add mo localization

src/mo_localization/84.mo_localization.bats

@@ -0,0 +1,97 @@
+#!/usr/bin/env bats
+
+source $QP_ROOT/tests/bats/common.bats.sh
+source $QP_ROOT/quantum_package.rc
+
+zero () {
+    if [ -z "$1" ]; then echo 0.0; else echo $1; fi
+}
+
+function run() {
+  thresh1=1e-10
+  thresh2=1e-12
+  thresh3=1e-4
+  test_exe scf || skip
+  qp set_file $1
+  qp edit --check
+  qp reset -d
+  qp set_frozen_core
+  qp set localization localization_method boys
+  file="$(echo $1 | sed 's/.ezfio//g')"
+  energy="$(cat $1/hartree_fock/energy)"
+  fb_err1="$(qp run debug_gradient_loc | grep 'Max error' | tail -n 1 | awk '{print $3}')"
+  fb_err2="$(qp run debug_hessian_loc | grep 'Max error' | tail -n 1 | awk '{print $3}')"
+  qp run localization > $file.loc.out
+  fb_energy="$(qp run print_energy | grep -A 1 'Nuclear repulsion energy' | tail -n 1 )"
+  fb_c="$(cat $file.loc.out | grep 'Criterion:Core' | tail -n 1 | awk '{print $3}')i"
+  fb_i="$(cat $file.loc.out | grep 'Criterion:Inactive' | tail -n 1 | awk '{print $3}')"
+  fb_a="$(cat $file.loc.out | grep 'Criterion:Active' | tail -n 1 | awk '{print $3}')"
+  fb_v="$(cat $file.loc.out | grep 'Criterion:Virtual' | tail -n 1 | awk '{print $3}')"
+  qp reset -a
+  qp run scf
+  qp set_frozen_core
+  qp set localization localization_method pipek 
+  pm_err1="$(qp run debug_gradient_loc | grep 'Max error' | tail -n 1 | awk '{print $3}')"
+  pm_err2="$(qp run debug_hessian_loc | grep 'Max error' | tail -n 1 | awk '{print $3}')"
+  qp run localization > $file.loc.out
+  pm_c="$(cat $file.loc.out | grep 'Criterion:Core' | tail -n 1 | awk '{print $3}')i"
+  pm_i="$(cat $file.loc.out | grep 'Criterion:Inactive' | tail -n 1 | awk '{print $3}')"
+  pm_a="$(cat $file.loc.out | grep 'Criterion:Active' | tail -n 1 | awk '{print $3}')"
+  pm_v="$(cat $file.loc.out | grep 'Criterion:Virtual' | tail -n 1 | awk '{print $3}')"
+  pm_energy="$(qp run print_energy | grep -A 1 'Nuclear repulsion energy' | tail -n 1 )"
+  qp set localization localization_method boys
+  qp reset -a
+  qp run scf
+  qp set_frozen_core
+  eq $energy $fb_energy $thresh1 
+  eq $fb_err1 0.0 $thresh2
+  eq $fb_err2 0.0 $thresh2
+  eq $energy $pm_energy $thresh1
+  eq $pm_err1 0.0 $thresh2
+  eq $pm_err2 0.0 $thresh2
+  fb_c=$(zero $fb_c)
+  fb_i=$(zero $fb_i)
+  fb_a=$(zero $fb_a)
+  fb_v=$(zero $fb_v)
+  pm_c=$(zero $pm_c)
+  pm_i=$(zero $pm_i)
+  pm_a=$(zero $pm_a)
+  pm_v=$(zero $pm_v)
+  eq $fb_c $2 $thresh3
+  eq $fb_i $3 $thresh3
+  eq $fb_a $4 $thresh3
+  eq $fb_v $5 $thresh3
+  eq $pm_c $6 $thresh3
+  eq $pm_i $7 $thresh3
+  eq $pm_a $8 $thresh3
+  eq $pm_v $9 $thresh3
+}
+
+@test "b2_stretched" {
+run  b2_stretched.ezfio -32.1357551678876 -47.0041982094667 0.0 -223.470015856259 -1.99990778964451 -2.51376723927071 0.0 -12.8490602539275
+}
+
+@test "clo" {
+run  clo.ezfio -44.1624001765291 -32.4386660941387 0.0 -103.666309287187 -5.99985418946811 -5.46871580225222 0.0 -20.2480064922275
+}
+
+@test "clf" {
+run  clf.ezfio -47.5143398826967 -35.7206886315104 0.0 -107.043029033468 -5.99994222062230 -6.63916513458470 0.0 -19.7035159913484
+}
+
+@test "h2o2" {
+run  h2o2.ezfio -7.76848143170524 -30.9694344369829 0.0 -175.898343829453 -1.99990497554575 -5.62980322957485 0.0 -33.5699813186666
+}
+
+@test "h2o" {
+run  h2o.ezfio 0.0 -2.52317434969591 0.0 -45.3136377925359 0.0 -3.01248365356981 0.0 -22.4470831240924
+}
+
+@test "h3coh" {
+run  h3coh.ezfio -3.66763692804590 -24.0463089480870 0.0 -111.485948435075 -1.99714061342078 -4.89242181322988 0.0 -23.6405412057679
+}
+
+@test "n2h4" {
+run  n2h4.ezfio -7.46608163002070 -35.7632174051822 0.0 -305.913449004632 -1.99989326143356 -4.62496615892268 0.0 -51.5171904685553
+}
+

src/mo_localization/EZFIO.cfg

@@ -0,0 +1,54 @@
+[localization_method]
+type: character*(32)
+doc: Method for the orbital localization. boys: Foster-Boys, pipek: Pipek-Mezey.
+interface: ezfio,provider,ocaml
+default: boys
+
+[localization_max_nb_iter]
+type: integer
+doc: Maximal number of iterations for the orbital localization.
+interface: ezfio,provider,ocaml
+default: 1000
+
+[localization_use_hessian]
+type: logical
+doc: If true, it uses the trust region algorithm with the gradient and the diagonal of the hessian. Else it computes the rotation between each pair of MOs that should be applied to maximize/minimize the localization criterion. The last option is not easy to converge. 
+interface: ezfio,provider,ocaml
+default: true
+
+[auto_mo_class]
+type: logical
+doc: If true, set automatically the classes.
+interface: ezfio,provider,ocaml
+default: true
+
+[thresh_loc_max_elem_grad]
+type: double precision
+doc: Threshold for the convergence, the localization exits when the largest element in the gradient is smaller than thresh_localization_max_elem_grad.
+interface: ezfio,provider,ocaml
+default: 1.e-6
+
+[kick_in_mos]
+type: logical
+doc: If True, it applies a rotation of an angle angle_pre_rot between the MOs of a same mo_class before the localization.
+interface: ezfio,provider,ocaml
+default: true
+
+[angle_pre_rot]
+type: double precision
+doc: To define the angle for the rotation of the MOs before the localization (in rad).
+interface: ezfio,provider,ocaml
+default: 0.1
+
+[sort_mos_by_e]
+type: logical
+doc: If True, the MOs are sorted using the diagonal elements of the Fock matrix.
+interface: ezfio,provider,ocaml
+default: false
+
+[debug_hf]
+type: logical
+doc: If True, prints the HF energy before/after the different steps of the localization. Only for debugging.
+interface: ezfio,provider,ocaml
+default: false
+

src/mo_localization/NEED

@@ -0,0 +1,3 @@
+hartree_fock
+utils_trust_region
+determinants

src/mo_localization/README.md

@@ -0,0 +1,113 @@
+# Orbital localisation
+To localize the MOs:  
+```
+qp run localization  
+```
+By default, the different otbital classes are automatically set by splitting  
+the orbitales in the following classes:  
+- Core -> Core  
+- Active, doubly occupied -> Inactive  
+- Active, singly occupied -> Active  
+- Active, empty -> Virtual  
+- Deleted -> Deleted  
+The orbitals will be localized among each class, excpect the deleted ones.
+If you want to choose another splitting, you can set
+```
+qp set mo_localization auto_mo_class false
+```
+and define the classes with
+```
+qp set_mo_class -c [] -a [] -v [] -i [] -d [] 
+```
+for more information
+```
+qp set_mo_class -q
+```
+We don't care about the name of the   
+mo classes. The algorithm just localizes all the MOs of  
+a given class between them, for all the classes, except the deleted MOs.  
+If you are using the last option don't forget to reset the initial mo classes  
+after the localization.
+
+Before the localization, a kick is done for each mo class  
+(except the deleted ones) to break the MOs. This is done by   
+doing a given rotation between the MOs.
+This feature can be removed by setting:
+```
+qp set localization kick_in_mos false
+```
+and the default angle for the rotation can be changed with:
+```
+qp set localization angle_pre_rot 1e-3 # or something else
+```
+
+After the localization, the MOs of each class (except the deleted ones)  
+can be sorted between them using the diagonal elements of  
+the fock matrix with:
+```
+qp set localization sort_mos_by_e true
+```
+
+You can check the Hartree-Fock energy before/during/after the localization  
+by putting (only for debugging):
+```
+qp set localization debug_hf true 
+```
+
+## Foster-Boys & Pipek-Mezey
+Foster-Boys:  
+``` 
+qp set localization localization_method boys 
+``` 
+ 
+Pipek-Mezey:  
+``` 
+qp set localization localization_method pipek 
+``` 
+
+# Break the spatial symmetry of the MOs
+This program work exactly as the localization.  
+To break the spatial symmetry of the MOs:   
+```
+qp run break_spatial_sym
+```
+The default angle for the rotations is too big for this kind of
+application, a value between 1e-3 and 1e-6 should break the spatial
+symmetry with just a small change in the energy:
+```
+qp set localization angle_pre_rot 1e-3
+``` 
+
+# With or without hessian + trust region
+With hessian +  trust region
+```
+qp set localization localisation_use_hessian true
+```
+It uses the trust region algorithm with the diagonal of the hessian of the 
+localization criterion with respect to the MO rotations.   
+
+Without the hessian and the trust region
+```
+qp set localization localisation_use_hessian false
+```
+By doing so it does not require to store the hessian but the
+convergence is not easy, in particular for virtual MOs.
+It seems that it not possible to converge with Pipek-Mezey
+localization with this approach.
+
+# Parameters
+Some other parameters are available for the localization (qp edit for more details).
+
+# Tests
+```
+qp test
+```
+
+# Org files
+The org files are stored in the directory org in order to avoid overwriting on user changes.
+The org files can be modified, to export the change to the source code, run
+```
+./TANGLE_org_mode.sh
+mv *.irp.f ../.
+```
+ 

src/mo_localization/break_spatial_sym.irp.f

@@ -0,0 +1,27 @@
+! ! A small program to break the spatial symmetry of the MOs.
+
+! ! You have to defined your MO classes or set security_mo_class to false
+! ! with:
+! ! qp set orbital_optimization security_mo_class false
+
+! ! The default angle for the rotations is too big for this kind of
+! ! application, a value between 1e-3 and 1e-6 should break the spatial
+! ! symmetry with just a small change in the energy. 
+
+
+program break_spatial_sym
+
+  !BEGIN_DOC
+  ! Break the symmetry of the MOs with a rotation
+  !END_DOC
+
+  implicit none
+
+  kick_in_mos = .True.
+  TOUCH kick_in_mos
+
+  call set_classes_loc 
+  call apply_pre_rotation
+  call unset_classes_loc 
+  
+end

src/mo_localization/debug_gradient_loc.irp.f

@@ -0,0 +1,65 @@
+program debug_gradient_loc
+
+  !BEGIN_DOC
+  ! Check if the gradient is correct
+  !END_DOC
+
+  implicit none
+
+  integer :: list_size, n
+  integer, allocatable :: list(:)
+  double precision, allocatable :: v_grad(:), v_grad2(:)
+  double precision :: norm, max_elem, threshold, max_error
+  integer :: i, nb_error
+
+  threshold = 1d-12
+
+  list_size = dim_list_act_orb
+
+  allocate(list(list_size))
+  
+  list = list_act
+
+  n = list_size*(list_size-1)/2
+  
+  allocate(v_grad(n),v_grad2(n))
+
+  if (localization_method == 'boys') then
+    print*,'Foster-Boys'
+    call gradient_FB(n,list_size,list,v_grad,max_elem,norm)
+    call gradient_FB_omp(n,list_size,list,v_grad2,max_elem,norm)
+  elseif (localization_method == 'pipek') then
+    print*,'Pipek-Mezey'
+    call gradient_PM(n,list_size,list,v_grad,max_elem,norm)
+    call gradient_PM(n,list_size,list,v_grad2,max_elem,norm) 
+  else
+    print*,'Unknown localization_method, please select boys or pipek'
+    call abort
+  endif
+ 
+  do i = 1, n
+    print*,i,v_grad(i)
+  enddo
+
+  v_grad = v_grad - v_grad2
+
+  nb_error = 0
+  max_elem = 0d0
+
+  do i = 1, n
+    if (dabs(v_grad(i)) > threshold) then
+      print*,v_grad(i)
+      nb_error = nb_error + 1
+      if (dabs(v_grad(i)) > max_elem) then
+        max_elem = v_grad(i)
+      endif
+    endif
+  enddo
+
+  print*,'Threshold error', threshold
+  print*, 'Nb error', nb_error
+  print*,'Max error', max_elem
+
+  deallocate(v_grad,v_grad2)
+ 
+end

src/mo_localization/debug_hessian_loc.irp.f

@@ -0,0 +1,65 @@
+program debug_hessian_loc
+
+  !BEGIN_DOC
+  ! Check if the hessian is correct
+  !END_DOC
+  
+  implicit none
+
+  integer :: list_size, n
+  integer, allocatable :: list(:)
+  double precision, allocatable :: H(:), H2(:)
+  double precision :: threshold, max_error, max_elem
+  integer :: i, nb_error
+
+  threshold = 1d-12
+
+  list_size = dim_list_act_orb
+
+  allocate(list(list_size))
+  
+  list = list_act
+
+  n = list_size*(list_size-1)/2
+  
+  allocate(H(n),H2(n))
+
+  if (localization_method == 'boys') then
+    print*,'Foster-Boys'
+    call hessian_FB(n,list_size,list,H)
+    call hessian_FB_omp(n,list_size,list,H2)
+  elseif(localization_method == 'pipek') then
+    print*,'Pipek-Mezey'
+    call hessian_PM(n,list_size,list,H)
+    call hessian_PM(n,list_size,list,H2)
+  else
+    print*,'Unknown localization_method, please select boys or pipek'
+    call abort
+  endif
+ 
+  do i = 1, n
+    print*,i,H(i)
+  enddo
+
+  H = H - H2
+
+  nb_error = 0
+  max_elem = 0d0
+
+  do i = 1, n
+    if (dabs(H(i)) > threshold) then
+      print*,H(i)
+      nb_error = nb_error + 1
+      if (dabs(H(i)) > max_elem) then
+        max_elem = H(i)
+      endif
+    endif
+  enddo
+
+  print*,'Threshold error', threshold
+  print*, 'Nb error', nb_error
+  print*,'Max error', max_elem
+
+  deallocate(H,H2)
+  
+end

src/mo_localization/kick_the_mos.irp.f

@@ -0,0 +1,16 @@
+program kick_the_mos
+
+  !BEGIN_DOC
+  ! To do a small rotation of the MOs
+  !END_DOC
+
+  implicit none
+
+  kick_in_mos = .True.
+  TOUCH kick_in_mos
+
+  call set_classes_loc
+  call apply_pre_rotation
+  call unset_classes_loc
+  
+end

src/mo_localization/localization.irp.f

@@ -0,0 +1,520 @@
+program localization
+
+  implicit none
+
+  call set_classes_loc
+  call run_localization
+  call unset_classes_loc
+  
+end
+
+
+
+
+! Variables:
+! | pre_rot(mo_num, mo_num)   | double precision | Matrix for the pre rotation                       |
+! | R(mo_num,mo_num)          | double precision | Rotation matrix                                   |
+! | tmp_R(:,:)                | double precision | Rottation matrix in a subsapce                    |
+! | prev_mos(ao_num, mo_num)  | double precision | Previous mo_coef                                  |
+! | spatial_extent(mo_num)    | double precision | Spatial extent of the orbitals                    |
+! | criterion                 | double precision | Localization criterion                            |
+! | prev_criterion            | double precision | Previous criterion                                |
+! | criterion_model           | double precision | Estimated next criterion                          |
+! | rho                       | double precision | Ratio to measure the agreement between the model  |
+! |                           |                  | and the reality                                   |
+! | delta                     | double precision | Radisu of the trust region                        |
+! | norm_grad                 | double precision | Norm of the gradient                              |
+! | info                      | integer          | for dsyev from Lapack                             |
+! | max_elem                  | double precision | maximal element in the gradient                   |
+! | v_grad(:)                 | double precision | Gradient                                          |
+! | H(:,:)                    | double precision | Hessian (diagonal)                                |
+! | e_val(:)                  | double precision | Eigenvalues of the hessian                        |
+! | W(:,:)                    | double precision | Eigenvectors of the hessian                       |
+! | tmp_x(:)                  | double precision | Step in 1D (in a subaspace)                       |
+! | tmp_m_x(:,:)              | double precision | Step in 2D (in a subaspace)                       |
+! | tmp_list(:)               | double precision | List of MOs in a mo_class                         |
+! | i,j,k                     | integer          | Indexes in the full MO space                      |
+! | tmp_i, tmp_j, tmp_k       | integer          | Indexes in a subspace                             |
+! | l                         | integer          | Index for the mo_class                            |
+! | key(:)                    | integer          | Key to sort the eigenvalues of the hessian        |
+! | nb_iter                   | integer          | Number of iterations                              |
+! | must_exit                 | logical          | To exit the trust region loop                     |
+! | cancel_step               | logical          | To cancel a step                                  |
+! | not_*converged            | logical          | To localize the different mo classes              |
+! | t*                        | double precision | To measure the time                               |
+! | n                         | integer          | mo_num*(mo_num-1)/2, number of orbital parameters |
+! | tmp_n                     | integer          | dim_subspace*(dim_subspace-1)/2                   |
+! |                           |                  | Number of dimension in the subspace               |
+
+! Variables in qp_edit for the localization:
+! | localization_method      |
+! | localization_max_nb_iter |
+! | default_mo_class         |
+! | thresh_loc_max_elem_grad |
+! | kick_in_mos              |
+! | angle_pre_rot            |
+
+! + all the variables for the trust region
+
+! Cf. qp_edit orbital optimization
+
+
+subroutine run_localization
+
+  include 'pi.h'
+
+  BEGIN_DOC
+  ! Orbital localization
+  END_DOC
+
+  implicit none
+
+  ! Variables
+  double precision, allocatable :: pre_rot(:,:), R(:,:)
+  double precision, allocatable :: prev_mos(:,:), spatial_extent(:), tmp_R(:,:)
+  double precision              :: criterion, norm_grad
+  integer                       :: i,j,k,l,p, tmp_i, tmp_j, tmp_k
+  integer                       :: info
+  integer                       :: n, tmp_n, tmp_list_size
+  double precision, allocatable :: v_grad(:), H(:), tmp_m_x(:,:), tmp_x(:),W(:),e_val(:)
+  double precision              :: max_elem, t1, t2, t3, t4, t5, t6
+  integer, allocatable          :: tmp_list(:), key(:)
+  double precision              :: prev_criterion, rho, delta, criterion_model
+  integer                       :: nb_iter, nb_sub_iter
+  logical                       :: not_converged, not_core_converged
+  logical                       :: not_act_converged, not_inact_converged, not_virt_converged
+  logical                       :: use_trust_region, must_exit, cancel_step,enforce_step_cancellation
+
+  n = mo_num*(mo_num-1)/2
+
+  ! Allocation
+  allocate(spatial_extent(mo_num))
+  allocate(pre_rot(mo_num, mo_num), R(mo_num, mo_num))
+  allocate(prev_mos(ao_num, mo_num))
+
+  ! Locality before the localization
+  call compute_spatial_extent(spatial_extent)
+
+  ! Choice of the method
+  print*,''
+  print*,'Localization method:',localization_method
+  if (localization_method == 'boys') then
+    print*,'Foster-Boys localization'
+  elseif (localization_method == 'pipek') then
+    print*,'Pipek-Mezey localization'
+  else
+    print*,'Unknown localization_method, please select boys or pipek'
+    call abort
+  endif
+  print*,''
+
+  ! Localization criterion (FB, PM, ...) for each mo_class
+  print*,'### Before the pre rotation'
+  
+  ! Debug
+  if (debug_hf) then
+    print*,'HF energy:', HF_energy
+  endif
+  
+  do l = 1, 4
+    if (l==1) then ! core
+      tmp_list_size = dim_list_core_orb
+    elseif (l==2) then ! act
+      tmp_list_size = dim_list_act_orb
+    elseif (l==3) then ! inact
+      tmp_list_size = dim_list_inact_orb
+    else ! virt
+      tmp_list_size = dim_list_virt_orb
+    endif
+
+     ! Allocation tmp array  
+    allocate(tmp_list(tmp_list_size))
+
+    ! To give the list of MOs in a mo_class
+    if (l==1) then ! core
+      tmp_list = list_core
+    elseif (l==2) then
+      tmp_list = list_act
+    elseif (l==3) then
+      tmp_list = list_inact
+    else
+      tmp_list = list_virt
+    endif
+
+    if (tmp_list_size >= 2) then
+      call criterion_localization(tmp_list_size, tmp_list,criterion)
+      print*,'Criterion:', criterion, mo_class(tmp_list(1))
+    endif
+
+    deallocate(tmp_list)    
+
+  enddo
+
+  ! Debug
+  !print*,'HF', HF_energy
+
+! Loc
+
+! Pre rotation, to give a little kick in the MOs
+  call apply_pre_rotation()
+
+  ! Criterion after the pre rotation
+  ! Localization criterion (FB, PM, ...) for each mo_class
+  print*,'### After the pre rotation'
+  
+  ! Debug
+  if (debug_hf) then
+    touch mo_coef
+    print*,'HF energy:', HF_energy
+  endif
+  
+  do l = 1, 4
+    if (l==1) then ! core
+      tmp_list_size = dim_list_core_orb
+    elseif (l==2) then ! act
+      tmp_list_size = dim_list_act_orb
+    elseif (l==3) then ! inact
+      tmp_list_size = dim_list_inact_orb
+    else ! virt
+      tmp_list_size = dim_list_virt_orb
+    endif
+    
+    if (tmp_list_size >= 2) then
+      ! Allocation tmp array  
+      allocate(tmp_list(tmp_list_size))
+
+      ! To give the list of MOs in a mo_class
+      if (l==1) then ! core
+        tmp_list = list_core
+      elseif (l==2) then
+        tmp_list = list_act
+      elseif (l==3) then
+        tmp_list = list_inact
+      else
+        tmp_list = list_virt
+      endif
+
+      call criterion_localization(tmp_list_size, tmp_list,criterion)
+      print*,'Criterion:', criterion, trim(mo_class(tmp_list(1)))
+      
+      deallocate(tmp_list)    
+    endif
+    
+  enddo
+
+  ! Debug
+  !print*,'HF', HF_energy
+
+  print*,''
+  print*,'========================'
+  print*,'  Orbital localization'
+  print*,'========================'
+  print*,'' 
+
+  !Initialization
+  not_converged = .TRUE.
+
+  ! To do the localization only if there is at least 2 MOs
+  if (dim_list_core_orb >= 2) then
+    not_core_converged = .TRUE.
+  else
+    not_core_converged = .FALSE. 
+  endif
+  
+  if (dim_list_act_orb >= 2) then
+    not_act_converged = .TRUE.
+  else
+    not_act_converged = .FALSE.
+  endif
+
+  if (dim_list_inact_orb >= 2) then
+    not_inact_converged = .TRUE.
+  else
+    not_inact_converged = .FALSE.
+  endif
+
+  if (dim_list_virt_orb >= 2) then
+    not_virt_converged = .TRUE.
+  else
+    not_virt_converged = .FALSE.
+  endif
+ 
+  ! Loop over the mo_classes
+  do l = 1, 4
+
+    if (l==1) then ! core
+      not_converged = not_core_converged
+      tmp_list_size = dim_list_core_orb
+    elseif (l==2) then ! act
+      not_converged = not_act_converged
+      tmp_list_size = dim_list_act_orb
+    elseif (l==3) then ! inact
+      not_converged = not_inact_converged
+      tmp_list_size = dim_list_inact_orb
+    else ! virt
+      not_converged = not_virt_converged
+      tmp_list_size = dim_list_virt_orb
+    endif
+
+    ! Next iteration if converged = true 
+    if (.not. not_converged) then
+      cycle
+    endif
+ 
+    ! Allocation tmp array  
+    allocate(tmp_list(tmp_list_size))
+
+    ! To give the list of MOs in a mo_class
+    if (l==1) then ! core
+      tmp_list = list_core
+    elseif (l==2) then
+      tmp_list = list_act
+    elseif (l==3) then
+      tmp_list = list_inact
+    else
+      tmp_list = list_virt
+    endif
+
+    ! Display
+    if (not_converged) then
+      print*,''
+      print*,'###', trim(mo_class(tmp_list(1))), 'MOs ###'
+      print*,''
+    endif
+
+    ! Size for the 2D -> 1D transformation 
+    tmp_n = tmp_list_size * (tmp_list_size - 1)/2
+
+    ! Without hessian + trust region 
+    if (.not. localization_use_hessian) then
+       
+      ! Allocation of temporary arrays
+      allocate(v_grad(tmp_n), tmp_m_x(tmp_list_size, tmp_list_size))
+      allocate(tmp_R(tmp_list_size, tmp_list_size), tmp_x(tmp_n))
+
+      ! Criterion
+      call criterion_localization(tmp_list_size, tmp_list, prev_criterion)
+
+      ! Init
+      nb_iter = 0
+      delta = 1d0
+
+      !Loop
+      do while (not_converged)
+         
+        print*,''
+        print*,'***********************'
+        print*,'Iteration', nb_iter
+        print*,'***********************'
+        print*,''
+        
+        ! Angles of rotation
+        call theta_localization(tmp_list, tmp_list_size, tmp_m_x, max_elem)
+        tmp_m_x = - tmp_m_x * delta
+
+        ! Rotation submatrix
+        call rotation_matrix(tmp_m_x, tmp_list_size, tmp_R, tmp_list_size, tmp_list_size, &
+             info, enforce_step_cancellation)
+
+        ! To ensure that the rotation matrix is unitary
+        if (enforce_step_cancellation) then
+          print*, 'Step cancellation, too large error in the rotation matrix'
+          delta = delta * 0.5d0
+          cycle
+        else
+          delta = min(delta * 2d0, 1d0)
+        endif
+
+        ! Full rotation matrix and application of the rotation
+        call sub_to_full_rotation_matrix(tmp_list_size, tmp_list, tmp_R, R)
+        call apply_mo_rotation(R, prev_mos)
+
+        ! Update the needed data
+        call update_data_localization()
+
+        ! New criterion
+        call criterion_localization(tmp_list_size, tmp_list, criterion)
+        print*,'Criterion:', trim(mo_class(tmp_list(1))), nb_iter, criterion
+        print*,'Max elem :', max_elem
+        print*,'Delta    :', delta
+        
+        nb_iter = nb_iter + 1
+
+        ! Exit
+        if (nb_iter >= localization_max_nb_iter .or. dabs(max_elem) < thresh_loc_max_elem_grad) then
+           not_converged = .False.
+        endif
+      enddo
+
+      ! Save the changes
+      call update_data_localization()
+      call save_mos()
+      TOUCH mo_coef
+
+      ! Deallocate
+      deallocate(v_grad, tmp_m_x, tmp_list)
+      deallocate(tmp_R, tmp_x)
+
+    ! Trust region
+    else
+    
+      ! Allocation of temporary arrays
+      allocate(v_grad(tmp_n), H(tmp_n), tmp_m_x(tmp_list_size, tmp_list_size))
+      allocate(tmp_R(tmp_list_size, tmp_list_size))
+      allocate(tmp_x(tmp_n), W(tmp_n), e_val(tmp_n), key(tmp_n))
+
+      ! ### Initialization ###
+      delta = 0d0 ! can be deleted (normally)
+      nb_iter = 0 ! Must start at 0 !!!
+      rho = 0.5d0 ! Must be 0.5
+
+      ! Compute the criterion before the loop
+      call criterion_localization(tmp_list_size, tmp_list, prev_criterion)
+
+      ! Loop until the convergence
+      do while (not_converged)
+
+        print*,''
+        print*,'***********************'
+        print*,'Iteration', nb_iter
+        print*,'***********************'
+        print*,''
+  
+        ! Gradient
+        call gradient_localization(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
+        ! Diagonal hessian
+        call hessian_localization(tmp_n, tmp_list_size, tmp_list, H)
+        
+        ! Diagonalization of the diagonal hessian by hands
+        !call diagonalization_hessian(tmp_n,H,e_val,w)
+        do i = 1, tmp_n
+          e_val(i) = H(i)
+        enddo
+
+        ! Key list for dsort
+        do i = 1, tmp_n 
+          key(i) = i
+        enddo
+
+        ! Sort of the eigenvalues
+        call dsort(e_val, key, tmp_n)
+
+        ! Eigenvectors
+        W = 0d0
+        do i = 1, tmp_n
+          W(i) = dble(key(i))
+        enddo
+
+        ! To enter in the loop just after
+        cancel_step = .True.
+        nb_sub_iter = 0 
+
+        ! Loop to reduce the trust radius until the criterion decreases and rho >= thresh_rho
+        do while (cancel_step)
+          print*,'-----------------------------'
+          print*, mo_class(tmp_list(1))
+          print*,'Iteration:', nb_iter
+          print*,'Sub iteration:', nb_sub_iter
+          print*,'Max elem grad:', max_elem
+          print*,'-----------------------------'
+
+          ! Hessian,gradient,Criterion -> x 
+          call trust_region_step_w_expected_e(tmp_n,1, H, W, e_val, v_grad, prev_criterion, &
+               rho, nb_iter, delta, criterion_model, tmp_x, must_exit)
+
+          ! Internal loop exit condition
+          if (must_exit) then
+            print*,'trust_region_step_w_expected_e sent: Exit'
+            exit 
+          endif
+
+          ! 1D tmp -> 2D tmp 
+          call vec_to_mat_v2(tmp_n, tmp_list_size, tmp_x, tmp_m_x)
+
+          ! Rotation submatrix (square matrix tmp_list_size by tmp_list_size)
+          call rotation_matrix(tmp_m_x, tmp_list_size, tmp_R, tmp_list_size, tmp_list_size, &
+               info, enforce_step_cancellation)
+
+          if (enforce_step_cancellation) then
+            print*, 'Step cancellation, too large error in the rotation matrix'
+            rho = 0d0
+            cycle
+          endif
+
+          ! tmp_R to R, subspace to full space
+          call sub_to_full_rotation_matrix(tmp_list_size, tmp_list, tmp_R, R)
+        
+          ! Rotation of the MOs
+          call apply_mo_rotation(R, prev_mos)   
+
+          ! Update the things related to mo_coef
+          call update_data_localization()
+
+          ! Update the criterion
+          call criterion_localization(tmp_list_size, tmp_list, criterion)
+          print*,'Criterion:', trim(mo_class(tmp_list(1))), nb_iter, criterion
+
+          ! Criterion -> step accepted or rejected 
+          call trust_region_is_step_cancelled(nb_iter, prev_criterion, criterion, &
+               criterion_model, rho, cancel_step)
+
+          ! Cancellation of the step, previous MOs
+          if (cancel_step) then
+            mo_coef = prev_mos
+          endif
+
+          nb_sub_iter = nb_sub_iter + 1
+        enddo
+        !call save_mos() !### depend of the time for 1 iteration
+
+        ! To exit the external loop if must_exti = .True.
+        if (must_exit) then
+          exit
+        endif 
+
+        ! Step accepted, nb iteration + 1
+        nb_iter = nb_iter + 1
+
+        ! External loop exit conditions
+        if (DABS(max_elem) < thresh_loc_max_elem_grad) then
+          not_converged = .False.
+        endif
+        if (nb_iter > localization_max_nb_iter) then
+          not_converged = .False.
+        endif
+      enddo
+
+      ! Deallocation of temporary arrays
+      deallocate(v_grad, H, tmp_m_x, tmp_R, tmp_list, tmp_x, W, e_val, key)
+      
+      ! Save the MOs
+      call save_mos()
+      TOUCH mo_coef
+ 
+      ! Debug
+      if (debug_hf) then
+        touch mo_coef
+        print*,'HF energy:', HF_energy
+      endif
+      
+    endif
+  enddo
+
+  ! Seems unecessary
+  TOUCH mo_coef 
+
+  ! To sort the MOs using the diagonal elements of the Fock matrix
+  if (sort_mos_by_e) then
+    call run_sort_by_fock_energies()
+  endif
+
+  ! Debug
+  if (debug_hf) then
+    touch mo_coef
+    print*,'HF energy:', HF_energy
+  endif
+
+  ! Locality after the localization
+  call compute_spatial_extent(spatial_extent)
+
+end

src/mo_localization/org/TANGLE_org_mode.sh

@@ -0,0 +1,7 @@
+#!/bin/sh   
+
+list='ls *.org'
+for element in $list    
+do   
+		emacs --batch $element -f org-babel-tangle
+done

src/mo_localization/org/break_spatial_sym.org

@@ -0,0 +1,28 @@
+! A small program to break the spatial symmetry of the MOs.
+
+! You have to defined your MO classes or set security_mo_class to false
+! with:
+! qp set orbital_optimization security_mo_class false
+
+! The default angle for the rotations is too big for this kind of
+! application, a value between 1e-3 and 1e-6 should break the spatial
+! symmetry with just a small change in the energy. 
+
+#+BEGIN_SRC f90 :comments org :tangle break_spatial_sym.irp.f
+program break_spatial_sym
+
+  !BEGIN_DOC
+  ! Break the symmetry of the MOs with a rotation
+  !END_DOC
+
+  implicit none
+
+  kick_in_mos = .True.
+  TOUCH kick_in_mos
+
+  call set_classes_loc 
+  call apply_pre_rotation
+  call unset_classes_loc 
+  
+end
+#+END_SRC

src/mo_localization/org/debug_gradient_loc.org

@@ -0,0 +1,67 @@
+#+BEGIN_SRC f90 :comments org :tangle debug_gradient_loc.irp.f
+program debug_gradient_loc
+
+  !BEGIN_DOC
+  ! Check if the gradient is correct
+  !END_DOC
+
+  implicit none
+
+  integer :: list_size, n
+  integer, allocatable :: list(:)
+  double precision, allocatable :: v_grad(:), v_grad2(:)
+  double precision :: norm, max_elem, threshold, max_error
+  integer :: i, nb_error
+
+  threshold = 1d-12
+
+  list_size = dim_list_act_orb
+
+  allocate(list(list_size))
+  
+  list = list_act
+
+  n = list_size*(list_size-1)/2
+  
+  allocate(v_grad(n),v_grad2(n))
+
+  if (localization_method == 'boys') then
+    print*,'Foster-Boys'
+    call gradient_FB(n,list_size,list,v_grad,max_elem,norm)
+    call gradient_FB_omp(n,list_size,list,v_grad2,max_elem,norm)
+  elseif (localization_method == 'pipek') then
+    print*,'Pipek-Mezey'
+    call gradient_PM(n,list_size,list,v_grad,max_elem,norm)
+    call gradient_PM(n,list_size,list,v_grad2,max_elem,norm) 
+  else
+    print*,'Unknown localization_method, please select boys or pipek'
+    call abort
+  endif
+ 
+  do i = 1, n
+    print*,i,v_grad(i)
+  enddo
+
+  v_grad = v_grad - v_grad2
+
+  nb_error = 0
+  max_elem = 0d0
+
+  do i = 1, n
+    if (dabs(v_grad(i)) > threshold) then
+      print*,v_grad(i)
+      nb_error = nb_error + 1
+      if (dabs(v_grad(i)) > max_elem) then
+        max_elem = v_grad(i)
+      endif
+    endif
+  enddo
+
+  print*,'Threshold error', threshold
+  print*, 'Nb error', nb_error
+  print*,'Max error', max_elem
+
+  deallocate(v_grad,v_grad2)
+ 
+end
+#+END_SRC

src/mo_localization/org/debug_hessian_loc.org

@@ -0,0 +1,67 @@
+#+BEGIN_SRC f90 :comments org :tangle debug_hessian_loc.irp.f
+program debug_hessian_loc
+
+  !BEGIN_DOC
+  ! Check if the hessian is correct
+  !END_DOC
+  
+  implicit none
+
+  integer :: list_size, n
+  integer, allocatable :: list(:)
+  double precision, allocatable :: H(:), H2(:)
+  double precision :: threshold, max_error, max_elem
+  integer :: i, nb_error
+
+  threshold = 1d-12
+
+  list_size = dim_list_act_orb
+
+  allocate(list(list_size))
+  
+  list = list_act
+
+  n = list_size*(list_size-1)/2
+  
+  allocate(H(n),H2(n))
+
+  if (localization_method == 'boys') then
+    print*,'Foster-Boys'
+    call hessian_FB(n,list_size,list,H)
+    call hessian_FB_omp(n,list_size,list,H2)
+  elseif(localization_method == 'pipek') then
+    print*,'Pipek-Mezey'
+    call hessian_PM(n,list_size,list,H)
+    call hessian_PM(n,list_size,list,H2)
+  else
+    print*,'Unknown localization_method, please select boys or pipek'
+    call abort
+  endif
+ 
+  do i = 1, n
+    print*,i,H(i)
+  enddo
+
+  H = H - H2
+
+  nb_error = 0
+  max_elem = 0d0
+
+  do i = 1, n
+    if (dabs(H(i)) > threshold) then
+      print*,H(i)
+      nb_error = nb_error + 1
+      if (dabs(H(i)) > max_elem) then
+        max_elem = H(i)
+      endif
+    endif
+  enddo
+
+  print*,'Threshold error', threshold
+  print*, 'Nb error', nb_error
+  print*,'Max error', max_elem
+
+  deallocate(H,H2)
+  
+end
+#+END_SRC

src/mo_localization/org/kick_the_mos.org

@@ -0,0 +1,18 @@
+#+BEGIN_SRC f90 :comments org :tangle kick_the_mos.irp.f
+program kick_the_mos
+
+  !BEGIN_DOC
+  ! To do a small rotation of the MOs
+  !END_DOC
+
+  implicit none
+
+  kick_in_mos = .True.
+  TOUCH kick_in_mos
+
+  call set_classes_loc
+  call apply_pre_rotation
+  call unset_classes_loc
+  
+end
+#+END_SRC