Merge branch 'dev-stable' of github.com:QuantumPackage/qp2 into dev-stable

bin/qp_set_frozen_core

@@ -83,6 +83,7 @@ def main(arguments):
                 elif charge <= 118: n_frozen += 43
 
         elif arguments["--small"]:
+            for charge in ezfio.nuclei_nucl_charge:
                 if   charge <=   4: pass
                 elif charge <=  18: n_frozen += 1
                 elif charge <=  36: n_frozen += 5

docs/source/appendix/contributors.rst

@@ -46,6 +46,7 @@ The following people have contributed to this project (by alphabetical order):
 * Nicolas Renon
 * Lorenzo Tenti
 * Julien Toulouse
+* Diata Traoré
 * Mikaël Véril
 
 

docs/source/index.rst

@@ -39,9 +39,10 @@
    programmers_guide/programming
    programmers_guide/ezfio
    programmers_guide/plugins
+   programmers_guide/plugins_tuto_intro
+   programmers_guide/plugins_tuto_I
    programmers_guide/new_ks
    programmers_guide/index
-   programmers_guide/plugins
 
 
 .. toctree::
@@ -52,5 +53,6 @@
    appendix/benchmarks
    appendix/license
    appendix/contributors
+   appendix/references
 
 

docs/source/programmers_guide/plugins_tuto_I.rst

@@ -0,0 +1 @@
+.. include:: ../../../plugins/local/tuto_plugins/tuto_I/tuto_I.rst

docs/source/programmers_guide/plugins_tuto_intro.rst

@@ -0,0 +1 @@
+.. include:: ../../../plugins/README.rst

external/irpf90

@@ -1 +1 @@
-Subproject commit ba1a2837aa61cb8f9892860cec544d7c6659badd
+Subproject commit 4ab1b175fc7ed0d96c1912f13dc53579b24157a6

plugins/README.rst

@@ -0,0 +1,131 @@
+==============================
+Tutorial for creating a plugin
+==============================
+
+Introduction: what is a plugin, and what tutorial will be about ?
+=================================================================
+
+The |QP| is split into two kinds of routines/global variables (i.e. *providers*): 
+ 1)  the **core modules** locatedin qp2/src/, which contains all the bulk of a quantum chemistry software (integrals, matrix elements between Slater determinants, linear algebra routines, DFT stuffs etc..)
+ 2) the **plugins** which are external routines/*providers* connected to the qp2/src/ routines/*providers*.
+ 
+More precisely, a **plugin** of the |QP| is a directory where you can create routines, 
+providers and executables that use all the global variables/functions/routines already created 
+in the modules of qp2/src or in other plugins. 
+
+Instead of giving a theoretical lecture on what is a plugin, 
+we will go through a series of examples that allow you to do the following thing: 
+
+1)   print out **one- and two-electron integrals** on the AO/MO basis, creates two providers which manipulate these objects, print out these providers, 
+
+2)  browse the **Slater determinants stored** in the |EZFIO| wave function and compute their matrix elements, 
+
+3) build the **Hamiltonian matrix** and **diagonalize** it either with **Lapack or Davidson**,
+
+4)  print out the **one- and two-electron rdms**, 
+
+5)   obtain the **AOs** and **MOs** on the **DFT grid**, together with the **density**,
+
+How the tutorial will be done
+-----------------------------
+
+This tuto is as follows: 
+
+ 1)  you **READ THIS FILE UNTIL THE END** in order to get the big picture and vocabulary, 
+
+ 2) you go to the directory :file:`qp2/plugins/tuto_plugins/` and you will find detailed tutorials for each of the 5 examples. 
+
+Creating a plugin: the basic
+----------------------------
+
+The first thing to do is to be in the QPSH mode: you execute the qp2/bin/qpsh script that essentially loads all 
+the environement variables and allows for the completion of command lines in bash (that is an AMAZING feature :) 
+
+Then, you need to known **where** you want to create your plugin, and what is the **name** of the plugin. 
+
+.. important::
+
+  The plugins are **NECESSARILY** located in qp2/plugins/, and from there you can create any structures of directories.
+
+
+Ex: If you want to create a plugin named "my_fancy_plugin" in the directory plugins/plugins_test/, 
+this goes with the command 
+
+.. code:: bash
+
+    qp plugins create -n my_fancy_plugin -r plugins_test/
+
+Then, to create the plugin of your dreams, the two questions you need to answer are the following: 
+
+1) What do I **need** to compute what I want, which means what are the **objects** that I need ?
+
+   There are two kind of objects:
+
+   + the *routines/functions*: 
+
+     Ex: Linear algebra routines, integration routines etc ...
+
+   + the global variables which are called the *providers*: 
+
+     Ex: one-electron integrals, Slater determinants, density matrices etc ...
+
+2) **Where do I find** these objects ? 
+
+   The objects (routines/functions/providers) are necessarily created in other *modules/plugins*.  
+
+.. seealso::
+
+   The routine :c:func:`lapack_diagd` (which diagonalises a real hermitian matrix) is located in the file 
+   :file:`qp2/src/utils/linear_algebra.irp.f` 
+   therefore it "belongs" to the module :ref:`module_utils`
+
+   The routine :c:func:`ao_to_mo` (which converts a given matrix A from the AO basis to the MO basis) is located in the file 
+   :file:`qp2/src/mo_one_e_ints/ao_to_mo.irp.f`
+   therefore it "belongs" to the module :ref:`module_mo_one_e_ints`
+
+   The provider :c:data:`ao_one_e_integrals` (which is the integrals of one-body part of H on the AO basis) is located in the file 
+   :file:`qp2/src/ao_one_e_ints/ao_one_e_ints.irp.f` 
+   therefore it belongs to the module :ref:`module_ao_one_e_ints`
+
+   The provider :c:data:`one_e_dm_mo_beta_average` (which is the state average beta density matrix on the MO basis) is located in the file 
+   :file:`qp2/src/determinants/density_matrix.irp.f`
+   therefore it belongs to the module :ref:`module_determinants`
+
+To import all the variables that you need, you just need to write the name of the plugins in the :file:`NEED` file .
+
+To import all the variables/routines of the module :ref:`module_utils`, :ref:`module_determinants` and :ref:`module_mo_one_e_ints`, the  :file:`NEED` file you will need is simply the following:
+
+.. code:: bash
+
+ cat NEED
+
+ utils
+ determinants
+ mo_one_e_ints
+
+
+.. important::
+
+  There are **many** routines/providers in the core modules of QP. 
+
+  Nevertheless, as everything is coded with the |IRPF90|, you can use the following amazing tools: :command:`irpman`
+
+  :command:`irpman` can be used in command line in bash to obtain all the info on a routine or variable ! 
+
+
+Example: execute the following command line : 
+
+.. code:: bash
+
+  irpman ao_one_e_integrals
+
+Then all the information you need on :c:data:`ao_one_e_integrals` will appear on the screen. 
+This includes
+
+ - **where** the provider is created, (*i.e.* the actual file where the provider is designed)
+ - the **type** of the provider (*i.e.* a logical, integer etc ...)
+ - the **dimension** if it is an array, 
+ - what other *providers* are **needed** to build this provider, 
+ - what other *providers* **need** this provider. 
+
+

plugins/local/cipsi_tc_bi_ortho/selection.irp.f

@@ -960,7 +960,7 @@ subroutine fill_buffer_double(i_generator, sp, h1, h2, bannedOrb, banned, fock_d
 !          endif
           e_pert(istate) = 0.25 * val / delta_E
 !          e_pert(istate) = 0.5d0 * (tmp - delta_E)
-          if(dsqrt(dabs(tmp)).gt.1.d-4.and.dabs(alpha_h_psi).gt.1.d-4)then
+          if(dsqrt(tmp).gt.1.d-4.and.dabs(psi_h_alpha).gt.1.d-4)then
            coef(istate)   = e_pert(istate) / psi_h_alpha
           else
            coef(istate)   = alpha_h_psi / delta_E

plugins/local/tuto_plugins/H2.xyz

@@ -0,0 +1,6 @@
+2
+H2, equilibrium geometry
+H   0.0   0.0    0.
+H   0.0   0.0    0.74
+
+

plugins/local/tuto_plugins/n2.xyz

@@ -0,0 +1,4 @@
+2
+N2 Geo: Experiment Mult: 1 symmetry: 14
+N    0.0    0.0    0.5488
+N    0.0    0.0    -0.5488

plugins/local/tuto_plugins/tuto_I/print_one_e_h.irp.f

@@ -0,0 +1,20 @@
+program my_program_to_print_stuffs
+  implicit none
+  BEGIN_DOC
+! TODO : Put the documentation of the program here
+  END_DOC
+ integer :: i,j
+ print*,'AO integrals '
+ do i = 1, ao_num
+  do j = 1, ao_num
+   print*,j,i,ao_one_e_integrals(j,i)
+  enddo
+ enddo
+
+ print*,'MO integrals '
+ do i = 1, mo_num
+  do j = 1, mo_num
+   print*,j,i,mo_one_e_integrals(j,i)
+  enddo
+ enddo
+end

plugins/local/tuto_plugins/tuto_I/print_traces_on_e.irp.f

@@ -0,0 +1,24 @@
+program my_program
+  implicit none
+  BEGIN_DOC
+! This program is there essentially to show how one can use providers in programs 
+  END_DOC
+ integer :: i,j
+ double precision :: accu
+ print*,'Trace on the AO basis '
+ print*,trace_ao_one_e_ints
+ print*,'Trace on the AO basis after projection on the MO basis'
+ print*,trace_ao_one_e_ints_from_mo
+ print*,'Trace of MO integrals '
+ print*,trace_mo_one_e_ints
+ print*,'ao_num = ',ao_num
+ print*,'mo_num = ',mo_num
+ if(ao_num .ne. mo_num)then
+  print*,'The AO basis and MO basis are different ...'
+  print*,'Trace on the AO basis should not be the same as Trace of MO integrals'
+  print*,'Only the second one must be equal to the trace on the MO integrals'
+ else 
+  print*,'The AO basis and MO basis are the same !'
+  print*,'All traces should coincide '
+ endif
+end

plugins/local/tuto_plugins/tuto_I/print_two_e_h.irp.f

@@ -0,0 +1,32 @@
+program my_program_to_print_stuffs
+  implicit none
+  BEGIN_DOC
+! TODO : Put the documentation of the program here
+  END_DOC
+ integer :: i,j,k,l
+ double precision :: integral 
+ double precision :: get_ao_two_e_integral, get_two_e_integral ! declaration of the functions 
+ print*,'AO integrals, physicist notations : <i j|k l>'
+ do i = 1, ao_num
+  do j = 1, ao_num
+   do k = 1, ao_num
+    do l = 1, ao_num
+     integral = get_ao_two_e_integral(i, j, k, l, ao_integrals_map)
+     print*,i,j,k,l,integral 
+    enddo
+   enddo
+  enddo
+ enddo
+
+ print*,'MO integrals, physicist notations : <i j|k l>'
+ do i = 1, mo_num
+  do j = 1, mo_num
+   do k = 1, mo_num
+    do l = 1, mo_num
+     integral = get_two_e_integral(i, j, k, l, mo_integrals_map)
+     print*,i,j,k,l,integral 
+    enddo
+   enddo
+  enddo
+ enddo
+end

plugins/local/tuto_plugins/tuto_I/traces_one_e.irp.f

@@ -0,0 +1,111 @@
+
+! This file is an example of the kind of manipulations that you can do with providers 
+!
+
+!!!!!!!!!!!!!!!!!!!!!!!!!! Main providers useful for the program !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
+
+!!!               type             name 
+BEGIN_PROVIDER [ double precision, trace_mo_one_e_ints]
+ implicit none
+ BEGIN_DOC
+! trace_mo_one_e_ints = Trace of the one-electron integrals on the MO basis
+!
+!                     = sum_i mo_one_e_integrals(i,i)
+ END_DOC
+ integer :: i
+ trace_mo_one_e_ints = 0.d0
+ do i = 1, mo_num
+  trace_mo_one_e_ints += mo_one_e_integrals(i,i)
+ enddo
+END_PROVIDER  
+
+BEGIN_PROVIDER [ double precision, trace_ao_one_e_ints]
+ implicit none
+ BEGIN_DOC
+! trace_ao_one_e_ints = Trace of the one-electron integrals on the AO basis taking into account the non orthogonality
+!
+! Be aware that the trace of an operator in a non orthonormal basis is Tr(A S^{-1}) = \sum_{m,n}(A_mn S^{-1}_mn) 
+! 
+! WARNING: it is equal to the trace on the MO basis if and only if the AO basis and MO basis 
+!          have the same number of functions
+ END_DOC
+ integer :: i,j
+ double precision, allocatable :: inv_overlap_times_integrals(:,:) ! = h S^{-1}
+ allocate(inv_overlap_times_integrals(ao_num,ao_num))
+ ! routine that computes the product of two matrices, you can check it with 
+ ! irpman get_AB_prod
+ call get_AB_prod(ao_one_e_integrals,ao_num,ao_num,s_inv,ao_num,inv_overlap_times_integrals)
+ ! Tr(inv_overlap_times_integrals) = Tr(h S^{-1})
+ trace_ao_one_e_ints = 0.d0
+ do i = 1, ao_num
+  trace_ao_one_e_ints += inv_overlap_times_integrals(i,i)
+ enddo
+ !
+ ! testing the formula Tr(A S^{-1}) = \sum_{m,n}(A_mn S^{-1}_mn)
+ double precision :: test
+ test = 0.d0
+ do i = 1, ao_num
+  do j = 1, ao_num
+   test += ao_one_e_integrals(j,i) * s_inv(i,j)
+  enddo
+ enddo
+ if(dabs(accu - trace_ao_one_e_ints).gt.1.d-12)then
+  print*,'Warning ! '
+  print*,'Something is wrong because Tr(AB) \ne sum_{mn}A_mn B_nm'
+ endif
+END_PROVIDER
+
+BEGIN_PROVIDER [ double precision, trace_ao_one_e_ints_from_mo]
+ implicit none
+ BEGIN_DOC
+! trace_ao_one_e_ints_from_mo = Trace of the one-electron integrals on the AO basis after projection on the MO basis 
+!
+!                             = Tr([SC h {SC}^+] S^{-1})
+!
+!                             = Be aware that the trace of an operator in a non orthonormal basis is = Tr(A S^{-1}) where S is the metric
+! Must be equal to the trace_mo_one_e_ints 
+ END_DOC
+ integer :: i
+ double precision, allocatable :: inv_overlap_times_integrals(:,:)
+ allocate(inv_overlap_times_integrals(ao_num,ao_num))
+ ! Using the provider ao_one_e_integrals_from_mo = [SC h {SC}^+] 
+ call get_AB_prod(ao_one_e_integrals_from_mo,ao_num,ao_num,s_inv,ao_num,inv_overlap_times_integrals)
+ ! inv_overlap_times_integrals = [SC h {SC}^+] S^{-1}
+ trace_ao_one_e_ints_from_mo = 0.d0
+ ! Computing the trace
+ do i = 1, ao_num
+  trace_ao_one_e_ints_from_mo += inv_overlap_times_integrals(i,i)
+ enddo
+END_PROVIDER  
+
+!!!!!!!!!!!!!!!!!!!!!!!!!!! Additional providers to check some stuffs !!!!!!!!!!!!!!!!!!!!!!!!!
+
+BEGIN_PROVIDER [ double precision, ao_one_e_int_no_ov_from_mo, (ao_num, ao_num) ]
+ BEGIN_DOC
+ ! ao_one_e_int_no_ov_from_mo = C mo_one_e_integrals C^T 
+ !
+ ! WARNING : NON EQUAL TO ao_one_e_integrals due to the non orthogonality 
+ END_DOC
+ call mo_to_ao_no_overlap(mo_one_e_integrals,mo_num,ao_one_e_int_no_ov_from_mo,ao_num) 
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, ao_one_e_int_no_ov_from_mo_ov_ov, (ao_num, ao_num)]
+ BEGIN_DOC
+ ! ao_one_e_int_no_ov_from_mo_ov_ov = S ao_one_e_int_no_ov_from_mo S = SC mo_one_e_integrals (SC)^T
+ !
+ ! EQUAL TO ao_one_e_integrals ONLY IF ao_num = mo_num
+ END_DOC
+ double precision, allocatable :: tmp(:,:)
+ allocate(tmp(ao_num, ao_num))
+ call get_AB_prod(ao_overlap,ao_num,ao_num,ao_one_e_int_no_ov_from_mo,ao_num,tmp)
+ call get_AB_prod(tmp,ao_num,ao_num,ao_overlap,ao_num,ao_one_e_int_no_ov_from_mo_ov_ov)
+END_PROVIDER 
+
+BEGIN_PROVIDER [ double precision, c_t_s_c, (mo_num, mo_num)]
+ implicit none
+ BEGIN_DOC
+! C^T S C = should be the identity 
+ END_DOC 
+ call get_AB_prod(mo_coef_transp,mo_num,ao_num,S_mo_coef,mo_num,c_t_s_c)
+END_PROVIDER 
+

plugins/local/tuto_plugins/tuto_I/tuto_I.rst

@@ -0,0 +1,218 @@
+=============================================
+Tuto I: One- and two-e integrals (20 minutes)
+=============================================
+
+Requirements 
+------------
+1) You know how to create an |EZFIO| file and run calculations with |QP| (check the tuto: `<https://quantumpackage.github.io/qp2/post/hartree-fock/>`_),
+
+2) You have an |EZFIO| file with MOs created (with the :ref:`scf` executable for instance). As we are going to print out some integrals, don't take a too large system/basis (Ex: H2, cc-pVDZ is ok :)
+
+3) You made an qp set_file YOUR_EZFIO_FILE_FOR_H2 in order to work on that ezfio folder. 
+
+4) You have READ the :file:`qp2/plugins/README.rst` file to HAVE THE **VOCABULARY**. 
+
+Our goals:
+----------
+We want to create a plugin to do the following things: 
+ 1) print out one- and two-electron integrals on the AO/MO basis,  
+
+ 2) creates two providers which manipulate these objects, 
+
+ 3) print out these providers. 
+
+I) Getting started: creating the plugin
+---------------------------------------
+We will go step-by-step through these plugins. 
+
+We will create a plugin named "plugin_I", and its location will be in "tuto_plugins". 
+Therefore to create the plugin, we do: 
+
+.. code:: bash
+
+ qp plugins create -n plugin_I -r tuto_plugins
+
+Then do an "ls" in qp2/plugins/tuto_plugins/ and you will find a directory called "plugin_I". 
+
+In that directory you will find: 
+
+1) a :file:`NEED` file that will eventually contain all the other modules/plugins needed by our "plugin_I",
+
+2) a :file:`README.rst` file that you can and **SHOULD** modify in order to **DOCUMENT** what is doing the plugin,
+
+3) a :file:`plugin_I.irp.f` file that is a program to be compiled and just printing "Hello world" 
+
+II) Specifying the dependencies
+-------------------------------
+The next step is to know what are the other modules/plugins that we need to do what we want. 
+We need here 
+
+a) the one-electron integrals on the AO basis, which are computed in :file:`qp2/src/ao_one_e_ints/`
+
+b) the one-electron integrals on the MO basis, which are computed in :file:`qp2/src/mo_one_e_ints/`
+
+c) the two-electron integrals on the AO basis, which are computed in :file:`qp2/src/ao_two_e_ints/`
+
+d) the two-electron integrals on the MO basis, which are computed in :file:`qp2/src/mo_two_e_ints/`
+
+Therefore, we will need the following four modules:
+
+ a) ao_one_e_ints
+ b) mo_one_e_ints
+ c) ao_two_e_ints
+ d) mo_two_e_ints
+
+You can then create the following "NEED" file by executing the following command 
+
+.. code:: bash
+
+ cat <<EOF > NEED
+ ao_one_e_ints
+ mo_one_e_ints 
+ ao_two_e_ints
+ mo_two_e_ints
+ EOF
+
+II) Installing the plugin 
+-------------------------
+Now that we have specified the various depenencies we need now to INSTALL the plugin, which means to create the equivalent of a Makefile for the compilation. 
+
+To do it we simply do 
+
+.. code:: bash
+
+ qp plugins install plugin_I
+
+
+III) Compiling the void plugin 
+------------------------------
+It is customary to compile first your "void" plugin, void in the sense that it does not contain anything else than the program printing "Hello world". 
+
+To do so, just go in the plugin and execute the following command
+
+.. code:: bash
+
+  ninja 
+
+It does a lot of stuffs, but it must conclude with something like 
+
+.. code:: bash
+
+ make: Leaving directory 'SOME_PATH_TOWARD_YOUR_QP2_DIRECTORY/qp2/ocaml'
+
+
+Since that it has compiled, an executable "plugin_I" has been created. 
+
+Also, if you make "ls" in the "plugin_I" you will notice that many symbolink links have been created, and among which the four modules that you included in the NEED file. 
+
+All the other modules (Ex::ref:`module_ao_basis`, :ref:`module_utils`) are here because they are need by some of the  four modules that you need. 
+The variables that we need are 
+
+:data:`ao_one_e_integrals`
+
+:data:`mo_one_e_integrals`
+
+You can check them with 
+
+.. code:: bash
+
+ irpman ao_one_e_integrals
+
+
+.. code:: bash
+
+ irpman mo_one_e_integrals
+
+in order to get some information on where they are created, and many more information. 
+We will now create an executable such that it prints out the integrals. 
+
+
+IV) Printing out the one-electron integrals
+--------------------------------------------
+We will now create a program that will print out the one-electron integrals on the AO and MO basis.
+
+You can then copy the file :file:`qp2/plugins/tuto_plugins/tuto_I/print_one_e_h.irp.f` in your plugin. 
+
+In this file you will see that we simply browse the two arrays :data:`ao_one_e_integrals` and :data:`mo_one_e_integrals`, which are the providers and we browse them until either :data:`ao_num` or :data:`mo_num` which are also providers representing the number of AOs or MOs. 
+
+
+.. seealso::
+
+ You can check these variables with :command:`irpman` ! 
+
+If you recompile using |ninja| as before, and another executable has been created "print_one_e_h". 
+Then, you can run the program on the ezfio file by doing 
+
+.. code:: bash
+
+ qp run print_one_e_h 
+
+and will print out the data you need :) 
+
+By the way, as the file :file:`plugin_I.irp.f` contains nothing but a "Hello world" print, you can simply remove it if you want. 
+
+V) Printing out the two-electron integrals
+------------------------------------------
+We will now create a file that prints out the two-electron integrals in the AO and MO basis.
+These can be accessed with the following subroutines :
+
+1- :c:func:`get_ao_two_e_integral` for the AO basis 
+
+2- :c:func:`get_two_e_integral` for the MO basis 
+
+
+.. seealso::
+
+ check them with irpman !
+
+To print the two-electron integrals, you can copy the file :file:`qp2/plugins/tuto_plugins/tuto_I/print_two_e_h.irp.f` in your plugin and recompile with |ninja|. 
+Then just run the program 
+
+.. code:: bash
+
+ qp run print_two_e_h
+
+and it will print all the things you want :)
+
+VI) Creating new providers and a program to print them
+------------------------------------------------------
+We will now create new providers that manipulates the objects that we just printed.
+As an example, we will compute the trace of the one electron integrals in the AO and MO basis. 
+In the file :file:`qp2/plugins/tuto_plugins/tuto_I/traces_one_e.irp.f` you will find the several new providers among which 
+
+ 1- :c:data:`trace_mo_one_e_ints` : simply the sum of the diagonal matrix element of the one-electron integrals
+
+ 2- :c:data:`trace_ao_one_e_ints` : the corresponding trace on the AO basis 
+   .. math::                                                                                                              
+
+      \text{Tr}({\bf h}{\bf S}^{-1}) =  \sum_{m,n} S^{-1}_{mn} h_{mn}
+
+
+ 3- :c:data:`trace_ao_one_e_ints_from_mo` : the trace on the AO basis with the integrals obtained first from the MO basis 
+   .. math::                                                                                                              
+
+      \text{Tr}({\bf \tilde{h}}{\bf S}^{-1}) = \text{Tr}\big({\bf SC h}({\bf SC }^T){\bf S}^{-1}\big) 
+
+Just copy the :file:`qp2/plugins/tuto_plugins/tuto_I/traces_one_e.irp.f` in your plugin and recompile. 
+
+.. seealso::
+
+ Once it has compiled, check your new providers with :command:`irpman` !
+
+As explained in the files :file:`qp2/plugins/tuto_plugins/tuto_I/traces_one_e.irp.f` and :file:`qp2/plugins/tuto_plugins/tuto_I/print_traces_on_e.irp.f`, :c:data:`trace_mo_one_e_ints` is equal to :c:data:`trace_ao_one_e_ints` only if the number of AO basis functions is equal to the number of MO basis functions, which means if you work with cartesian functions. 
+
+
+.. seealso::
+
+ You can check with :command:`qp create_ezfio -h` for the option to create an |EZFIO| with cartesian basis functions
+
+In the file :file:`qp2/plugins/tuto_plugins/tuto_I/print_traces_on_e.irp.f` you will find an example of executable that prints out the various providers. 
+Copy these two files in your plugin and recompile to execute it.
+
+Execute the program print_traces_on_e and check for the results with 
+
+.. code:: bash
+
+ qp run print_traces_on_e
+
+The code in  :file:`qp2/plugins/tuto_plugins/tuto_I/print_traces_on_e.irp.f` should be easy to read, I let the reader interpret it.

src/ao_one_e_ints/ao_one_e_ints.irp.f

@@ -45,3 +45,13 @@ BEGIN_PROVIDER [ double precision, ao_one_e_integrals_imag,(ao_num,ao_num)]
 
 END_PROVIDER
 
+
+BEGIN_PROVIDER [ double precision, ao_one_e_integrals_from_mo, (ao_num, ao_num)]
+ implicit none
+ BEGIN_DOC
+! Integrals of the one e hamiltonian obtained from the integrals on the MO basis 
+!
+! WARNING : this is equal to ao_one_e_integrals only if the AO and MO basis have the same number of functions
+ END_DOC
+ call mo_to_ao(mo_one_e_integrals,mo_num,ao_one_e_integrals_from_mo,ao_num)
+END_PROVIDER 

src/davidson/diagonalization_hs2_dressed.irp.f

@@ -522,6 +522,84 @@ subroutine davidson_diag_hjj_sjj(dets_in,u_in,H_jj,s2_out,energies,dim_in,sze,N_
         enddo
       endif
 
+      if (state_following) then
+         if (.not. only_expected_s2) then
+           print*,''
+           print*,'!!! State following only available with only_expected_s2 = .True. !!!'
+           STOP
+         endif
+       endif
+
+      if (state_following) then
+
+        integer ::  state(N_st), idx
+        double precision :: omax
+        logical :: used
+        logical, allocatable :: ok(:)
+        double precision, allocatable :: overlp(:,:)
+
+        allocate(overlp(shift2,N_st),ok(shift2))
+
+        overlp = 0d0
+        do j = 1, shift2-1, N_st_diag
+
+          ! Computes some states from the guess vectors
+          ! Psi(:,j:j+N_st_diag) = U y(:,j:j+N_st_diag) and put them
+          ! in U(1,shift2+1:shift2+1+N_st_diag) as temporary array
+          call dgemm('N','N', sze, N_st_diag, shift2,                    &
+          1.d0, U, size(U,1), y(1,j), size(y,1), 0.d0, U(1,shift2+1), size(U,1))
+
+          ! Overlap
+          do l = 1, N_st
+            do k = 1, N_st_diag
+              do i = 1, sze
+                overlp(k+j-1,l) += U(i,l) * U(i,shift2+k)
+              enddo
+            enddo
+          enddo
+
+        enddo
+
+        state = 0
+        do l = 1, N_st
+
+          omax = 0d0
+          idx = 0
+          do k = 1, shift2
+
+            ! Already used ?
+            used = .False.
+            do i = 1, N_st
+              if (state(i) == k) then
+                used = .True.
+              endif
+            enddo
+
+            ! Maximum overlap
+            if (dabs(overlp(k,l)) > omax .and. .not. used .and. state_ok(k)) then
+              omax = dabs(overlp(k,l))
+              idx = k
+            endif
+          enddo
+
+          state(l) = idx
+        enddo
+
+        ! tmp array before setting state_ok
+        ok = .False.
+        do l = 1, N_st
+          ok(state(l)) = .True.
+        enddo
+
+        do k = 1, shift2
+          if (.not. ok(k)) then
+            state_ok(k) = .False.
+          endif
+        enddo
+
+        deallocate(overlp,ok)
+      endif
+
       do k=1,shift2
         if (.not. state_ok(k)) then
           do l=k+1,shift2
@@ -537,46 +615,46 @@ subroutine davidson_diag_hjj_sjj(dets_in,u_in,H_jj,s2_out,energies,dim_in,sze,N_
         endif
       enddo
 
-      if (state_following) then
-
-        overlap = -1.d0
-        do k=1,shift2
-          do i=1,shift2
-            overlap(k,i) = dabs(y(k,i))
-          enddo
-        enddo
-        do k=1,N_st
-          cmax = -1.d0
-          do i=1,N_st
-            if (overlap(i,k) > cmax) then
-              cmax = overlap(i,k)
-              order(k) = i
-            endif
-          enddo
-          do i=1,N_st_diag
-            overlap(order(k),i) = -1.d0
-          enddo
-        enddo
-        overlap = y
-        do k=1,N_st
-          l = order(k)
-          if (k /= l) then
-            y(1:shift2,k) = overlap(1:shift2,l)
-          endif
-        enddo
-        do k=1,N_st
-          overlap(k,1) = lambda(k)
-          overlap(k,2) = s2(k)
-        enddo
-        do k=1,N_st
-          l = order(k)
-          if (k /= l) then
-            lambda(k) = overlap(l,1)
-            s2(k) = overlap(l,2)
-          endif
-        enddo
-
-      endif
+!      if (state_following) then
+!
+!        overlap = -1.d0
+!        do k=1,shift2
+!          do i=1,shift2
+!            overlap(k,i) = dabs(y(k,i))
+!          enddo
+!        enddo
+!        do k=1,N_st
+!          cmax = -1.d0
+!          do i=1,N_st
+!            if (overlap(i,k) > cmax) then
+!              cmax = overlap(i,k)
+!              order(k) = i
+!            endif
+!          enddo
+!          do i=1,N_st_diag
+!            overlap(order(k),i) = -1.d0
+!          enddo
+!        enddo
+!        overlap = y
+!        do k=1,N_st
+!          l = order(k)
+!          if (k /= l) then
+!            y(1:shift2,k) = overlap(1:shift2,l)
+!          endif
+!        enddo
+!        do k=1,N_st
+!          overlap(k,1) = lambda(k)
+!          overlap(k,2) = s2(k)
+!        enddo
+!        do k=1,N_st
+!          l = order(k)
+!          if (k /= l) then
+!            lambda(k) = overlap(l,1)
+!            s2(k) = overlap(l,2)
+!          endif
+!        enddo
+!
+!      endif
 
 
       ! Express eigenvectors of h in the determinant basis

src/davidson/diagonalize_ci.irp.f

@@ -123,6 +123,7 @@ END_PROVIDER
         endif
 
      enddo
+
      if (N_states_diag > N_states_diag_save) then
        N_states_diag = N_states_diag_save
        TOUCH N_states_diag
@@ -133,24 +134,101 @@ END_PROVIDER
      print *,  'Diagonalization of H using Lapack'
      allocate (eigenvectors(size(H_matrix_all_dets,1),N_det))
      allocate (eigenvalues(N_det))
+
      if (s2_eig) then
+
        double precision, parameter :: alpha = 0.1d0
        allocate (H_prime(N_det,N_det) )
+
        H_prime(1:N_det,1:N_det) = H_matrix_all_dets(1:N_det,1:N_det) +  &
          alpha * S2_matrix_all_dets(1:N_det,1:N_det)
+
        do j=1,N_det
          H_prime(j,j) = H_prime(j,j) - alpha*expected_s2
        enddo
+
        call lapack_diag(eigenvalues,eigenvectors,H_prime,size(H_prime,1),N_det)
        call nullify_small_elements(N_det,N_det,eigenvectors,size(eigenvectors,1),1.d-12)
+
        CI_electronic_energy(:) = 0.d0
        i_state = 0
+
        allocate (s2_eigvalues(N_det))
        allocate(index_good_state_array(N_det),good_state_array(N_det))
+
        good_state_array = .False.
        call u_0_S2_u_0(s2_eigvalues,eigenvectors,N_det,psi_det,N_int,&
          N_det,size(eigenvectors,1))
-       if (only_expected_s2) then
+
+       if (state_following) then
+         if (.not. only_expected_s2) then
+           print*,''
+           print*,'!!! State following only available with only_expected_s2 = .True. !!!'
+           STOP
+         endif
+         if (N_det < N_states) then
+           print*,''
+           print*,'!!! State following requires at least N_states determinants to be activated !!!'
+           STOP
+         endif
+       endif
+
+       if (state_following .and. only_expected_s2) then
+
+         integer :: state(N_states), idx,l
+         double precision :: omax
+         double precision, allocatable :: overlp(:)
+         logical :: used
+         logical, allocatable :: ok(:)
+
+         allocate(overlp(N_det), ok(N_det))
+
+         i_state = 0
+         state = 0
+         do l = 1, N_states
+
+           ! Overlap wrt each state
+           overlp = 0d0
+           do k = 1, N_det
+             do i = 1, N_det
+               overlp(k) = overlp(k) + psi_coef(i,l) * eigenvectors(i,k)
+             enddo
+           enddo
+
+           ! Idx of the state with the maximum overlap not already "used"
+           omax = 0d0
+           idx = 0
+           do k = 1, N_det
+
+             ! Already used ?
+             used = .False.
+             do i = 1, N_states
+               if (state(i) == k) then
+                 used = .True.
+               endif
+             enddo
+
+             ! Maximum overlap
+             if (dabs(overlp(k)) > omax .and. .not. used) then
+               if (dabs(s2_eigvalues(k)-expected_s2) > 0.5d0) cycle
+               omax = dabs(overlp(k))
+               idx = k
+             endif
+           enddo
+
+           state(l) = idx
+           i_state +=1
+         enddo
+
+         deallocate(overlp, ok)
+
+         do i = 1, i_state
+           index_good_state_array(i) = state(i)
+           good_state_array(i) = .True.
+         enddo
+
+       else if (only_expected_s2) then
+
          do j=1,N_det
            ! Select at least n_states states with S^2 values closed to "expected_s2"
            if(dabs(s2_eigvalues(j)-expected_s2).le.0.5d0)then
@@ -158,17 +236,23 @@ END_PROVIDER
              index_good_state_array(i_state) = j
              good_state_array(j) = .True.
            endif
+
            if(i_state.eq.N_states) then
              exit
            endif
          enddo
+
        else
+
          do j=1,N_det
            index_good_state_array(j) = j
            good_state_array(j) = .True.
          enddo
+
        endif
+
        if(i_state .ne.0)then
+
          ! Fill the first "i_state" states that have a correct S^2 value
          do j = 1, i_state
            do i=1,N_det
@@ -177,6 +261,7 @@ END_PROVIDER
            CI_electronic_energy(j) = eigenvalues(index_good_state_array(j))
            CI_s2(j) = s2_eigvalues(index_good_state_array(j))
          enddo
+
          i_other_state = 0
          do j = 1, N_det
            if(good_state_array(j))cycle
@@ -201,6 +286,7 @@ END_PROVIDER
          print*,'  as the CI_eigenvectors'
          print*,'  You should consider more states and maybe ask for s2_eig to be .True. or just enlarge the CI space'
          print*,''
+
          do j=1,min(N_states_diag,N_det)
            do i=1,N_det
              CI_eigenvectors(i,j) = eigenvectors(i,j)
@@ -209,14 +295,18 @@ END_PROVIDER
            CI_s2(j) = s2_eigvalues(j)
          enddo
        endif
+
        deallocate(index_good_state_array,good_state_array)
        deallocate(s2_eigvalues)
+
      else
+
        call lapack_diag(eigenvalues,eigenvectors,                    &
            H_matrix_all_dets,size(H_matrix_all_dets,1),N_det)
        CI_electronic_energy(:) = 0.d0
        call u_0_S2_u_0(CI_s2,eigenvectors,N_det,psi_det,N_int,       &
            min(N_det,N_states_diag),size(eigenvectors,1))
+
        ! Select the "N_states_diag" states of lowest energy
        do j=1,min(N_det,N_states_diag)
          do i=1,N_det
@@ -224,7 +314,9 @@ END_PROVIDER
          enddo
          CI_electronic_energy(j) = eigenvalues(j)
        enddo
+
      endif
+
      do k=1,N_states_diag
        CI_electronic_energy(k) = 0.d0
        do j=1,N_det
@@ -235,6 +327,7 @@ END_PROVIDER
          enddo
        enddo
      enddo
+
      deallocate(eigenvectors,eigenvalues)
    endif
 

src/scf_utils/fock_matrix.irp.f

@@ -166,6 +166,10 @@
 
    if(frozen_orb_scf)then
      integer                        :: iorb,jorb
+     !       active|core|active
+     !active |     | 0  |      
+     !core   |  0  |    |   0
+     !active |     | 0  |       
      do i = 1, n_core_orb
       iorb = list_core(i)
       do j = 1, n_act_orb

src/utils/linear_algebra.irp.f

@@ -2041,3 +2041,22 @@ subroutine get_A_squared(A,n,A2)
  double precision, intent(out):: A2(n,n) 
  call dgemm('N','N',n,n,n,1.d0,A,size(A,1),A,size(A,1),0.d0,A2,size(A2,1))
 end
+
+subroutine get_AB_prod(A,n,m,B,l,AB)
+ implicit none
+ BEGIN_DOC
+! AB = A B where A is n x m, B is m x l. Use the dgemm routine 
+ END_DOC
+ double precision, intent(in) :: A(n,m),B(m,l)
+ integer, intent(in) :: n,m,l
+ double precision, intent(out):: AB(n,l) 
+ if(size(A,2).ne.m.or.size(B,1).ne.m)then
+  print*,'error in get_AB_prod ! '
+  print*,'matrices do not have the good dimension '
+  print*,'size(A,2) = ',size(A,2)
+  print*,'size(B,1) = ',size(B,1)
+  print*,'m         = ',m
+  stop
+ endif
+ call dgemm('N','N',n,l,m,1.d0,A,size(A,1),B,size(B,1),0.d0,AB,size(AB,1))
+end