added some providers and the first tutorial for plugins

plugins/README.rst

@@ -22,6 +22,8 @@ we will go through a series of examples that allow you to do the following thing
  IV)  print out the one- and two-electron rdms, 
  V)   obtain the AOs and MOs on the DFT grid, together with the density,
 
+How the tutorial will be done
+-----------------------------
 This tuto is as follows: 
  i)  you READ THIS FILE UNTIL THE END in order to get the big picture and vocabulary, 
  ii) you go to the directory qp2/plugins/tuto_plugins/ and you will find detailed tuto there for each of the 5 examples. 
@@ -32,7 +34,7 @@ The first thing to do is to be in the QPSH mode: you execute the qp2/bin/qpsh sc
 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. 
-!!!! WARINING: The plugins are NECESSARILY located in qp2/plugins/ !!!!
+!!!! WARNING: The plugins are NECESSARILY located in qp2/plugins/ !!!!
 Ex: If you want to create a plugin named "my_fancy_plugin" in the directory plugins/plugins_test/, 
 this goes with the command 
 qp plugins create -n my_fancy_plugin -r plugins_test/

plugins/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/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/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/tuto_plugins/tuto_I/tuto_I.rst

@@ -1,14 +1,15 @@
-======================================
-Tutorial for plugin I: One-e integrals
-======================================
+=====================================================================
+Tutorial for plugin I: One-e integrals (duration: 20 minutes at most)
+=====================================================================
 
-!!! Requirements: 
- a) you know how to create an EZFIO file and run calculations with QP 
+Requirements 
+------------
+ a) You know how to create an EZFIO file and run calculations with QP 
  (check the tuto: `<https://quantumpackage.github.io/qp2/post/hartree-fock/>`),
- b) you have an EZFIO file in the sto-3g from the file H2.xyz in plugins/tuto_plugins,  
-    and you have run an HF calculation giving an energy of -1.116759 a.u.,
- c) you made an qp set_file YOUR_EZFIO_FILE_FOR_H2 in order to be, 
- d) you have READ the ../README.rst file to HAVE THE VOCABULARY.  
+ b) You have an EZFIO file with MOs created (with the '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 :)
+ c) You made an qp set_file YOUR_EZFIO_FILE_FOR_H2 in order to work on that ezfio folder, 
+ d) You have READ the ../README.rst file to HAVE THE VOCABULARY.  
 
 Our goals:
 ----------
@@ -22,14 +23,14 @@ I) Starting: creating the plugin
 We will go step-by-step through these plugins. 
 
 The name of the plugin will be "plugin_I", and its location is in "tuto_plugins". 
-Therefore to create the plugin, we do 
+Therefore to create the plugin, we do: 
 
-$ qp plugins create -n plugin_I -r tuto_plugins
-Then to an "ls" in qp2/plugins/tuto_plugins/ 
-and you will find a directory called "plugin_I". 
+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: 
- i)  a "NEED" file that will eventually contain all the other modules/plugins needed by our "plugin_I"
- ii) a "README.rst" file that you can AND SHOULD modify in order to document what is doing the plugin. 
+ i)   a "NEED" file that will eventually contain all the other modules/plugins needed by our "plugin_I"
+ ii)  a "README.rst" file that you can AND SHOULD modify in order to document what is doing the plugin. 
  iii) a "plugin_I.irp.f" file that is a program to be compiled and just printing "Hello world" 
 
 II) Specifying the dependencies
@@ -78,8 +79,8 @@ The variables that we need are
 ao_one_e_integrals 
 mo_one_e_integrals
 You can check them with 
-irpman ao_one_e_integral
-irpman mo_one_e_integral
+irpman ao_one_e_integrals
+irpman mo_one_e_integrals
 in order to get some information on where they are created, and many more information. 
 We will modify the executable such that it prints out the integrals. 
 
@@ -87,7 +88,7 @@ We will modify the executable such that it prints out the integrals.
 IV) Printing out the one-electron integrals
 --------------------------------------------
 We will create a program that will print out the one-electron integrals on the AO and MO basis.
-You can then copy the file "print_one_e_h.irp.f" in your plugin. 
+You can then copy the file "print_one_e_h.irp.f" located in "plugins/tuto_plugins/tuto_I" in your plugin. 
 In the file you will see that we simply browse the two arrays "ao_one_e_integrals" and "mo_one_e_integrals", which are global variables (providers) and we browse them until either "ao_num" or "mo_num" which are also providers representing the number of AOs or MOs. 
 You can check these variables with irpman ! 
 If you recompile using "ninja" as before, and another executable has been created "print_one_e_h". 
@@ -95,3 +96,31 @@ Then, you can run the program on the ezfio file by doing
 qp run print_one_e_h 
 and will print out the data you need :) 
 
+By the way, as the 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 :
++) get_ao_two_e_integral for the AO basis 
++) get_two_e_integral for the MO basis 
+check them with irpman !
+To print the two-electron integrals, you can copy the file "print_two_e_h.irp.f" in your plugin and recompile. 
+Then just run the program 
+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 "traces_one_e.irp.f" you will find the several new providers among which 
+ a) trace_mo_one_e_ints         : simply the sum of the diagonal matrix element of the one-electron integrals
+ b) trace_ao_one_e_ints         : the corresponding trace on the AO basis : Sum(m,n) S^{-1}_{mn} h_{mn}
+ c) trace_ao_one_e_ints_from_mo : the trace on the AO basis with the integrals obtained first from the MO basis 
+As explained in these files, "trace_mo_one_e_ints" is equal to "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. 
+(You can check with "qp create_ezfio -h" for the option to create an EZFIO with cartesian basis functions)
+
+In the file "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 !

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/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