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option to use or not trust region + hessian

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Yann Damour 2022-11-10 09:31:33 +01:00
parent 0f6572bde1
commit a119d5943b
5 changed files with 1068 additions and 304 deletions
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20
src/mo_localization/EZFIO.cfg
View File

@ -1,42 +1,48 @@
[localization_method]
type: character*(32)
doc: Method for the orbital localization. boys : Foster-Boys, pipek : Pipek-Mezey
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
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 requieres a way smaller amount of memory but is not easy to converge.
interface: ezfio,provider,ocaml
default: true
[security_mo_class]
type: logical
doc: If true, call abort if the number of active orbital or the number of core + active orbitals is equal to the number of molecular orbitals, else uses the actual mo_class. It is a security if you forget to set the mo_class before the localization
doc: If true, call abort if the number of active orbital or the number of core + active orbitals is equal to the number of molecular orbitals, else uses the actual mo_class. It is a security if you forget to set the mo_class before the localization.
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
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, apply a rotation of an angle angle_pre_rot between the MOs of a same mo_class before the localization
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: Define the angle for the rotation of the MOs before the localization (in rad)
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, sorts the MOs using the diagonal elements of the Fock matrix
doc: If True, the MOs are sorted using the diagonal elements of the Fock matrix.
interface: ezfio,provider,ocaml
default: false

17
src/mo_localization/README.md
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@ -85,6 +85,23 @@ symmetry with just a small change in the energy:
qp set mo_localization angle_pre_rot 1e-3
```
# With or without hessian + trust region
With hessian + trust region
```
qp set mo_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 mo_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.
# Further improvements:
- Cleaner repo
- Correction of the errors in the documentations

299
src/mo_localization/localization.irp.f
View File

@ -295,148 +295,223 @@ subroutine run_localization
! Size for the 2D -> 1D transformation
tmp_n = tmp_list_size * (tmp_list_size - 1)/2
! Allocation of temporary arrays
allocate(v_grad(tmp_n), H(tmp_n, 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,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
! 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))
! Compute the criterion before the loop
call criterion_localization(tmp_list_size, tmp_list, prev_criterion)
! Criterion
call criterion_localization(tmp_list_size, tmp_list, prev_criterion)
! Loop until the convergence
do while (not_converged)
! Init
nb_iter = 0
delta = 1d0
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,i)
enddo
!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
! 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
j = key(i)
W(j,i) = 1d0
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*,'-----------------------------'
! Hessian,gradient,Criterion -> x
call trust_region_step_w_expected_e(tmp_n, 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)
! 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'
rho = 0d0
delta = delta * 0.5d0
cycle
else
delta = min(delta * 2d0, 1d0)
endif
! tmp_R to R, subspace to full space
! Full rotation matrix and application of the rotation
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)
call apply_mo_rotation(R, prev_mos)
! Update the things related to mo_coef
! Update the needed data
call update_data_localization()
! Update the criterion
! 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
! 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
! Exit
if (nb_iter >= localization_max_nb_iter .or. dabs(max_elem) < thresh_loc_max_elem_grad) then
not_converged = .False.
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
! Save the changes
call update_data_localization()
call save_mos()
TOUCH mo_coef
! Step accepted, nb iteration + 1
nb_iter = nb_iter + 1
! Deallocate
deallocate(v_grad, tmp_m_x, tmp_list)
deallocate(tmp_R, tmp_x)
! 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)
! Trust region
else
! Save the MOs
call save_mos()
TOUCH mo_coef
! Allocation of temporary arrays
allocate(v_grad(tmp_n), H(tmp_n, 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,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,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
j = key(i)
W(j,i) = 1d0
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*,'-----------------------------'
! Hessian,gradient,Criterion -> x
call trust_region_step_w_expected_e(tmp_n, 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
! Debug
if (debug_hf) then
touch mo_coef
print*,'HF energy:', HF_energy
endif
endif
enddo
TOUCH mo_coef
! To sort the MOs using the diagonal elements of the Fock matrix

697
src/mo_localization/localization.org
View File

@ -29,9 +29,29 @@ WARNING:
to have the right mo class for his next calculation...
For more information on the mo_class:
lpqp set_mo_class -h
qp set_mo_class -h
*** Foster-Boys localization
Boys, S. F., 1960, Rev. Mod. Phys. 32, 296.
DOI:https://doi.org/10.1103/RevModPhys.32.300
Boys, S. F., 1966, in Quantum Theory of Atoms, Molecules,
and the Solid State, edited by P.-O. Löwdin (Academic
Press, New York), p. 253.
Daniel A. Kleier, Thomas A. Halgren, John H. Hall Jr., and William
N. Lipscomb, J. Chem. Phys. 61, 3905 (1974)
doi: 10.1063/1.1681683
Høyvik, I.-M., Jansik, B., Jørgensen, P., J. Comput. Chem. 2013, 34,
1456– 1462. DOI: 10.1002/jcc.23281
Høyvik, I.-M., Jansik, B., Jørgensen, P., J. Chem. Theory
Comput. 2012, 8, 9, 3137–3146
DOI: https://doi.org/10.1021/ct300473g
Høyvik, I.-M., Jansik, B., Jørgensen, P., J. Chem. Phys. 137, 224114
(2012)
DOI: https://doi.org/10.1063/1.4769866
Nicola Marzari, Arash A. Mostofi, Jonathan R. Yates, Ivo Souza, and David Vanderbilt
Rev. Mod. Phys. 84, 1419
https://doi.org/10.1103/RevModPhys.84.1419
The Foster-Boys localization is a method to generate localized MOs
(LMOs) by minimizing the Foster-Boys criterion:
$$ C_{FB} = \sum_{i=1}^N \left[ < \phi_i | r^2 | \phi_i > - < \phi_i | r |
@ -481,148 +501,223 @@ subroutine run_localization
! Size for the 2D -> 1D transformation
tmp_n = tmp_list_size * (tmp_list_size - 1)/2
! Allocation of temporary arrays
allocate(v_grad(tmp_n), H(tmp_n, 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,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
! 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))
! Compute the criterion before the loop
call criterion_localization(tmp_list_size, tmp_list, prev_criterion)
! Criterion
call criterion_localization(tmp_list_size, tmp_list, prev_criterion)
! Loop until the convergence
do while (not_converged)
! Init
nb_iter = 0
delta = 1d0
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,i)
enddo
!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
! 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
j = key(i)
W(j,i) = 1d0
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*,'-----------------------------'
! Hessian,gradient,Criterion -> x
call trust_region_step_w_expected_e(tmp_n, 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)
! 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'
rho = 0d0
delta = delta * 0.5d0
cycle
else
delta = min(delta * 2d0, 1d0)
endif
! tmp_R to R, subspace to full space
! Full rotation matrix and application of the rotation
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)
call apply_mo_rotation(R, prev_mos)
! Update the things related to mo_coef
! Update the needed data
call update_data_localization()
! Update the criterion
! 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
! 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
! Exit
if (nb_iter >= localization_max_nb_iter .or. dabs(max_elem) < thresh_loc_max_elem_grad) then
not_converged = .False.
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
! Save the changes
call update_data_localization()
call save_mos()
TOUCH mo_coef
! Step accepted, nb iteration + 1
nb_iter = nb_iter + 1
! Deallocate
deallocate(v_grad, tmp_m_x, tmp_list)
deallocate(tmp_R, tmp_x)
! 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)
! Trust region
else
! Save the MOs
call save_mos()
TOUCH mo_coef
! Allocation of temporary arrays
allocate(v_grad(tmp_n), H(tmp_n, 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,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,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
j = key(i)
W(j,i) = 1d0
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*,'-----------------------------'
! Hessian,gradient,Criterion -> x
call trust_region_step_w_expected_e(tmp_n, 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
! Debug
if (debug_hf) then
touch mo_coef
print*,'HF energy:', HF_energy
endif
endif
enddo
TOUCH mo_coef
! To sort the MOs using the diagonal elements of the Fock matrix
@ -682,9 +777,8 @@ subroutine gradient_localization(tmp_n, tmp_list_size, tmp_list, v_grad, max_ele
elseif (localization_method== 'pipek') then
call gradient_PM(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
else
v_grad = 0d0
max_elem = 0d0
norm_grad = 0d0
print*,'Unkown method:'//localization_method
call abort
endif
end
@ -717,7 +811,8 @@ subroutine hessian_localization(tmp_n, tmp_list_size, tmp_list, H)
elseif (localization_method == 'pipek') then
call hessian_PM(tmp_n, tmp_list_size, tmp_list, H)
else
H = 0d0
print*,'Unkown method: '//localization_method
call abort
endif
end
@ -748,7 +843,8 @@ subroutine criterion_localization(tmp_list_size, tmp_list,criterion)
!call criterion_PM(tmp_list_size, tmp_list,criterion)
call criterion_PM_v3(tmp_list_size, tmp_list, criterion)
else
criterion = 0d0
print*,'Unkown method: '//localization_method
call abort
endif
end
@ -770,10 +866,45 @@ subroutine update_data_localization()
elseif (localization_method == 'pipek') then
! Nothing required
else
print*,'Unkown method: '//localization_method
call abort
endif
end
#+END_SRC
Angles:
Output:
| tmp_m_x(tmp_list_size, tmp_list_size) | double precision | Angles for the rotations in the subspace |
| max_elem | double precision | Maximal angle |
#+BEGIN_SRC f90 :comments org :tangle localization_sub.irp.f
subroutine theta_localization(tmp_list, tmp_list_size, tmp_m_x, max_elem)
include 'pi.h'
implicit none
BEGIN_DOC
! Compute the rotation angles between the MOs for the chosen localization method
END_DOC
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: tmp_m_x(tmp_list_size,tmp_list_size), max_elem
if (localization_method == 'boys') then
call theta_FB(tmp_list, tmp_list_size, tmp_m_x, max_elem)
elseif (localization_method== 'pipek') then
call theta_PM(tmp_list, tmp_list_size, tmp_m_x, max_elem)
else
print*,'Unkown method: '//localization_method
call abort
endif
end
#+END_SRC
** Foster-Boys
*** Gradient
Input:
@ -1174,7 +1305,7 @@ subroutine grad_pipek(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_gra
BEGIN_DOC
! Compute gradient for the Pipek-Mezey localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
double precision, allocatable :: m_grad(:,:), tmp_int(:,:)
@ -1187,54 +1318,54 @@ subroutine grad_pipek(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_gra
m_grad = 0d0
do a = 1, nucl_num ! loop over the nuclei
tmp_int = 0d0 ! Initialization for each nuclei
tmp_int = 0d0 ! Initialization for each nuclei
! Loop over the MOs of the a given mo_class to compute <i|Q_a|j>
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b) ! AO centered on atom a
! Loop over the MOs of the a given mo_class to compute <i|P_a|j>
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b) ! AO centered on atom a
tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
enddo
enddo
enddo
enddo
enddo
enddo
enddo
enddo
! Gradient
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
! Gradient
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
m_grad(tmp_i,tmp_j) = m_grad(tmp_i,tmp_j) + 4d0 * tmp_int(tmp_i,tmp_j) * (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))
m_grad(tmp_i,tmp_j) = m_grad(tmp_i,tmp_j) + 4d0 * tmp_int(tmp_i,tmp_j) * (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))
enddo
enddo
enddo
enddo
enddo
! 2D -> 1D
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
enddo
! Maximum element in the gradient
max_elem = 0d0
do tmp_k = 1, tmp_n
if (ABS(v_grad(tmp_k)) > max_elem) then
max_elem = ABS(v_grad(tmp_k))
endif
enddo
if (ABS(v_grad(tmp_k)) > max_elem) then
max_elem = ABS(v_grad(tmp_k))
endif
enddo
! Norm of the gradient
norm_grad = 0d0
do tmp_k = 1, tmp_n
norm_grad = norm_grad + v_grad(tmp_k)**2
norm_grad = norm_grad + v_grad(tmp_k)**2
enddo
norm_grad = dsqrt(norm_grad)
@ -1244,7 +1375,7 @@ subroutine grad_pipek(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_gra
! Deallocation
deallocate(m_grad,tmp_int)
end
end subroutine grad_pipek
#+END_SRC
*** Gradient
@ -1971,6 +2102,274 @@ subroutine criterion_FB(tmp_list_size, tmp_list, criterion)
end subroutine
#+END_SRC
** Theta
In:
| n | integer | number of MOs in the considered MO class |
| l | integer | list of MOs of the considered class |
Out:
| m_x(n,n) | double precision | Matrix containing the rotation angle between all the different |
| | | pairs of MOs to apply the rotations (need a minus sign) |
| max_elem | double precision | Maximal angle in absolute value |
$$\cos(4 \theta) = \frac{-A{ij}}{\sqrt{(A_{ij}^2 + B_{ij}^2)} $$
$$\sin(4 \theta) = \frac{B{ij}}{\sqrt{(A_{ij}^2 + B_{ij}^2)} $$
$$\tan(4 \theta) = \frac{\sin(4 \theta)}{\cos(4 \theta)}$$
where $\theta$ is in fact $\theta_{ij}$
For Foster-Boys localization:
$$A_{ij} = <i|r|j>^2 - \frac{1}{4} (<i|r|i> - <j|r|j>)^2$$
$$B_{ij} = <i|r|j> (<i|r|i> - <j|r|j>)$$
For Pipek-Mezey localization:
$$A_{ij} = \sum_A <i|P_A|j>^2 - \frac{1}{4} (<i|P_A|i> - <j|P_A|j>)^2$$
$$B_{ij} = \sum_A <i|P_A|j> (<i|P_A|i> - <j|P_A|j>)$$
with
$$<i|P_A|j> = \frac{1}{2} \sum_\rho \sum_{\mu \in A} ( c_\rho^{i*} S_{\rho
\mu} c_\mu^j + c_\mu^{i*} S_{\mu \rho} c_\rho^j)$$
$i,j$ MOs
$\mu, \rho$ AOs
$A$ nucleus
$S$ overlap matrix
$c$ MO coefficient
$r$ position operator
#+begin_src f90 :tangle localization_sub.irp.f
subroutine theta_FB(l, n, m_x, max_elem)
include 'pi.h'
BEGIN_DOC
! Compute the angles to minimize the Foster-Boys criterion by using pairwise rotations of the MOs
! Warning: you must give - the angles to build the rotation matrix...
END_DOC
implicit none
integer, intent(in) :: n, l(n)
double precision, intent(out) :: m_x(n,n), max_elem
integer :: i,j, tmp_i, tmp_j
double precision, allocatable :: cos4theta(:,:), sin4theta(:,:)
double precision, allocatable :: A(:,:), B(:,:), beta(:,:), gamma(:,:)
integer :: idx_i,idx_j
allocate(cos4theta(n, n), sin4theta(n, n))
allocate(A(n,n), B(n,n), beta(n,n), gamma(n,n))
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
A(tmp_i,tmp_j) = mo_dipole_x(i,j)**2 - 0.25d0 * (mo_dipole_x(i,i) - mo_dipole_x(j,j))**2 &
+ mo_dipole_y(i,j)**2 - 0.25d0 * (mo_dipole_y(i,i) - mo_dipole_y(j,j))**2 &
+ mo_dipole_z(i,j)**2 - 0.25d0 * (mo_dipole_z(i,i) - mo_dipole_z(j,j))**2
enddo
A(j,j) = 0d0
enddo
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
B(tmp_i,tmp_j) = mo_dipole_x(i,j) * (mo_dipole_x(i,i) - mo_dipole_x(j,j)) &
+ mo_dipole_y(i,j) * (mo_dipole_y(i,i) - mo_dipole_y(j,j)) &
+ mo_dipole_z(i,j) * (mo_dipole_z(i,i) - mo_dipole_z(j,j))
enddo
enddo
!do tmp_j = 1, n
! j = l(tmp_j)
! do tmp_i = 1, n
! i = l(tmp_i)
! beta(tmp_i,tmp_j) = (mo_dipole_x(i,i) - mo_dipole_x(j,j)) - 4d0 * mo_dipole_x(i,j)**2 &
! + (mo_dipole_y(i,i) - mo_dipole_y(j,j)) - 4d0 * mo_dipole_y(i,j)**2 &
! + (mo_dipole_z(i,i) - mo_dipole_z(j,j)) - 4d0 * mo_dipole_z(i,j)**2
! enddo
!enddo
!do tmp_j = 1, n
! j = l(tmp_j)
! do tmp_i = 1, n
! i = l(tmp_i)
! gamma(tmp_i,tmp_j) = 4d0 * ( mo_dipole_x(i,j) * (mo_dipole_x(i,i) - mo_dipole_x(j,j)) &
! + mo_dipole_y(i,j) * (mo_dipole_y(i,i) - mo_dipole_y(j,j)) &
! + mo_dipole_z(i,j) * (mo_dipole_z(i,i) - mo_dipole_z(j,j)))
! enddo
!enddo
!
!do j = 1, n
! do i = 1, n
! cos4theta(i,j) = - A(i,j) / dsqrt(A(i,j)**2 + B(i,j)**2)
! enddo
!enddo
!do j = 1, n
! do i = 1, n
! sin4theta(i,j) = B(i,j) / dsqrt(A(i,j)**2 + B(i,j)**2)
! enddo
!enddo
! Theta
do j = 1, n
do i = 1, n
m_x(i,j) = 0.25d0 * atan2(B(i,j), -A(i,j))
!m_x(i,j) = 0.25d0 * atan2(sin4theta(i,j), cos4theta(i,j))
enddo
enddo
! Enforce a perfect antisymmetry
do j = 1, n-1
do i = j+1, n
m_x(j,i) = - m_x(i,j)
enddo
enddo
do i = 1, n
m_x(i,i) = 0d0
enddo
! Max
max_elem = 0d0
do j = 1, n-1
do i = j+1, n
if (dabs(m_x(i,j)) > dabs(max_elem)) then
max_elem = m_x(i,j)
!idx_i = i
!idx_j = j
endif
enddo
enddo
! Debug
!print*,''
!print*,'sin/B'
!do i = 1, n
! write(*,'(100F10.4)') sin4theta(i,:)
! !B(i,:)
!enddo
!print*,'cos/A'
!do i = 1, n
! write(*,'(100F10.4)') cos4theta(i,:)
! !A(i,:)
!enddo
!print*,'X'
!!m_x = 0d0
!!m_x(idx_i,idx_j) = max_elem
!!m_x(idx_j,idx_i) = -max_elem
!do i = 1, n
! write(*,'(100F10.4)') m_x(i,:)
!enddo
!print*,idx_i,idx_j,max_elem
max_elem = dabs(max_elem)
deallocate(cos4theta, sin4theta)
deallocate(A,B,beta,gamma)
end
#+end_src
#+begin_src f90 :comments org :tangle localization_sub.irp.f
subroutine theta_PM(l, n, m_x, max_elem)
include 'pi.h'
BEGIN_DOC
! Compute the angles to minimize the Foster-Boys criterion by using pairwise rotations of the MOs
! Warning: you must give - the angles to build the rotation matrix...
END_DOC
implicit none
integer, intent(in) :: n, l(n)
double precision, intent(out) :: m_x(n,n), max_elem
integer :: a,b,i,j,tmp_i,tmp_j,rho,mu,nu,idx_i,idx_j
double precision, allocatable :: Aij(:,:), Bij(:,:), Pa(:,:)
allocate(Aij(n,n), Bij(n,n), Pa(n,n))
do a = 1, nucl_num ! loop over the nuclei
Pa = 0d0 ! Initialization for each nuclei
! Loop over the MOs of the a given mo_class to compute <i|P_a|j>
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b) ! AO centered on atom a
Pa(tmp_i,tmp_j) = Pa(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
enddo
enddo
enddo
enddo
! A
do j = 1, n
do i = 1, n
Aij(i,j) = Aij(i,j) + Pa(i,j)**2 - 0.25d0 * (Pa(i,i) - Pa(j,j))**2
enddo
enddo
! B
do j = 1, n
do i = 1, n
Bij(i,j) = Bij(i,j) + Pa(i,j) * (Pa(i,i) - Pa(j,j))
enddo
enddo
enddo
! Theta
do j = 1, n
do i = 1, n
m_x(i,j) = 0.25d0 * atan2(Bij(i,j), -Aij(i,j))
enddo
enddo
! Enforce a perfect antisymmetry
do j = 1, n-1
do i = j+1, n
m_x(j,i) = - m_x(i,j)
enddo
enddo
do i = 1, n
m_x(i,i) = 0d0
enddo
! Max
max_elem = 0d0
do j = 1, n-1
do i = j+1, n
if (dabs(m_x(i,j)) > dabs(max_elem)) then
max_elem = m_x(i,j)
idx_i = i
idx_j = j
endif
enddo
enddo
! Debug
!do i = 1, n
! write(*,'(100F10.4)') m_x(i,:)
!enddo
!print*,'Max',idx_i,idx_j,max_elem
max_elem = dabs(max_elem)
deallocate(Aij,Bij,Pa)
end
#+end_src
** Spatial extent
The spatial extent of an orbital $i$ is computed as

339
src/mo_localization/localization_sub.irp.f
View File

@ -38,9 +38,8 @@ subroutine gradient_localization(tmp_n, tmp_list_size, tmp_list, v_grad, max_ele
elseif (localization_method== 'pipek') then
call gradient_PM(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
else
v_grad = 0d0
max_elem = 0d0
norm_grad = 0d0
print*,'Unkown method:'//localization_method
call abort
endif
end
@ -74,7 +73,8 @@ subroutine hessian_localization(tmp_n, tmp_list_size, tmp_list, H)
elseif (localization_method == 'pipek') then
call hessian_PM(tmp_n, tmp_list_size, tmp_list, H)
else
H = 0d0
print*,'Unkown method: '//localization_method
call abort
endif
end
@ -106,7 +106,8 @@ subroutine criterion_localization(tmp_list_size, tmp_list,criterion)
!call criterion_PM(tmp_list_size, tmp_list,criterion)
call criterion_PM_v3(tmp_list_size, tmp_list, criterion)
else
criterion = 0d0
print*,'Unkown method: '//localization_method
call abort
endif
end
@ -129,9 +130,45 @@ subroutine update_data_localization()
elseif (localization_method == 'pipek') then
! Nothing required
else
print*,'Unkown method: '//localization_method
call abort
endif
end
! Angles:
! Output:
! | tmp_m_x(tmp_list_size, tmp_list_size) | double precision | Angles for the rotations in the subspace |
! | max_elem | double precision | Maximal angle |
subroutine theta_localization(tmp_list, tmp_list_size, tmp_m_x, max_elem)
include 'pi.h'
implicit none
BEGIN_DOC
! Compute the rotation angles between the MOs for the chosen localization method
END_DOC
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: tmp_m_x(tmp_list_size,tmp_list_size), max_elem
if (localization_method == 'boys') then
call theta_FB(tmp_list, tmp_list_size, tmp_m_x, max_elem)
elseif (localization_method== 'pipek') then
call theta_PM(tmp_list, tmp_list_size, tmp_m_x, max_elem)
else
print*,'Unkown method: '//localization_method
call abort
endif
end
! Gradient
! Input:
! | tmp_n | integer | Number of parameters in the MO subspace |
@ -526,7 +563,7 @@ subroutine grad_pipek(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_gra
BEGIN_DOC
! Compute gradient for the Pipek-Mezey localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
double precision, allocatable :: m_grad(:,:), tmp_int(:,:)
@ -539,54 +576,54 @@ subroutine grad_pipek(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_gra
m_grad = 0d0
do a = 1, nucl_num ! loop over the nuclei
tmp_int = 0d0 ! Initialization for each nuclei
tmp_int = 0d0 ! Initialization for each nuclei
! Loop over the MOs of the a given mo_class to compute <i|Q_a|j>
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b) ! AO centered on atom a
! Loop over the MOs of the a given mo_class to compute <i|P_a|j>
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b) ! AO centered on atom a
tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
enddo
enddo
enddo
enddo
enddo
enddo
enddo
enddo
! Gradient
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
! Gradient
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
m_grad(tmp_i,tmp_j) = m_grad(tmp_i,tmp_j) + 4d0 * tmp_int(tmp_i,tmp_j) * (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))
m_grad(tmp_i,tmp_j) = m_grad(tmp_i,tmp_j) + 4d0 * tmp_int(tmp_i,tmp_j) * (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))
enddo
enddo
enddo
enddo
enddo
! 2D -> 1D
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
enddo
! Maximum element in the gradient
max_elem = 0d0
do tmp_k = 1, tmp_n
if (ABS(v_grad(tmp_k)) > max_elem) then
max_elem = ABS(v_grad(tmp_k))
endif
enddo
if (ABS(v_grad(tmp_k)) > max_elem) then
max_elem = ABS(v_grad(tmp_k))
endif
enddo
! Norm of the gradient
norm_grad = 0d0
do tmp_k = 1, tmp_n
norm_grad = norm_grad + v_grad(tmp_k)**2
norm_grad = norm_grad + v_grad(tmp_k)**2
enddo
norm_grad = dsqrt(norm_grad)
@ -596,7 +633,7 @@ subroutine grad_pipek(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_gra
! Deallocation
deallocate(m_grad,tmp_int)
end
end subroutine grad_pipek
! Gradient
@ -1312,6 +1349,236 @@ subroutine criterion_FB(tmp_list_size, tmp_list, criterion)
end subroutine
subroutine theta_FB(l, n, m_x, max_elem)
include 'pi.h'
BEGIN_DOC
! Compute the angles to minimize the Foster-Boys criterion by using pairwise rotations of the MOs
! Warning: you must give - the angles to build the rotation matrix...
END_DOC
implicit none
integer, intent(in) :: n, l(n)
double precision, intent(out) :: m_x(n,n), max_elem
integer :: i,j, tmp_i, tmp_j
double precision, allocatable :: cos4theta(:,:), sin4theta(:,:)
double precision, allocatable :: A(:,:), B(:,:), beta(:,:), gamma(:,:)
integer :: idx_i,idx_j
allocate(cos4theta(n, n), sin4theta(n, n))
allocate(A(n,n), B(n,n), beta(n,n), gamma(n,n))
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
A(tmp_i,tmp_j) = mo_dipole_x(i,j)**2 - 0.25d0 * (mo_dipole_x(i,i) - mo_dipole_x(j,j))**2 &
+ mo_dipole_y(i,j)**2 - 0.25d0 * (mo_dipole_y(i,i) - mo_dipole_y(j,j))**2 &
+ mo_dipole_z(i,j)**2 - 0.25d0 * (mo_dipole_z(i,i) - mo_dipole_z(j,j))**2
enddo
A(j,j) = 0d0
enddo
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
B(tmp_i,tmp_j) = mo_dipole_x(i,j) * (mo_dipole_x(i,i) - mo_dipole_x(j,j)) &
+ mo_dipole_y(i,j) * (mo_dipole_y(i,i) - mo_dipole_y(j,j)) &
+ mo_dipole_z(i,j) * (mo_dipole_z(i,i) - mo_dipole_z(j,j))
enddo
enddo
!do tmp_j = 1, n
! j = l(tmp_j)
! do tmp_i = 1, n
! i = l(tmp_i)
! beta(tmp_i,tmp_j) = (mo_dipole_x(i,i) - mo_dipole_x(j,j)) - 4d0 * mo_dipole_x(i,j)**2 &
! + (mo_dipole_y(i,i) - mo_dipole_y(j,j)) - 4d0 * mo_dipole_y(i,j)**2 &
! + (mo_dipole_z(i,i) - mo_dipole_z(j,j)) - 4d0 * mo_dipole_z(i,j)**2
! enddo
!enddo
!do tmp_j = 1, n
! j = l(tmp_j)
! do tmp_i = 1, n
! i = l(tmp_i)
! gamma(tmp_i,tmp_j) = 4d0 * ( mo_dipole_x(i,j) * (mo_dipole_x(i,i) - mo_dipole_x(j,j)) &
! + mo_dipole_y(i,j) * (mo_dipole_y(i,i) - mo_dipole_y(j,j)) &
! + mo_dipole_z(i,j) * (mo_dipole_z(i,i) - mo_dipole_z(j,j)))
! enddo
!enddo
!
!do j = 1, n
! do i = 1, n
! cos4theta(i,j) = - A(i,j) / dsqrt(A(i,j)**2 + B(i,j)**2)
! enddo
!enddo
!do j = 1, n
! do i = 1, n
! sin4theta(i,j) = B(i,j) / dsqrt(A(i,j)**2 + B(i,j)**2)
! enddo
!enddo
! Theta
do j = 1, n
do i = 1, n
m_x(i,j) = 0.25d0 * atan2(B(i,j), -A(i,j))
!m_x(i,j) = 0.25d0 * atan2(sin4theta(i,j), cos4theta(i,j))
enddo
enddo
! Enforce a perfect antisymmetry
do j = 1, n-1
do i = j+1, n
m_x(j,i) = - m_x(i,j)
enddo
enddo
do i = 1, n
m_x(i,i) = 0d0
enddo
! Max
max_elem = 0d0
do j = 1, n-1
do i = j+1, n
if (dabs(m_x(i,j)) > dabs(max_elem)) then
max_elem = m_x(i,j)
!idx_i = i
!idx_j = j
endif
enddo
enddo
! Debug
!print*,''
!print*,'sin/B'
!do i = 1, n
! write(*,'(100F10.4)') sin4theta(i,:)
! !B(i,:)
!enddo
!print*,'cos/A'
!do i = 1, n
! write(*,'(100F10.4)') cos4theta(i,:)
! !A(i,:)
!enddo
!print*,'X'
!!m_x = 0d0
!!m_x(idx_i,idx_j) = max_elem
!!m_x(idx_j,idx_i) = -max_elem
!do i = 1, n
! write(*,'(100F10.4)') m_x(i,:)
!enddo
!print*,idx_i,idx_j,max_elem
max_elem = dabs(max_elem)
deallocate(cos4theta, sin4theta)
deallocate(A,B,beta,gamma)
end
subroutine theta_PM(l, n, m_x, max_elem)
include 'pi.h'
BEGIN_DOC
! Compute the angles to minimize the Foster-Boys criterion by using pairwise rotations of the MOs
! Warning: you must give - the angles to build the rotation matrix...
END_DOC
implicit none
integer, intent(in) :: n, l(n)
double precision, intent(out) :: m_x(n,n), max_elem
integer :: a,b,i,j,tmp_i,tmp_j,rho,mu,nu,idx_i,idx_j
double precision, allocatable :: Aij(:,:), Bij(:,:), Pa(:,:)
allocate(Aij(n,n), Bij(n,n), Pa(n,n))
do a = 1, nucl_num ! loop over the nuclei
Pa = 0d0 ! Initialization for each nuclei
! Loop over the MOs of the a given mo_class to compute <i|P_a|j>
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b) ! AO centered on atom a
Pa(tmp_i,tmp_j) = Pa(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
enddo
enddo
enddo
enddo
! A
do j = 1, n
do i = 1, n
Aij(i,j) = Aij(i,j) + Pa(i,j)**2 - 0.25d0 * (Pa(i,i) - Pa(j,j))**2
enddo
enddo
! B
do j = 1, n
do i = 1, n
Bij(i,j) = Bij(i,j) + Pa(i,j) * (Pa(i,i) - Pa(j,j))
enddo
enddo
enddo
! Theta
do j = 1, n
do i = 1, n
m_x(i,j) = 0.25d0 * atan2(Bij(i,j), -Aij(i,j))
enddo
enddo
! Enforce a perfect antisymmetry
do j = 1, n-1
do i = j+1, n
m_x(j,i) = - m_x(i,j)
enddo
enddo
do i = 1, n
m_x(i,i) = 0d0
enddo
! Max
max_elem = 0d0
do j = 1, n-1
do i = j+1, n
if (dabs(m_x(i,j)) > dabs(max_elem)) then
max_elem = m_x(i,j)
idx_i = i
idx_j = j
endif
enddo
enddo
! Debug
!do i = 1, n
! write(*,'(100F10.4)') m_x(i,:)
!enddo
!print*,'Max',idx_i,idx_j,max_elem
max_elem = dabs(max_elem)
deallocate(Aij,Bij,Pa)
end
! Spatial extent
! The spatial extent of an orbital $i$ is computed as