicit none
integer :: i, j, ipoint
do ipoint = 1, n_points_final_grid
do i = 1, ao_num
do j = 1, ao_num
int2_grad1_u12_ao_t(ipoint,1,j,i) = int2_grad1_u12_ao(j,i,ipoint,1)
int2_grad1_u12_ao_t(ipoint,2,j,i) = int2_grad1_u12_ao(j,i,ipoint,2)
int2_grad1_u12_ao_t(ipoint,3,j,i) = int2_grad1_u12_ao(j,i,ipoint,3)
enddo
enddo
enddo
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, ipoint
do i = 1, mo_num
do j = 1, mo_num
do ipoint = 1, n_points_final_grid
mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,1,j,i) = mo_x_v_ki_bi_ortho_erf_rk_cst_mu(j,i,1,ipoint)
mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,2,j,i) = mo_x_v_ki_bi_ortho_erf_rk_cst_mu(j,i,2,ipoint)
mo_x_v_ki_bi_ortho_erf_rk_cst_mu_transp(ipoint,3,j,i) = mo_x_v_ki_bi_ortho_erf_rk_cst_mu(j,i,3,ipoint)
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) \frac{(1 - erf(mu |r-R_ip|))}{2|r-R_ip|} (x(m)-R_ip(m)) 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
! ---

366
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! ---
BEGIN_PROVIDER [ double precision, three_e_3_idx_direct_bi_ort, (mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator ON A BI ORTHONORMAL BASIS for the direct terms
!
! three_e_3_idx_direct_bi_ort(m,j,i) = <mji|-L|mji>
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, m
double precision :: integral, wall1, wall0
three_e_3_idx_direct_bi_ort = 0.d0
print *, ' Providing the three_e_3_idx_direct_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,m,integral) &
!$OMP SHARED (mo_num,three_e_3_idx_direct_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do j = 1, mo_num
do m = j, mo_num
call give_integrals_3_body_bi_ort(m, j, i, m, j, i, integral)
three_e_3_idx_direct_bi_ort(m,j,i) = -1.d0 * integral
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do i = 1, mo_num
do j = 1, mo_num
do m = 1, j
three_e_3_idx_direct_bi_ort(m,j,i) = three_e_3_idx_direct_bi_ort(j,m,i)
enddo
enddo
enddo
call wall_time(wall1)
print *, ' wall time for three_e_3_idx_direct_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_3_idx_cycle_1_bi_ort, (mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator ON A BI ORTHONORMAL BASIS for the first cyclic permutation
!
! three_e_3_idx_cycle_1_bi_ort(m,j,i) = <mji|-L|jim>
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, m
double precision :: integral, wall1, wall0
three_e_3_idx_cycle_1_bi_ort = 0.d0
print *, ' Providing the three_e_3_idx_cycle_1_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,m,integral) &
!$OMP SHARED (mo_num,three_e_3_idx_cycle_1_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do j = 1, mo_num
do m = j, mo_num
call give_integrals_3_body_bi_ort(m, j, i, j, i, m, integral)
three_e_3_idx_cycle_1_bi_ort(m,j,i) = -1.d0 * integral
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do i = 1, mo_num
do j = 1, mo_num
do m = 1, j
three_e_3_idx_cycle_1_bi_ort(m,j,i) = three_e_3_idx_cycle_1_bi_ort(j,m,i)
enddo
enddo
enddo
call wall_time(wall1)
print *, ' wall time for three_e_3_idx_cycle_1_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_3_idx_cycle_2_bi_ort, (mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator ON A BI ORTHONORMAL BASIS for the second cyclic permutation
!
! three_e_3_idx_direct_bi_ort(m,j,i) = <mji|-L|imj>
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, m
double precision :: integral, wall1, wall0
three_e_3_idx_cycle_2_bi_ort = 0.d0
print *, ' Providing the three_e_3_idx_cycle_2_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,m,integral) &
!$OMP SHARED (mo_num,three_e_3_idx_cycle_2_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do j = 1, mo_num
do m = j, mo_num
call give_integrals_3_body_bi_ort(m, j, i, i, m, j, integral)
three_e_3_idx_cycle_2_bi_ort(m,j,i) = -1.d0 * integral
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do i = 1, mo_num
do j = 1, mo_num
do m = 1, j
three_e_3_idx_cycle_2_bi_ort(m,j,i) = three_e_3_idx_cycle_2_bi_ort(j,m,i)
enddo
enddo
enddo
call wall_time(wall1)
print *, ' wall time for three_e_3_idx_cycle_2_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_3_idx_exch23_bi_ort, (mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator ON A BI ORTHONORMAL BASIS for the permutations of particle 2 and 3
!
! three_e_3_idx_exch23_bi_ort(m,j,i) = <mji|-L|jmi>
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, m
double precision :: integral, wall1, wall0
three_e_3_idx_exch23_bi_ort = 0.d0
print*,'Providing the three_e_3_idx_exch23_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,m,integral) &
!$OMP SHARED (mo_num,three_e_3_idx_exch23_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do j = 1, mo_num
do m = j, mo_num
call give_integrals_3_body_bi_ort(m, j, i, j, m, i, integral)
three_e_3_idx_exch23_bi_ort(m,j,i) = -1.d0 * integral
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do i = 1, mo_num
do j = 1, mo_num
do m = 1, j
three_e_3_idx_exch23_bi_ort(m,j,i) = three_e_3_idx_exch23_bi_ort(j,m,i)
enddo
enddo
enddo
call wall_time(wall1)
print *, ' wall time for three_e_3_idx_exch23_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_3_idx_exch13_bi_ort, (mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator ON A BI ORTHONORMAL BASIS for the permutations of particle 1 and 3
!
! three_e_3_idx_exch13_bi_ort(m,j,i) = <mji|-L|ijm>
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i,j,m
double precision :: integral, wall1, wall0
three_e_3_idx_exch13_bi_ort = 0.d0
print *, ' Providing the three_e_3_idx_exch13_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,m,integral) &
!$OMP SHARED (mo_num,three_e_3_idx_exch13_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do j = 1, mo_num
do m = j, mo_num
call give_integrals_3_body_bi_ort(m, j, i, i, j, m,integral)
three_e_3_idx_exch13_bi_ort(m,j,i) = -1.d0 * integral
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do i = 1, mo_num
do j = 1, mo_num
do m = 1, j
three_e_3_idx_exch13_bi_ort(m,j,i) = three_e_3_idx_exch13_bi_ort(j,m,i)
enddo
enddo
enddo
call wall_time(wall1)
print *, ' wall time for three_e_3_idx_exch13_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_3_idx_exch12_bi_ort, (mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator ON A BI ORTHONORMAL BASIS for the permutations of particle 1 and 2
!
! three_e_3_idx_exch12_bi_ort(m,j,i) = <mji|-L|mij>
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, m
double precision :: integral, wall1, wall0
three_e_3_idx_exch12_bi_ort = 0.d0
print *, ' Providing the three_e_3_idx_exch12_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,m,integral) &
!$OMP SHARED (mo_num,three_e_3_idx_exch12_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, j, i, m, i, j, integral)
three_e_3_idx_exch12_bi_ort(m,j,i) = -1.d0 * integral
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_3_idx_exch12_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_3_idx_exch12_bi_ort_new, (mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator ON A BI ORTHONORMAL BASIS for the permutations of particle 1 and 2
!
! three_e_3_idx_exch12_bi_ort_new(m,j,i) = <mji|-L|mij>
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, m
double precision :: integral, wall1, wall0
three_e_3_idx_exch12_bi_ort_new = 0.d0
print *, ' Providing the three_e_3_idx_exch12_bi_ort_new ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,m,integral) &
!$OMP SHARED (mo_num,three_e_3_idx_exch12_bi_ort_new)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do j = 1, mo_num
do m = j, mo_num
call give_integrals_3_body_bi_ort(m, j, i, m, i, j, integral)
three_e_3_idx_exch12_bi_ort_new(m,j,i) = -1.d0 * integral
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
do i = 1, mo_num
do j = 1, mo_num
do m = 1, j
three_e_3_idx_exch12_bi_ort_new(m,j,i) = three_e_3_idx_exch12_bi_ort_new(j,m,i)
enddo
enddo
enddo
call wall_time(wall1)
print *, ' wall time for three_e_3_idx_exch12_bi_ort_new', wall1 - wall0
END_PROVIDER
! ---

284
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! ---
BEGIN_PROVIDER [ double precision, three_e_4_idx_direct_bi_ort, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF SINGLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_4_idx_direct_bi_ort(m,j,k,i) = <mjk|-L|mji> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m
double precision :: integral, wall1, wall0
three_e_4_idx_direct_bi_ort = 0.d0
print *, ' Providing the three_e_4_idx_direct_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,integral) &
!$OMP SHARED (mo_num,three_e_4_idx_direct_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, j, k, m, j, i, integral)
three_e_4_idx_direct_bi_ort(m,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_4_idx_direct_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_4_idx_cycle_1_bi_ort, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE FIRST CYCLIC PERMUTATION TERMS OF SINGLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_4_idx_cycle_1_bi_ort(m,j,k,i) = <mjk|-L|jim> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m
double precision :: integral, wall1, wall0
three_e_4_idx_cycle_1_bi_ort = 0.d0
print *, ' Providing the three_e_4_idx_cycle_1_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,integral) &
!$OMP SHARED (mo_num,three_e_4_idx_cycle_1_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, j, k, j, i, m, integral)
three_e_4_idx_cycle_1_bi_ort(m,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_4_idx_cycle_1_bi_ort', wall1 - wall0
END_PROVIDER
! --
BEGIN_PROVIDER [ double precision, three_e_4_idx_cycle_2_bi_ort, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE FIRST CYCLIC PERMUTATION TERMS OF SINGLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_4_idx_cycle_2_bi_ort(m,j,k,i) = <mjk|-L|imj> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m
double precision :: integral, wall1, wall0
three_e_4_idx_cycle_2_bi_ort = 0.d0
print *, ' Providing the three_e_4_idx_cycle_2_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,integral) &
!$OMP SHARED (mo_num,three_e_4_idx_cycle_2_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, j, k, i, m, j, integral)
three_e_4_idx_cycle_2_bi_ort(m,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_4_idx_cycle_2_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_4_idx_exch23_bi_ort, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF SINGLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_4_idx_exch23_bi_ort(m,j,k,i) = <mjk|-L|jmi> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m
double precision :: integral, wall1, wall0
three_e_4_idx_exch23_bi_ort = 0.d0
print *, ' Providing the three_e_4_idx_exch23_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,integral) &
!$OMP SHARED (mo_num,three_e_4_idx_exch23_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, j, k, j, m, i, integral)
three_e_4_idx_exch23_bi_ort(m,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_4_idx_exch23_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_4_idx_exch13_bi_ort, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF SINGLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_4_idx_exch13_bi_ort(m,j,k,i) = <mjk|-L|ijm> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
END_DOC
implicit none
integer :: i, j, k, m
double precision :: integral, wall1, wall0
three_e_4_idx_exch13_bi_ort = 0.d0
print *, ' Providing the three_e_4_idx_exch13_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,integral) &
!$OMP SHARED (mo_num,three_e_4_idx_exch13_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, j, k, i, j, m, integral)
three_e_4_idx_exch13_bi_ort(m,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_4_idx_exch13_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_4_idx_exch12_bi_ort, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF SINGLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_4_idx_exch12_bi_ort(m,j,k,i) = <mjk|-L|mij> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m
double precision :: integral, wall1, wall0
three_e_4_idx_exch12_bi_ort = 0.d0
print *, ' Providing the three_e_4_idx_exch12_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,integral) &
!$OMP SHARED (mo_num,three_e_4_idx_exch12_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, j, k, m, i, j, integral)
three_e_4_idx_exch12_bi_ort(m,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_4_idx_exch12_bi_ort', wall1 - wall0
END_PROVIDER
! ---

296
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! ---
BEGIN_PROVIDER [ double precision, three_e_5_idx_direct_bi_ort, (mo_num, mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF DOUBLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_5_idx_direct_bi_ort(m,l,j,k,i) = <mlk|-L|mji> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
END_DOC
implicit none
integer :: i, j, k, m, l
double precision :: integral, wall1, wall0
three_e_5_idx_direct_bi_ort = 0.d0
print *, ' Providing the three_e_5_idx_direct_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,l,integral) &
!$OMP SHARED (mo_num,three_e_5_idx_direct_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do l = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, l, k, m, j, i, integral)
three_e_5_idx_direct_bi_ort(m,l,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_5_idx_direct_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_5_idx_cycle_1_bi_ort, (mo_num, mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE FIRST CYCLIC PERMUTATION TERMS OF DOUBLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_5_idx_cycle_1_bi_ort(m,l,j,k,i) = <mlk|-L|jim> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m, l
double precision :: integral, wall1, wall0
three_e_5_idx_cycle_1_bi_ort = 0.d0
print *, ' Providing the three_e_5_idx_cycle_1_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,l,integral) &
!$OMP SHARED (mo_num,three_e_5_idx_cycle_1_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do l = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, l, k, j, i, m, integral)
three_e_5_idx_cycle_1_bi_ort(m,l,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_5_idx_cycle_1_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_5_idx_cycle_2_bi_ort, (mo_num, mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE FIRST CYCLIC PERMUTATION TERMS OF DOUBLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_5_idx_cycle_2_bi_ort(m,l,j,k,i) = <mlk|-L|imj> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m, l
double precision :: integral, wall1, wall0
three_e_5_idx_cycle_2_bi_ort = 0.d0
print *, ' Providing the three_e_5_idx_cycle_2_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,l,integral) &
!$OMP SHARED (mo_num,three_e_5_idx_cycle_2_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
do l = 1, mo_num
call give_integrals_3_body_bi_ort(m, l, k, i, m, j, integral)
three_e_5_idx_cycle_2_bi_ort(m,l,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_5_idx_cycle_2_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_5_idx_exch23_bi_ort, (mo_num, mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF DOUBLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_5_idx_exch23_bi_ort(m,l,j,k,i) = <mlk|-L|jmi> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m, l
double precision :: integral, wall1, wall0
three_e_5_idx_exch23_bi_ort = 0.d0
print *, ' Providing the three_e_5_idx_exch23_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,l,integral) &
!$OMP SHARED (mo_num,three_e_5_idx_exch23_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do l = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, l, k, j, m, i, integral)
three_e_5_idx_exch23_bi_ort(m,l,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_5_idx_exch23_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_5_idx_exch13_bi_ort, (mo_num, mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF DOUBLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_5_idx_exch13_bi_ort(m,l,j,k,i) = <mlk|-L|ijm> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m, l
double precision :: integral, wall1, wall0
three_e_5_idx_exch13_bi_ort = 0.d0
print *, ' Providing the three_e_5_idx_exch13_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,l,integral) &
!$OMP SHARED (mo_num,three_e_5_idx_exch13_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do l = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, l, k, i, j, m, integral)
three_e_5_idx_exch13_bi_ort(m,l,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_5_idx_exch13_bi_ort', wall1 - wall0
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, three_e_5_idx_exch12_bi_ort, (mo_num, mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! matrix element of the -L three-body operator FOR THE DIRECT TERMS OF DOUBLE EXCITATIONS AND BI ORTHO MOs
!
! three_e_5_idx_exch12_bi_ort(m,l,j,k,i) = <mlk|-L|mij> ::: notice that i is the RIGHT MO and k is the LEFT MO
!
! notice the -1 sign: in this way three_e_3_idx_direct_bi_ort can be directly used to compute Slater rules with a + sign
!
END_DOC
implicit none
integer :: i, j, k, m, l
double precision :: integral, wall1, wall0
three_e_5_idx_exch12_bi_ort = 0.d0
print *, ' Providing the three_e_5_idx_exch12_bi_ort ...'
call wall_time(wall0)
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,m,l,integral) &
!$OMP SHARED (mo_num,three_e_5_idx_exch12_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
do l = 1, mo_num
do m = 1, mo_num
call give_integrals_3_body_bi_ort(m, l, k, m, i, j, integral)
three_e_5_idx_exch12_bi_ort(m,l,j,k,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
call wall_time(wall1)
print *, ' wall time for three_e_5_idx_exch12_bi_ort', wall1 - wall0
END_PROVIDER
! ---

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! ---
BEGIN_PROVIDER [ double precision, three_body_ints_bi_ort, (mo_num, mo_num, mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
! matrix element of the -L three-body operator
!
! notice the -1 sign: in this way three_body_ints_bi_ort can be directly used to compute Slater rules :)
END_DOC
implicit none
integer :: i, j, k, l, m, n
double precision :: integral, wall1, wall0
character*(128) :: name_file
three_body_ints_bi_ort = 0.d0
print *, ' Providing the three_body_ints_bi_ort ...'
call wall_time(wall0)
name_file = 'six_index_tensor'
! if(read_three_body_ints_bi_ort)then
! call read_fcidump_3_tc(three_body_ints_bi_ort)
! else
! if(read_three_body_ints_bi_ort)then
! print*,'Reading three_body_ints_bi_ort from disk ...'
! call read_array_6_index_tensor(mo_num,three_body_ints_bi_ort,name_file)
! else
!provide x_W_ki_bi_ortho_erf_rk
provide mos_r_in_r_array_transp mos_l_in_r_array_transp
!$OMP PARALLEL &
!$OMP DEFAULT (NONE) &
!$OMP PRIVATE (i,j,k,l,m,n,integral) &
!$OMP SHARED (mo_num,three_body_ints_bi_ort)
!$OMP DO SCHEDULE (dynamic)
do i = 1, mo_num
do j = 1, mo_num
do m = 1, mo_num
do k = 1, mo_num
do l = 1, mo_num
do n = 1, mo_num
call give_integrals_3_body_bi_ort(n, l, k, m, j, i, integral)
three_body_ints_bi_ort(n,l,k,m,j,i) = -1.d0 * integral
enddo
enddo
enddo
enddo
enddo
enddo
!$OMP END DO
!$OMP END PARALLEL
! endif
! endif
call wall_time(wall1)
print *, ' wall time for three_body_ints_bi_ort', wall1 - wall0
! if(write_three_body_ints_bi_ort)then
! print*,'Writing three_body_ints_bi_ort on disk ...'
! call write_array_6_index_tensor(mo_num,three_body_ints_bi_ort,name_file)
! call ezfio_set_three_body_ints_bi_ort_io_three_body_ints_bi_ort("Read")
! endif
END_PROVIDER
! ---
subroutine give_integrals_3_body_bi_ort(n, l, k, m, j, i, integral)
BEGIN_DOC
!
! < n l k | -L | m j i > with a BI-ORTHONORMAL MOLECULAR ORBITALS
!
END_DOC
implicit none
integer, intent(in) :: n, l, k, m, j, i
double precision, intent(out) :: integral
integer :: ipoint
double precision :: weight
integral = 0.d0
do ipoint = 1, n_points_final_grid
weight = final_weight_at_r_vector(ipoint)
integral += weight * mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,i) &
* ( int2_grad1_u12_bimo_t(ipoint,1,n,m) * int2_grad1_u12_bimo_t(ipoint,1,l,j) &
+ int2_grad1_u12_bimo_t(ipoint,2,n,m) * int2_grad1_u12_bimo_t(ipoint,2,l,j) &
+ int2_grad1_u12_bimo_t(ipoint,3,n,m) * int2_grad1_u12_bimo_t(ipoint,3,l,j) )
integral += weight * mos_l_in_r_array_transp(ipoint,l) * mos_r_in_r_array_transp(ipoint,j) &
* ( int2_grad1_u12_bimo_t(ipoint,1,n,m) * int2_grad1_u12_bimo_t(ipoint,1,k,i) &
+ int2_grad1_u12_bimo_t(ipoint,2,n,m) * int2_grad1_u12_bimo_t(ipoint,2,k,i) &
+ int2_grad1_u12_bimo_t(ipoint,3,n,m) * int2_grad1_u12_bimo_t(ipoint,3,k,i) )
integral += weight * mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,m) &
* ( int2_grad1_u12_bimo_t(ipoint,1,l,j) * int2_grad1_u12_bimo_t(ipoint,1,k,i) &
+ int2_grad1_u12_bimo_t(ipoint,2,l,j) * int2_grad1_u12_bimo_t(ipoint,2,k,i) &
+ int2_grad1_u12_bimo_t(ipoint,3,l,j) * int2_grad1_u12_bimo_t(ipoint,3,k,i) )
enddo
end subroutine give_integrals_3_body_bi_ort
! ---
subroutine give_integrals_3_body_bi_ort_old(n, l, k, m, j, i, integral)
BEGIN_DOC
!
! < n l k | -L | m j i > with a BI-ORTHONORMAL MOLECULAR ORBITALS
!
END_DOC
implicit none
integer, intent(in) :: n, l, k, m, j, i
double precision, intent(out) :: integral
integer :: ipoint
double precision :: weight
integral = 0.d0
do ipoint = 1, n_points_final_grid
weight = final_weight_at_r_vector(ipoint)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! integral += weight * mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,i) &
! * ( x_W_ki_bi_ortho_erf_rk(ipoint,1,n,m) * x_W_ki_bi_ortho_erf_rk(ipoint,1,l,j) &
! + x_W_ki_bi_ortho_erf_rk(ipoint,2,n,m) * x_W_ki_bi_ortho_erf_rk(ipoint,2,l,j) &
! + x_W_ki_bi_ortho_erf_rk(ipoint,3,n,m) * x_W_ki_bi_ortho_erf_rk(ipoint,3,l,j) )
! integral += weight * mos_l_in_r_array_transp(ipoint,l) * mos_r_in_r_array_transp(ipoint,j) &
! * ( x_W_ki_bi_ortho_erf_rk(ipoint,1,n,m) * x_W_ki_bi_ortho_erf_rk(ipoint,1,k,i) &
! + x_W_ki_bi_ortho_erf_rk(ipoint,2,n,m) * x_W_ki_bi_ortho_erf_rk(ipoint,2,k,i) &
! + x_W_ki_bi_ortho_erf_rk(ipoint,3,n,m) * x_W_ki_bi_ortho_erf_rk(ipoint,3,k,i) )
! integral += weight * mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,m) &
! * ( x_W_ki_bi_ortho_erf_rk(ipoint,1,l,j) * x_W_ki_bi_ortho_erf_rk(ipoint,1,k,i) &
! + x_W_ki_bi_ortho_erf_rk(ipoint,2,l,j) * x_W_ki_bi_ortho_erf_rk(ipoint,2,k,i) &
! + x_W_ki_bi_ortho_erf_rk(ipoint,3,l,j) * x_W_ki_bi_ortho_erf_rk(ipoint,3,k,i) )
! integral += weight * mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,i) &
! * ( int2_grad1_u12_bimo(1,n,m,ipoint) * int2_grad1_u12_bimo(1,l,j,ipoint) &
! + int2_grad1_u12_bimo(2,n,m,ipoint) * int2_grad1_u12_bimo(2,l,j,ipoint) &
! + int2_grad1_u12_bimo(3,n,m,ipoint) * int2_grad1_u12_bimo(3,l,j,ipoint) )
! integral += weight * mos_l_in_r_array_transp(ipoint,l) * mos_r_in_r_array_transp(ipoint,j) &
! * ( int2_grad1_u12_bimo(1,n,m,ipoint) * int2_grad1_u12_bimo(1,k,i,ipoint) &
! + int2_grad1_u12_bimo(2,n,m,ipoint) * int2_grad1_u12_bimo(2,k,i,ipoint) &
! + int2_grad1_u12_bimo(3,n,m,ipoint) * int2_grad1_u12_bimo(3,k,i,ipoint) )
! integral += weight * mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,m) &
! * ( int2_grad1_u12_bimo(1,l,j,ipoint) * int2_grad1_u12_bimo(1,k,i,ipoint) &
! + int2_grad1_u12_bimo(2,l,j,ipoint) * int2_grad1_u12_bimo(2,k,i,ipoint) &
! + int2_grad1_u12_bimo(3,l,j,ipoint) * int2_grad1_u12_bimo(3,k,i,ipoint) )
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
integral += weight * mos_l_in_r_array_transp(ipoint,k) * mos_r_in_r_array_transp(ipoint,i) &
* ( int2_grad1_u12_bimo_transp(n,m,1,ipoint) * int2_grad1_u12_bimo_transp(l,j,1,ipoint) &
+ int2_grad1_u12_bimo_transp(n,m,2,ipoint) * int2_grad1_u12_bimo_transp(l,j,2,ipoint) &
+ int2_grad1_u12_bimo_transp(n,m,3,ipoint) * int2_grad1_u12_bimo_transp(l,j,3,ipoint) )
integral += weight * mos_l_in_r_array_transp(ipoint,l) * mos_r_in_r_array_transp(ipoint,j) &
* ( int2_grad1_u12_bimo_transp(n,m,1,ipoint) * int2_grad1_u12_bimo_transp(k,i,1,ipoint) &
+ int2_grad1_u12_bimo_transp(n,m,2,ipoint) * int2_grad1_u12_bimo_transp(k,i,2,ipoint) &
+ int2_grad1_u12_bimo_transp(n,m,3,ipoint) * int2_grad1_u12_bimo_transp(k,i,3,ipoint) )
integral += weight * mos_l_in_r_array_transp(ipoint,n) * mos_r_in_r_array_transp(ipoint,m) &
* ( int2_grad1_u12_bimo_transp(l,j,1,ipoint) * int2_grad1_u12_bimo_transp(k,i,1,ipoint) &
+ int2_grad1_u12_bimo_transp(l,j,2,ipoint) * int2_grad1_u12_bimo_transp(k,i,2,ipoint) &
+ int2_grad1_u12_bimo_transp(l,j,3,ipoint) * int2_grad1_u12_bimo_transp(k,i,3,ipoint) )
enddo
end subroutine give_integrals_3_body_bi_ort_old
! ---
subroutine give_integrals_3_body_bi_ort_ao(n, l, k, m, j, i, integral)
BEGIN_DOC
!
! < n l k | -L | m j i > with a BI-ORTHONORMAL ATOMIC ORBITALS
!
END_DOC
implicit none
integer, intent(in) :: n, l, k, m, j, i
double precision, intent(out) :: integral
integer :: ipoint
double precision :: weight
integral = 0.d0
do ipoint = 1, n_points_final_grid
weight = final_weight_at_r_vector(ipoint)
integral += weight * aos_in_r_array_transp(ipoint,k) * aos_in_r_array_transp(ipoint,i) &
* ( int2_grad1_u12_ao_t(ipoint,1,n,m) * int2_grad1_u12_ao_t(ipoint,1,l,j) &
+ int2_grad1_u12_ao_t(ipoint,2,n,m) * int2_grad1_u12_ao_t(ipoint,2,l,j) &
+ int2_grad1_u12_ao_t(ipoint,3,n,m) * int2_grad1_u12_ao_t(ipoint,3,l,j) )
integral += weight * aos_in_r_array_transp(ipoint,l) * aos_in_r_array_transp(ipoint,j) &
* ( int2_grad1_u12_ao_t(ipoint,1,n,m) * int2_grad1_u12_ao_t(ipoint,1,k,i) &
+ int2_grad1_u12_ao_t(ipoint,2,n,m) * int2_grad1_u12_ao_t(ipoint,2,k,i) &
+ int2_grad1_u12_ao_t(ipoint,3,n,m) * int2_grad1_u12_ao_t(ipoint,3,k,i) )
integral += weight * aos_in_r_array_transp(ipoint,n) * aos_in_r_array_transp(ipoint,m) &
* ( int2_grad1_u12_ao_t(ipoint,1,l,j) * int2_grad1_u12_ao_t(ipoint,1,k,i) &
+ int2_grad1_u12_ao_t(ipoint,2,l,j) * int2_grad1_u12_ao_t(ipoint,2,k,i) &
+ int2_grad1_u12_ao_t(ipoint,3,l,j) * int2_grad1_u12_ao_t(ipoint,3,k,i) )
enddo
end subroutine give_integrals_3_body_bi_ort_ao
! ---

271
src/bi_ort_ints/total_twoe_pot.irp.f Normal file
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! ---
BEGIN_PROVIDER [double precision, ao_two_e_vartc_tot, (ao_num, ao_num, ao_num, ao_num) ]
integer :: i, j, k, l
provide j1b_type
provide mo_r_coef mo_l_coef
do j = 1, ao_num
do l = 1, ao_num
do i = 1, ao_num
do k = 1, ao_num
ao_two_e_vartc_tot(k,i,l,j) = ao_vartc_int_chemist(k,i,l,j)
enddo
enddo
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, ao_two_e_tc_tot, (ao_num, ao_num, ao_num, ao_num) ]
BEGIN_DOC
!
! ao_two_e_tc_tot(k,i,l,j) = (ki|V^TC(r_12)|lj) = <lk| V^TC(r_12) |ji> where V^TC(r_12) is the total TC operator
!
! including both hermitian and non hermitian parts. THIS IS IN CHEMIST NOTATION.
!
! WARNING :: non hermitian ! acts on "the right functions" (i,j)
!
END_DOC
integer :: i, j, k, l
double precision :: integral_sym, integral_nsym
double precision, external :: get_ao_tc_sym_two_e_pot
provide j1b_type
if(j1b_type .eq. 3) then
do j = 1, ao_num
do l = 1, ao_num
do i = 1, ao_num
do k = 1, ao_num
ao_two_e_tc_tot(k,i,l,j) = ao_tc_int_chemist(k,i,l,j)
!write(222,*) ao_two_e_tc_tot(k,i,l,j)
enddo
enddo
enddo
enddo
else
PROVIDE ao_tc_sym_two_e_pot_in_map
do j = 1, ao_num
do l = 1, ao_num
do i = 1, ao_num
do k = 1, ao_num
integral_sym = get_ao_tc_sym_two_e_pot(i, j, k, l, ao_tc_sym_two_e_pot_map)
! ao_non_hermit_term_chemist(k,i,l,j) = < k l | [erf( mu r12) - 1] d/d_r12 | i j > on the AO basis
integral_nsym = ao_non_hermit_term_chemist(k,i,l,j)
!print *, ' sym integ = ', integral_sym
!print *, ' non-sym integ = ', integral_nsym
ao_two_e_tc_tot(k,i,l,j) = integral_sym + integral_nsym
!write(111,*) ao_two_e_tc_tot(k,i,l,j)
enddo
enddo
enddo
enddo
endif
END_PROVIDER
! ---
double precision function bi_ortho_mo_ints(l, k, j, i)
BEGIN_DOC
!
! <mo^L_k mo^L_l | V^TC(r_12) | mo^R_i mo^R_j>
!
! WARNING :: very naive, super slow, only used to DEBUG.
!
END_DOC
implicit none
integer, intent(in) :: i, j, k, l
integer :: m, n, p, q
bi_ortho_mo_ints = 0.d0
do m = 1, ao_num
do p = 1, ao_num
do n = 1, ao_num
do q = 1, ao_num
! p1h1p2h2 l1 l2 r1 r2
bi_ortho_mo_ints += ao_two_e_tc_tot(n,q,m,p) * mo_l_coef(m,l) * mo_l_coef(n,k) * mo_r_coef(p,j) * mo_r_coef(q,i)
enddo
enddo
enddo
enddo
end function bi_ortho_mo_ints
! ---
! TODO :: transform into DEGEMM
BEGIN_PROVIDER [double precision, mo_bi_ortho_tc_two_e_chemist, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! mo_bi_ortho_tc_two_e_chemist(k,i,l,j) = <k l|V(r_12)|i j> where i,j are right MOs and k,l are left MOs
!
END_DOC
implicit none
integer :: i, j, k, l, m, n, p, q
double precision, allocatable :: mo_tmp_1(:,:,:,:), mo_tmp_2(:,:,:,:)
allocate(mo_tmp_1(mo_num,ao_num,ao_num,ao_num))
mo_tmp_1 = 0.d0
do m = 1, ao_num
do p = 1, ao_num
do n = 1, ao_num
do q = 1, ao_num
do k = 1, mo_num
! (k n|p m) = sum_q c_qk * (q n|p m)
mo_tmp_1(k,n,p,m) += mo_l_coef_transp(k,q) * ao_two_e_tc_tot(q,n,p,m)
enddo
enddo
enddo
enddo
enddo
allocate(mo_tmp_2(mo_num,mo_num,ao_num,ao_num))
mo_tmp_2 = 0.d0
do m = 1, ao_num
do p = 1, ao_num
do n = 1, ao_num
do i = 1, mo_num
do k = 1, mo_num
! (k i|p m) = sum_n c_ni * (k n|p m)
mo_tmp_2(k,i,p,m) += mo_r_coef_transp(i,n) * mo_tmp_1(k,n,p,m)
enddo
enddo
enddo
enddo
enddo
deallocate(mo_tmp_1)
allocate(mo_tmp_1(mo_num,mo_num,mo_num,ao_num))
mo_tmp_1 = 0.d0
do m = 1, ao_num
do p = 1, ao_num
do l = 1, mo_num
do i = 1, mo_num
do k = 1, mo_num
mo_tmp_1(k,i,l,m) += mo_l_coef_transp(l,p) * mo_tmp_2(k,i,p,m)
enddo
enddo
enddo
enddo
enddo
deallocate(mo_tmp_2)
mo_bi_ortho_tc_two_e_chemist = 0.d0
do m = 1, ao_num
do j = 1, mo_num
do l = 1, mo_num
do i = 1, mo_num
do k = 1, mo_num
mo_bi_ortho_tc_two_e_chemist(k,i,l,j) += mo_r_coef_transp(j,m) * mo_tmp_1(k,i,l,m)
enddo
enddo
enddo
enddo
enddo
deallocate(mo_tmp_1)
END_PROVIDER
! ---
BEGIN_PROVIDER [double precision, mo_bi_ortho_tc_two_e, (mo_num, mo_num, mo_num, mo_num)]
BEGIN_DOC
!
! mo_bi_ortho_tc_two_e(k,l,i,j) = <k l| V(r_12) |i j> where i,j are right MOs and k,l are left MOs
!
! the potential V(r_12) contains ALL TWO-E CONTRIBUTION OF THE TC-HAMILTONIAN
!
END_DOC
implicit none
integer :: i, j, k, l
do j = 1, mo_num
do i = 1, mo_num
do l = 1, mo_num
do k = 1, mo_num
! < k l | V12 | i j > (k i|l j)
mo_bi_ortho_tc_two_e(k,l,i,j) = mo_bi_ortho_tc_two_e_chemist(k,i,l,j)
enddo
enddo
enddo
enddo
END_PROVIDER
! ---
BEGIN_PROVIDER [ double precision, mo_bi_ortho_tc_two_e_jj, (mo_num,mo_num) ]
&BEGIN_PROVIDER [ double precision, mo_bi_ortho_tc_two_e_jj_exchange, (mo_num,mo_num) ]
&BEGIN_PROVIDER [ double precision, mo_bi_ortho_tc_two_e_jj_anti, (mo_num,mo_num) ]
implicit none
BEGIN_DOC
! mo_bi_ortho_tc_two_e_jj(i,j) = J_ij = <ji|W-K|ji>
! mo_bi_ortho_tc_two_e_jj_exchange(i,j) = K_ij = <ij|W-K|ji>
! mo_bi_ortho_tc_two_e_jj_anti(i,j) = J_ij - K_ij
END_DOC
integer :: i,j
double precision :: get_two_e_integral
mo_bi_ortho_tc_two_e_jj = 0.d0
mo_bi_ortho_tc_two_e_jj_exchange = 0.d0
do i=1,mo_num
do j=1,mo_num
mo_bi_ortho_tc_two_e_jj(i,j) = mo_bi_ortho_tc_two_e(j,i,j,i)
mo_bi_ortho_tc_two_e_jj_exchange(i,j) = mo_bi_ortho_tc_two_e(i,j,j,i)
mo_bi_ortho_tc_two_e_jj_anti(i,j) = mo_bi_ortho_tc_two_e_jj(i,j) - mo_bi_ortho_tc_two_e_jj_exchange(i,j)
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, tc_2e_3idx_coulomb_integrals, (mo_num,mo_num, mo_num)]
&BEGIN_PROVIDER [double precision, tc_2e_3idx_exchange_integrals,(mo_num,mo_num, mo_num)]
implicit none
BEGIN_DOC
! tc_2e_3idx_coulomb_integrals(j,k,i) = <jk|ji>
!
! tc_2e_3idx_exchange_integrals(j,k,i) = <kj|ji>
END_DOC
integer :: i,j,k,l
double precision :: get_two_e_integral
double precision :: integral
do i = 1, mo_num
do k = 1, mo_num
do j = 1, mo_num
tc_2e_3idx_coulomb_integrals(j, k,i) = mo_bi_ortho_tc_two_e(j ,k ,j ,i )
tc_2e_3idx_exchange_integrals(j,k,i) = mo_bi_ortho_tc_two_e(k ,j ,j ,i )
enddo
enddo
enddo
END_PROVIDER

11
src/bi_ortho_mos/EZFIO.cfg Normal file
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[mo_r_coef]
type: double precision
doc: right-coefficient of the i-th |AO| on the j-th |MO|
interface: ezfio
size: (ao_basis.ao_num,mo_basis.mo_num)
[mo_l_coef]
type: double precision
doc: right-coefficient of the i-th |AO| on the j-th |MO|
interface: ezfio
size: (ao_basis.ao_num,mo_basis.mo_num)

3
src/bi_ortho_mos/NEED Normal file
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@ -0,0 +1,3 @@
mo_basis
becke_numerical_grid
dft_utils_in_r

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