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qp2/src/functionals/pbe.irp.f

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Develop (#15) * fixed laplacian of aos * corrected the laplacians of aos * added dft_one_e * added new feature for new dft functionals * changed the configure to add new functionals * changed the configure * added dft_one_e/README.rst * added README.rst in new_functionals * added source/programmers_guide/new_ks.rst * Thesis Yann * Added gmp installation in configure * improved qp_e_conv_fci * Doc * Typos * Added variance_max * Fixed completion in qp_create * modif TODO * fixed DFT potential for n_states gt 1 * improved pot pbe * trying to improve sr PBE * fixed potential pbe * fixed the vxc smashed for pbe sr and normal * Comments in selection * bug fixed by peter * Fixed bug with zero beta electrons * Update README.rst * Update e_xc_new_func.irp.f * Update links.rst * Update quickstart.rst * Update quickstart.rst * updated cipsi * Fixed energies of non-expected s2 (#9) * Moved diag_algorithm in Davdison * Add print_ci_vector in tools (#11) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Merge develop-toto and manus (#12) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Frozen core for heavy atoms * Improved molden module * In sync with manus * Fixed some of the documentation errors * Develop toto (#13) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Frozen core for heavy atoms * Improved molden module * In sync with manus * Fixed some of the documentation errors * Develop manus (#14) * modified printing for rpt2 * Comment * Fixed plugins * Scripting for functionals * Documentation * Develop (#10) * fixed laplacian of aos * corrected the laplacians of aos * added dft_one_e * added new feature for new dft functionals * changed the configure to add new functionals * changed the configure * added dft_one_e/README.rst * added README.rst in new_functionals * added source/programmers_guide/new_ks.rst * Thesis Yann * Added gmp installation in configure * improved qp_e_conv_fci * Doc * Typos * Added variance_max * Fixed completion in qp_create * modif TODO * fixed DFT potential for n_states gt 1 * improved pot pbe * trying to improve sr PBE * fixed potential pbe * fixed the vxc smashed for pbe sr and normal * Comments in selection * bug fixed by peter * Fixed bug with zero beta electrons * Update README.rst * Update e_xc_new_func.irp.f * Update links.rst * Update quickstart.rst * Update quickstart.rst * updated cipsi * Fixed energies of non-expected s2 (#9) * Moved diag_algorithm in Davdison * some modifs * modified gfortran_debug.cfg * fixed automatization of functionals * modified e_xc_general.irp.f * minor modifs in ref_bitmask.irp.f * modifying functionals * rs_ks_scf and ks_scf compiles with the automatic handling of functionals * removed prints * fixed configure * fixed the new functionals * Merge toto * modified automatic functionals * Changed python into python2 * from_xyz suppressed * Cleaning repo * Update README.md * Update README.md * Contributors * Update GITHUB.md * bibtex
2019-03-07 16:29:06 +01:00
BEGIN_PROVIDER[double precision, energy_x_pbe, (N_states) ]
implicit none
BEGIN_DOC
! exchange/correlation energy with the short range pbe functional
END_DOC
integer :: istate,i,j,m
double precision :: r(3)
double precision :: mu,weight
double precision, allocatable :: ex(:), ec(:)
double precision, allocatable :: rho_a(:),rho_b(:),grad_rho_a(:,:),grad_rho_b(:,:),grad_rho_a_2(:),grad_rho_b_2(:),grad_rho_a_b(:)
double precision, allocatable :: contrib_grad_xa(:,:),contrib_grad_xb(:,:),contrib_grad_ca(:,:),contrib_grad_cb(:,:)
double precision, allocatable :: vc_rho_a(:), vc_rho_b(:), vx_rho_a(:), vx_rho_b(:)
double precision, allocatable :: vx_grad_rho_a_2(:), vx_grad_rho_b_2(:), vx_grad_rho_a_b(:), vc_grad_rho_a_2(:), vc_grad_rho_b_2(:), vc_grad_rho_a_b(:)
allocate(vc_rho_a(N_states), vc_rho_b(N_states), vx_rho_a(N_states), vx_rho_b(N_states))
allocate(vx_grad_rho_a_2(N_states), vx_grad_rho_b_2(N_states), vx_grad_rho_a_b(N_states), vc_grad_rho_a_2(N_states), vc_grad_rho_b_2(N_states), vc_grad_rho_a_b(N_states))
allocate(rho_a(N_states), rho_b(N_states),grad_rho_a(3,N_states),grad_rho_b(3,N_states))
allocate(grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_a_b(N_states), ex(N_states), ec(N_states))
energy_x_pbe = 0.d0
do istate = 1, N_states
do i = 1, n_points_final_grid
r(1) = final_grid_points(1,i)
r(2) = final_grid_points(2,i)
r(3) = final_grid_points(3,i)
weight = final_weight_at_r_vector(i)
rho_a(istate) = one_e_dm_and_grad_alpha_in_r(4,i,istate)
rho_b(istate) = one_e_dm_and_grad_beta_in_r(4,i,istate)
grad_rho_a(1:3,istate) = one_e_dm_and_grad_alpha_in_r(1:3,i,istate)
grad_rho_b(1:3,istate) = one_e_dm_and_grad_beta_in_r(1:3,i,istate)
grad_rho_a_2 = 0.d0
grad_rho_b_2 = 0.d0
grad_rho_a_b = 0.d0
do m = 1, 3
grad_rho_a_2(istate) += grad_rho_a(m,istate) * grad_rho_a(m,istate)
grad_rho_b_2(istate) += grad_rho_b(m,istate) * grad_rho_b(m,istate)
grad_rho_a_b(istate) += grad_rho_a(m,istate) * grad_rho_b(m,istate)
enddo
! inputs
call GGA_type_functionals(r,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_a_b, & ! outputs exchange
ex,vx_rho_a,vx_rho_b,vx_grad_rho_a_2,vx_grad_rho_b_2,vx_grad_rho_a_b, & ! outputs correlation
ec,vc_rho_a,vc_rho_b,vc_grad_rho_a_2,vc_grad_rho_b_2,vc_grad_rho_a_b )
energy_x_pbe += ex * weight
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER[double precision, energy_c_pbe, (N_states) ]
implicit none
BEGIN_DOC
! exchange/correlation energy with the short range pbe functional
END_DOC
integer :: istate,i,j,m
double precision :: r(3)
double precision :: mu,weight
double precision, allocatable :: ex(:), ec(:)
double precision, allocatable :: rho_a(:),rho_b(:),grad_rho_a(:,:),grad_rho_b(:,:),grad_rho_a_2(:),grad_rho_b_2(:),grad_rho_a_b(:)
double precision, allocatable :: contrib_grad_xa(:,:),contrib_grad_xb(:,:),contrib_grad_ca(:,:),contrib_grad_cb(:,:)
double precision, allocatable :: vc_rho_a(:), vc_rho_b(:), vx_rho_a(:), vx_rho_b(:)
double precision, allocatable :: vx_grad_rho_a_2(:), vx_grad_rho_b_2(:), vx_grad_rho_a_b(:), vc_grad_rho_a_2(:), vc_grad_rho_b_2(:), vc_grad_rho_a_b(:)
allocate(vc_rho_a(N_states), vc_rho_b(N_states), vx_rho_a(N_states), vx_rho_b(N_states))
allocate(vx_grad_rho_a_2(N_states), vx_grad_rho_b_2(N_states), vx_grad_rho_a_b(N_states), vc_grad_rho_a_2(N_states), vc_grad_rho_b_2(N_states), vc_grad_rho_a_b(N_states))
allocate(rho_a(N_states), rho_b(N_states),grad_rho_a(3,N_states),grad_rho_b(3,N_states))
allocate(grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_a_b(N_states), ex(N_states), ec(N_states))
energy_c_pbe = 0.d0
do istate = 1, N_states
do i = 1, n_points_final_grid
r(1) = final_grid_points(1,i)
r(2) = final_grid_points(2,i)
r(3) = final_grid_points(3,i)
weight = final_weight_at_r_vector(i)
rho_a(istate) = one_e_dm_and_grad_alpha_in_r(4,i,istate)
rho_b(istate) = one_e_dm_and_grad_beta_in_r(4,i,istate)
grad_rho_a(1:3,istate) = one_e_dm_and_grad_alpha_in_r(1:3,i,istate)
grad_rho_b(1:3,istate) = one_e_dm_and_grad_beta_in_r(1:3,i,istate)
grad_rho_a_2 = 0.d0
grad_rho_b_2 = 0.d0
grad_rho_a_b = 0.d0
do m = 1, 3
grad_rho_a_2(istate) += grad_rho_a(m,istate) * grad_rho_a(m,istate)
grad_rho_b_2(istate) += grad_rho_b(m,istate) * grad_rho_b(m,istate)
grad_rho_a_b(istate) += grad_rho_a(m,istate) * grad_rho_b(m,istate)
enddo
! inputs
call GGA_type_functionals(r,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_a_b, & ! outputs exchange
ex,vx_rho_a,vx_rho_b,vx_grad_rho_a_2,vx_grad_rho_b_2,vx_grad_rho_a_b, & ! outputs correlation
ec,vc_rho_a,vc_rho_b,vc_grad_rho_a_2,vc_grad_rho_b_2,vc_grad_rho_a_b )
energy_c_pbe += ec * weight
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, potential_x_alpha_ao_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, potential_x_beta_ao_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, potential_c_alpha_ao_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, potential_c_beta_ao_pbe,(ao_num,ao_num,N_states)]
implicit none
BEGIN_DOC
! exchange / correlation potential for alpha / beta electrons with the Perdew-Burke-Ernzerhof GGA functional
END_DOC
integer :: i,j,istate
do istate = 1, n_states
do i = 1, ao_num
do j = 1, ao_num
potential_x_alpha_ao_pbe(j,i,istate) = pot_scal_x_alpha_ao_pbe(j,i,istate) + pot_grad_x_alpha_ao_pbe(j,i,istate) + pot_grad_x_alpha_ao_pbe(i,j,istate)
potential_x_beta_ao_pbe(j,i,istate) = pot_scal_x_beta_ao_pbe(j,i,istate) + pot_grad_x_beta_ao_pbe(j,i,istate) + pot_grad_x_beta_ao_pbe(i,j,istate)
potential_c_alpha_ao_pbe(j,i,istate) = pot_scal_c_alpha_ao_pbe(j,i,istate) + pot_grad_c_alpha_ao_pbe(j,i,istate) + pot_grad_c_alpha_ao_pbe(i,j,istate)
potential_c_beta_ao_pbe(j,i,istate) = pot_scal_c_beta_ao_pbe(j,i,istate) + pot_grad_c_beta_ao_pbe(j,i,istate) + pot_grad_c_beta_ao_pbe(i,j,istate)
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, potential_xc_alpha_ao_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, potential_xc_beta_ao_pbe,(ao_num,ao_num,N_states)]
implicit none
BEGIN_DOC
! exchange / correlation potential for alpha / beta electrons with the Perdew-Burke-Ernzerhof GGA functional
END_DOC
integer :: i,j,istate
do istate = 1, n_states
do i = 1, ao_num
do j = 1, ao_num
potential_xc_alpha_ao_pbe(j,i,istate) = pot_scal_xc_alpha_ao_pbe(j,i,istate) + pot_grad_xc_alpha_ao_pbe(j,i,istate) + pot_grad_xc_alpha_ao_pbe(i,j,istate)
potential_xc_beta_ao_pbe(j,i,istate) = pot_scal_xc_beta_ao_pbe(j,i,istate) + pot_grad_xc_beta_ao_pbe(j,i,istate) + pot_grad_xc_beta_ao_pbe(i,j,istate)
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER[double precision, aos_vc_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_vc_beta_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_vx_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_vx_beta_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_dvc_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_dvc_beta_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_dvx_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_dvx_beta_pbe_w , (ao_num,n_points_final_grid,N_states)]
implicit none
BEGIN_DOC
! aos_vxc_alpha_pbe_w(j,i) = ao_i(r_j) * (v^x_alpha(r_j) + v^c_alpha(r_j)) * W(r_j)
END_DOC
integer :: istate,i,j,m
double precision :: r(3)
double precision :: mu,weight
double precision, allocatable :: ex(:), ec(:)
double precision, allocatable :: rho_a(:),rho_b(:),grad_rho_a(:,:),grad_rho_b(:,:),grad_rho_a_2(:),grad_rho_b_2(:),grad_rho_a_b(:)
double precision, allocatable :: contrib_grad_xa(:,:),contrib_grad_xb(:,:),contrib_grad_ca(:,:),contrib_grad_cb(:,:)
double precision, allocatable :: vc_rho_a(:), vc_rho_b(:), vx_rho_a(:), vx_rho_b(:)
double precision, allocatable :: vx_grad_rho_a_2(:), vx_grad_rho_b_2(:), vx_grad_rho_a_b(:), vc_grad_rho_a_2(:), vc_grad_rho_b_2(:), vc_grad_rho_a_b(:)
allocate(vc_rho_a(N_states), vc_rho_b(N_states), vx_rho_a(N_states), vx_rho_b(N_states))
allocate(vx_grad_rho_a_2(N_states), vx_grad_rho_b_2(N_states), vx_grad_rho_a_b(N_states), vc_grad_rho_a_2(N_states), vc_grad_rho_b_2(N_states), vc_grad_rho_a_b(N_states))
allocate(rho_a(N_states), rho_b(N_states),grad_rho_a(3,N_states),grad_rho_b(3,N_states))
allocate(grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_a_b(N_states), ex(N_states), ec(N_states))
allocate(contrib_grad_xa(3,N_states),contrib_grad_xb(3,N_states),contrib_grad_ca(3,N_states),contrib_grad_cb(3,N_states))
aos_dvc_alpha_pbe_w = 0.d0
aos_dvc_beta_pbe_w = 0.d0
aos_dvx_alpha_pbe_w = 0.d0
aos_dvx_beta_pbe_w = 0.d0
do istate = 1, N_states
do i = 1, n_points_final_grid
r(1) = final_grid_points(1,i)
r(2) = final_grid_points(2,i)
r(3) = final_grid_points(3,i)
weight = final_weight_at_r_vector(i)
rho_a(istate) = one_e_dm_and_grad_alpha_in_r(4,i,istate)
rho_b(istate) = one_e_dm_and_grad_beta_in_r(4,i,istate)
grad_rho_a(1:3,istate) = one_e_dm_and_grad_alpha_in_r(1:3,i,istate)
grad_rho_b(1:3,istate) = one_e_dm_and_grad_beta_in_r(1:3,i,istate)
grad_rho_a_2 = 0.d0
grad_rho_b_2 = 0.d0
grad_rho_a_b = 0.d0
do m = 1, 3
grad_rho_a_2(istate) += grad_rho_a(m,istate) * grad_rho_a(m,istate)
grad_rho_b_2(istate) += grad_rho_b(m,istate) * grad_rho_b(m,istate)
grad_rho_a_b(istate) += grad_rho_a(m,istate) * grad_rho_b(m,istate)
enddo
! inputs
call GGA_type_functionals(r,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_a_b, & ! outputs exchange
ex,vx_rho_a,vx_rho_b,vx_grad_rho_a_2,vx_grad_rho_b_2,vx_grad_rho_a_b, & ! outputs correlation
ec,vc_rho_a,vc_rho_b,vc_grad_rho_a_2,vc_grad_rho_b_2,vc_grad_rho_a_b )
vx_rho_a(istate) *= weight
vc_rho_a(istate) *= weight
vx_rho_b(istate) *= weight
vc_rho_b(istate) *= weight
do m= 1,3
contrib_grad_ca(m,istate) = weight * (2.d0 * vc_grad_rho_a_2(istate) * grad_rho_a(m,istate) + vc_grad_rho_a_b(istate) * grad_rho_b(m,istate))
contrib_grad_xa(m,istate) = weight * (2.d0 * vx_grad_rho_a_2(istate) * grad_rho_a(m,istate) + vx_grad_rho_a_b(istate) * grad_rho_b(m,istate))
contrib_grad_cb(m,istate) = weight * (2.d0 * vc_grad_rho_b_2(istate) * grad_rho_b(m,istate) + vc_grad_rho_a_b(istate) * grad_rho_a(m,istate))
contrib_grad_xb(m,istate) = weight * (2.d0 * vx_grad_rho_b_2(istate) * grad_rho_b(m,istate) + vx_grad_rho_a_b(istate) * grad_rho_a(m,istate))
enddo
do j = 1, ao_num
aos_vc_alpha_pbe_w(j,i,istate) = vc_rho_a(istate) * aos_in_r_array(j,i)
aos_vc_beta_pbe_w (j,i,istate) = vc_rho_b(istate) * aos_in_r_array(j,i)
aos_vx_alpha_pbe_w(j,i,istate) = vx_rho_a(istate) * aos_in_r_array(j,i)
aos_vx_beta_pbe_w (j,i,istate) = vx_rho_b(istate) * aos_in_r_array(j,i)
enddo
do j = 1, ao_num
do m = 1,3
aos_dvc_alpha_pbe_w(j,i,istate) += contrib_grad_ca(m,istate) * aos_grad_in_r_array_transp_xyz(m,j,i)
aos_dvc_beta_pbe_w (j,i,istate) += contrib_grad_cb(m,istate) * aos_grad_in_r_array_transp_xyz(m,j,i)
aos_dvx_alpha_pbe_w(j,i,istate) += contrib_grad_xa(m,istate) * aos_grad_in_r_array_transp_xyz(m,j,i)
aos_dvx_beta_pbe_w (j,i,istate) += contrib_grad_xb(m,istate) * aos_grad_in_r_array_transp_xyz(m,j,i)
enddo
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, pot_scal_x_alpha_ao_pbe, (ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_scal_c_alpha_ao_pbe, (ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_scal_x_beta_ao_pbe, (ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_scal_c_beta_ao_pbe, (ao_num,ao_num,N_states)]
implicit none
integer :: istate
BEGIN_DOC
! intermediate quantity for the calculation of the vxc potentials for the GGA functionals related to the scalar part of the potential
END_DOC
pot_scal_c_alpha_ao_pbe = 0.d0
pot_scal_x_alpha_ao_pbe = 0.d0
pot_scal_c_beta_ao_pbe = 0.d0
pot_scal_x_beta_ao_pbe = 0.d0
double precision :: wall_1,wall_2
call wall_time(wall_1)
do istate = 1, N_states
! correlation alpha
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vc_alpha_pbe_w(1,1,istate),size(aos_vc_alpha_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_c_alpha_ao_pbe(1,1,istate),size(pot_scal_c_alpha_ao_pbe,1))
! correlation beta
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vc_beta_pbe_w(1,1,istate),size(aos_vc_beta_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_c_beta_ao_pbe(1,1,istate),size(pot_scal_c_beta_ao_pbe,1))
! exchange alpha
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vx_alpha_pbe_w(1,1,istate),size(aos_vx_alpha_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_x_alpha_ao_pbe(1,1,istate),size(pot_scal_x_alpha_ao_pbe,1))
! exchange beta
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vx_beta_pbe_w(1,1,istate),size(aos_vx_beta_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_x_beta_ao_pbe(1,1,istate), size(pot_scal_x_beta_ao_pbe,1))
enddo
call wall_time(wall_2)
END_PROVIDER
BEGIN_PROVIDER [double precision, pot_grad_x_alpha_ao_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_grad_x_beta_ao_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_grad_c_alpha_ao_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_grad_c_beta_ao_pbe,(ao_num,ao_num,N_states)]
implicit none
BEGIN_DOC
! intermediate quantity for the calculation of the vxc potentials for the GGA functionals related to the gradienst of the density and orbitals
END_DOC
integer :: istate
double precision :: wall_1,wall_2
call wall_time(wall_1)
pot_grad_c_alpha_ao_pbe = 0.d0
pot_grad_x_alpha_ao_pbe = 0.d0
pot_grad_c_beta_ao_pbe = 0.d0
pot_grad_x_beta_ao_pbe = 0.d0
do istate = 1, N_states
! correlation alpha
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_dvc_alpha_pbe_w(1,1,istate),size(aos_dvc_alpha_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_c_alpha_ao_pbe(1,1,istate),size(pot_grad_c_alpha_ao_pbe,1))
! correlation beta
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_dvc_beta_pbe_w(1,1,istate),size(aos_dvc_beta_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_c_beta_ao_pbe(1,1,istate),size(pot_grad_c_beta_ao_pbe,1))
! exchange alpha
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_dvx_alpha_pbe_w(1,1,istate),size(aos_dvx_alpha_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_x_alpha_ao_pbe(1,1,istate),size(pot_grad_x_alpha_ao_pbe,1))
! exchange beta
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_dvx_beta_pbe_w(1,1,istate),size(aos_dvx_beta_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_x_beta_ao_pbe(1,1,istate),size(pot_grad_x_beta_ao_pbe,1))
enddo
call wall_time(wall_2)
END_PROVIDER
BEGIN_PROVIDER[double precision, aos_vxc_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_vxc_beta_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_dvxc_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_dvxc_beta_pbe_w , (ao_num,n_points_final_grid,N_states)]
implicit none
BEGIN_DOC
! aos_vxc_alpha_pbe_w(j,i) = ao_i(r_j) * (v^x_alpha(r_j) + v^c_alpha(r_j)) * W(r_j)
END_DOC
integer :: istate,i,j,m
double precision :: r(3)
double precision :: mu,weight
double precision, allocatable :: ex(:), ec(:)
double precision, allocatable :: rho_a(:),rho_b(:),grad_rho_a(:,:),grad_rho_b(:,:),grad_rho_a_2(:),grad_rho_b_2(:),grad_rho_a_b(:)
double precision, allocatable :: contrib_grad_xa(:,:),contrib_grad_xb(:,:),contrib_grad_ca(:,:),contrib_grad_cb(:,:)
double precision, allocatable :: vc_rho_a(:), vc_rho_b(:), vx_rho_a(:), vx_rho_b(:)
double precision, allocatable :: vx_grad_rho_a_2(:), vx_grad_rho_b_2(:), vx_grad_rho_a_b(:), vc_grad_rho_a_2(:), vc_grad_rho_b_2(:), vc_grad_rho_a_b(:)
allocate(vc_rho_a(N_states), vc_rho_b(N_states), vx_rho_a(N_states), vx_rho_b(N_states))
allocate(vx_grad_rho_a_2(N_states), vx_grad_rho_b_2(N_states), vx_grad_rho_a_b(N_states), vc_grad_rho_a_2(N_states), vc_grad_rho_b_2(N_states), vc_grad_rho_a_b(N_states))
allocate(rho_a(N_states), rho_b(N_states),grad_rho_a(3,N_states),grad_rho_b(3,N_states))
allocate(grad_rho_a_2(N_states),grad_rho_b_2(N_states),grad_rho_a_b(N_states), ex(N_states), ec(N_states))
allocate(contrib_grad_xa(3,N_states),contrib_grad_xb(3,N_states),contrib_grad_ca(3,N_states),contrib_grad_cb(3,N_states))
aos_dvxc_alpha_pbe_w = 0.d0
aos_dvxc_beta_pbe_w = 0.d0
do istate = 1, N_states
do i = 1, n_points_final_grid
r(1) = final_grid_points(1,i)
r(2) = final_grid_points(2,i)
r(3) = final_grid_points(3,i)
weight = final_weight_at_r_vector(i)
rho_a(istate) = one_e_dm_and_grad_alpha_in_r(4,i,istate)
rho_b(istate) = one_e_dm_and_grad_beta_in_r(4,i,istate)
grad_rho_a(1:3,istate) = one_e_dm_and_grad_alpha_in_r(1:3,i,istate)
grad_rho_b(1:3,istate) = one_e_dm_and_grad_beta_in_r(1:3,i,istate)
grad_rho_a_2 = 0.d0
grad_rho_b_2 = 0.d0
grad_rho_a_b = 0.d0
do m = 1, 3
grad_rho_a_2(istate) += grad_rho_a(m,istate) * grad_rho_a(m,istate)
grad_rho_b_2(istate) += grad_rho_b(m,istate) * grad_rho_b(m,istate)
grad_rho_a_b(istate) += grad_rho_a(m,istate) * grad_rho_b(m,istate)
enddo
! inputs
call GGA_type_functionals(r,rho_a,rho_b,grad_rho_a_2,grad_rho_b_2,grad_rho_a_b, & ! outputs exchange
ex,vx_rho_a,vx_rho_b,vx_grad_rho_a_2,vx_grad_rho_b_2,vx_grad_rho_a_b, & ! outputs correlation
ec,vc_rho_a,vc_rho_b,vc_grad_rho_a_2,vc_grad_rho_b_2,vc_grad_rho_a_b )
vx_rho_a(istate) *= weight
vc_rho_a(istate) *= weight
vx_rho_b(istate) *= weight
vc_rho_b(istate) *= weight
do m= 1,3
contrib_grad_ca(m,istate) = weight * (2.d0 * vc_grad_rho_a_2(istate) * grad_rho_a(m,istate) + vc_grad_rho_a_b(istate) * grad_rho_b(m,istate))
contrib_grad_xa(m,istate) = weight * (2.d0 * vx_grad_rho_a_2(istate) * grad_rho_a(m,istate) + vx_grad_rho_a_b(istate) * grad_rho_b(m,istate))
contrib_grad_cb(m,istate) = weight * (2.d0 * vc_grad_rho_b_2(istate) * grad_rho_b(m,istate) + vc_grad_rho_a_b(istate) * grad_rho_a(m,istate))
contrib_grad_xb(m,istate) = weight * (2.d0 * vx_grad_rho_b_2(istate) * grad_rho_b(m,istate) + vx_grad_rho_a_b(istate) * grad_rho_a(m,istate))
enddo
do j = 1, ao_num
aos_vxc_alpha_pbe_w(j,i,istate) = ( vc_rho_a(istate) + vx_rho_a(istate) ) * aos_in_r_array(j,i)
aos_vxc_beta_pbe_w (j,i,istate) = ( vc_rho_b(istate) + vx_rho_b(istate) ) * aos_in_r_array(j,i)
enddo
do j = 1, ao_num
do m = 1,3
aos_dvxc_alpha_pbe_w(j,i,istate) += ( contrib_grad_ca(m,istate) + contrib_grad_xa(m,istate) ) * aos_grad_in_r_array_transp_xyz(m,j,i)
aos_dvxc_beta_pbe_w (j,i,istate) += ( contrib_grad_cb(m,istate) + contrib_grad_xb(m,istate) ) * aos_grad_in_r_array_transp_xyz(m,j,i)
enddo
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, pot_scal_xc_alpha_ao_pbe, (ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_scal_xc_beta_ao_pbe, (ao_num,ao_num,N_states)]
implicit none
integer :: istate
BEGIN_DOC
! intermediate quantity for the calculation of the vxc potentials for the GGA functionals related to the scalar part of the potential
END_DOC
pot_scal_xc_alpha_ao_pbe = 0.d0
pot_scal_xc_beta_ao_pbe = 0.d0
double precision :: wall_1,wall_2
call wall_time(wall_1)
do istate = 1, N_states
! exchange - correlation alpha
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vxc_alpha_pbe_w(1,1,istate),size(aos_vxc_alpha_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_xc_alpha_ao_pbe(1,1,istate),size(pot_scal_xc_alpha_ao_pbe,1))
! exchange - correlation beta
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vxc_beta_pbe_w(1,1,istate),size(aos_vxc_beta_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_xc_beta_ao_pbe(1,1,istate),size(pot_scal_xc_beta_ao_pbe,1))
enddo
call wall_time(wall_2)
END_PROVIDER
BEGIN_PROVIDER [double precision, pot_grad_xc_alpha_ao_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_grad_xc_beta_ao_pbe,(ao_num,ao_num,N_states)]
implicit none
BEGIN_DOC
! intermediate quantity for the calculation of the vxc potentials for the GGA functionals related to the gradienst of the density and orbitals
END_DOC
integer :: istate
double precision :: wall_1,wall_2
call wall_time(wall_1)
pot_grad_xc_alpha_ao_pbe = 0.d0
pot_grad_xc_beta_ao_pbe = 0.d0
do istate = 1, N_states
! correlation alpha
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_dvxc_alpha_pbe_w(1,1,istate),size(aos_dvxc_alpha_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_xc_alpha_ao_pbe(1,1,istate),size(pot_grad_xc_alpha_ao_pbe,1))
! correlation beta
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_dvxc_beta_pbe_w(1,1,istate),size(aos_dvxc_beta_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_xc_beta_ao_pbe(1,1,istate),size(pot_grad_xc_beta_ao_pbe,1))
enddo
call wall_time(wall_2)
END_PROVIDER
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