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qp2/src/functionals/sr_pbe.irp.f
Emmanuel Giner LCT 6db77c320b parallel sections for dft_utils_in_r
2020-04-05 13:58:17 +02:00

381 lines
18 KiB
Fortran
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BEGIN_PROVIDER[double precision, energy_x_sr_pbe, (N_states) ]
&BEGIN_PROVIDER[double precision, energy_c_sr_pbe, (N_states) ]
implicit none
BEGIN_DOC
! exchange / correlation energies with the short-range version Perdew-Burke-Ernzerhof GGA functional
!
! defined in Chem. Phys.329, 276 (2006)
END_DOC
BEGIN_DOC
! exchange/correlation energy with the short range pbe functional
END_DOC
integer :: istate,i,j,m
double precision :: mu,weight
double precision :: ex, ec
double precision :: rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),grad_rho_a_2,grad_rho_b_2,grad_rho_a_b
double precision :: vc_rho_a, vc_rho_b, vx_rho_a, vx_rho_b
double precision :: 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
energy_x_sr_pbe = 0.d0
energy_c_sr_pbe = 0.d0
do istate = 1, N_states
do i = 1, n_points_final_grid
weight = final_weight_at_r_vector(i)
rho_a = one_e_dm_and_grad_alpha_in_r(4,i,istate)
rho_b = one_e_dm_and_grad_beta_in_r(4,i,istate)
grad_rho_a(1:3) = one_e_dm_and_grad_alpha_in_r(1:3,i,istate)
grad_rho_b(1:3) = 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 += grad_rho_a(m) * grad_rho_a(m)
grad_rho_b_2 += grad_rho_b(m) * grad_rho_b(m)
grad_rho_a_b += grad_rho_a(m) * grad_rho_b(m)
enddo
! inputs
call GGA_sr_type_functionals(mu_erf_dft,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_sr_pbe(istate) += ex * weight
energy_c_sr_pbe(istate) += ec * weight
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, potential_x_alpha_ao_sr_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, potential_x_beta_ao_sr_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, potential_c_alpha_ao_sr_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, potential_c_beta_ao_sr_pbe,(ao_num,ao_num,N_states)]
implicit none
BEGIN_DOC
! exchange / correlation potential for alpha / beta electrons with the short-range version Perdew-Burke-Ernzerhof GGA functional
!
! defined in Chem. Phys.329, 276 (2006)
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_sr_pbe(j,i,istate) = pot_scal_x_alpha_ao_sr_pbe(j,i,istate) + pot_grad_x_alpha_ao_sr_pbe(j,i,istate) + pot_grad_x_alpha_ao_sr_pbe(i,j,istate)
potential_x_beta_ao_sr_pbe(j,i,istate) = pot_scal_x_beta_ao_sr_pbe(j,i,istate) + pot_grad_x_beta_ao_sr_pbe(j,i,istate) + pot_grad_x_beta_ao_sr_pbe(i,j,istate)
potential_c_alpha_ao_sr_pbe(j,i,istate) = pot_scal_c_alpha_ao_sr_pbe(j,i,istate) + pot_grad_c_alpha_ao_sr_pbe(j,i,istate) + pot_grad_c_alpha_ao_sr_pbe(i,j,istate)
potential_c_beta_ao_sr_pbe(j,i,istate) = pot_scal_c_beta_ao_sr_pbe(j,i,istate) + pot_grad_c_beta_ao_sr_pbe(j,i,istate) + pot_grad_c_beta_ao_sr_pbe(i,j,istate)
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, potential_xc_alpha_ao_sr_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, potential_xc_beta_ao_sr_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_sr_pbe(j,i,istate) = pot_scal_xc_alpha_ao_sr_pbe(j,i,istate) + pot_grad_xc_alpha_ao_sr_pbe(j,i,istate) + pot_grad_xc_alpha_ao_sr_pbe(i,j,istate)
potential_xc_beta_ao_sr_pbe(j,i,istate) = pot_scal_xc_beta_ao_sr_pbe(j,i,istate) + pot_grad_xc_beta_ao_sr_pbe(j,i,istate) + pot_grad_xc_beta_ao_sr_pbe(i,j,istate)
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER[double precision, aos_vc_alpha_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_vc_beta_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_vx_alpha_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_vx_beta_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_d_vc_alpha_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_d_vc_beta_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_d_vx_alpha_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_d_vx_beta_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
implicit none
BEGIN_DOC
! intermediates to compute the sr_pbe potentials
!
! aos_vxc_alpha_sr_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 :: mu,weight
double precision :: ex, ec
double precision :: rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),grad_rho_a_2,grad_rho_b_2,grad_rho_a_b
double precision :: contrib_grad_xa(3),contrib_grad_xb(3),contrib_grad_ca(3),contrib_grad_cb(3)
double precision :: vc_rho_a, vc_rho_b, vx_rho_a, vx_rho_b
double precision :: 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
aos_d_vc_alpha_sr_pbe_w= 0.d0
aos_d_vc_beta_sr_pbe_w = 0.d0
aos_d_vx_alpha_sr_pbe_w= 0.d0
aos_d_vx_beta_sr_pbe_w = 0.d0
do istate = 1, N_states
do i = 1, n_points_final_grid
weight = final_weight_at_r_vector(i)
rho_a = one_e_dm_and_grad_alpha_in_r(4,i,istate)
rho_b = one_e_dm_and_grad_beta_in_r(4,i,istate)
grad_rho_a(1:3) = one_e_dm_and_grad_alpha_in_r(1:3,i,istate)
grad_rho_b(1:3) = 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 += grad_rho_a(m) * grad_rho_a(m)
grad_rho_b_2 += grad_rho_b(m) * grad_rho_b(m)
grad_rho_a_b += grad_rho_a(m) * grad_rho_b(m)
enddo
! inputs
call GGA_sr_type_functionals(mu_erf_dft,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 *= weight
vc_rho_a *= weight
vx_rho_b *= weight
vc_rho_b *= weight
do m= 1,3
contrib_grad_ca(m) = weight * (2.d0 * vc_grad_rho_a_2 * grad_rho_a(m) + vc_grad_rho_a_b * grad_rho_b(m) )
contrib_grad_xa(m) = weight * (2.d0 * vx_grad_rho_a_2 * grad_rho_a(m) + vx_grad_rho_a_b * grad_rho_b(m) )
contrib_grad_cb(m) = weight * (2.d0 * vc_grad_rho_b_2 * grad_rho_b(m) + vc_grad_rho_a_b * grad_rho_a(m) )
contrib_grad_xb(m) = weight * (2.d0 * vx_grad_rho_b_2 * grad_rho_b(m) + vx_grad_rho_a_b * grad_rho_a(m) )
enddo
do j = 1, ao_num
aos_vc_alpha_sr_pbe_w(j,i,istate) = vc_rho_a * aos_in_r_array(j,i)
aos_vc_beta_sr_pbe_w (j,i,istate) = vc_rho_b * aos_in_r_array(j,i)
aos_vx_alpha_sr_pbe_w(j,i,istate) = vx_rho_a * aos_in_r_array(j,i)
aos_vx_beta_sr_pbe_w (j,i,istate) = vx_rho_b * aos_in_r_array(j,i)
enddo
do j = 1, ao_num
do m = 1,3
aos_d_vc_alpha_sr_pbe_w(j,i,istate) += contrib_grad_ca(m) * aos_grad_in_r_array_transp(m,j,i)
aos_d_vc_beta_sr_pbe_w (j,i,istate) += contrib_grad_cb(m) * aos_grad_in_r_array_transp(m,j,i)
aos_d_vx_alpha_sr_pbe_w(j,i,istate) += contrib_grad_xa(m) * aos_grad_in_r_array_transp(m,j,i)
aos_d_vx_beta_sr_pbe_w (j,i,istate) += contrib_grad_xb(m) * aos_grad_in_r_array_transp(m,j,i)
enddo
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, pot_scal_x_alpha_ao_sr_pbe, (ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_scal_c_alpha_ao_sr_pbe, (ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_scal_x_beta_ao_sr_pbe, (ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_scal_c_beta_ao_sr_pbe, (ao_num,ao_num,N_states)]
implicit none
! intermediates to compute the sr_pbe potentials
!
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_sr_pbe = 0.d0
pot_scal_x_alpha_ao_sr_pbe = 0.d0
pot_scal_c_beta_ao_sr_pbe = 0.d0
pot_scal_x_beta_ao_sr_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_sr_pbe_w(1,1,istate),size(aos_vc_alpha_sr_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_c_alpha_ao_sr_pbe(1,1,istate),size(pot_scal_c_alpha_ao_sr_pbe,1))
! correlation beta
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vc_beta_sr_pbe_w(1,1,istate),size(aos_vc_beta_sr_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_c_beta_ao_sr_pbe(1,1,istate),size(pot_scal_c_beta_ao_sr_pbe,1))
! exchange alpha
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vx_alpha_sr_pbe_w(1,1,istate),size(aos_vx_alpha_sr_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_x_alpha_ao_sr_pbe(1,1,istate),size(pot_scal_x_alpha_ao_sr_pbe,1))
! exchange beta
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vx_beta_sr_pbe_w(1,1,istate),size(aos_vx_beta_sr_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_x_beta_ao_sr_pbe(1,1,istate), size(pot_scal_x_beta_ao_sr_pbe,1))
enddo
call wall_time(wall_2)
END_PROVIDER
BEGIN_PROVIDER [double precision, pot_grad_x_alpha_ao_sr_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_grad_x_beta_ao_sr_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_grad_c_alpha_ao_sr_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_grad_c_beta_ao_sr_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_sr_pbe = 0.d0
pot_grad_x_alpha_ao_sr_pbe = 0.d0
pot_grad_c_beta_ao_sr_pbe = 0.d0
pot_grad_x_beta_ao_sr_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_d_vc_alpha_sr_pbe_w(1,1,istate),size(aos_d_vc_alpha_sr_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_c_alpha_ao_sr_pbe(1,1,istate),size(pot_grad_c_alpha_ao_sr_pbe,1))
! correlation beta
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_d_vc_beta_sr_pbe_w(1,1,istate),size(aos_d_vc_beta_sr_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_c_beta_ao_sr_pbe(1,1,istate),size(pot_grad_c_beta_ao_sr_pbe,1))
! exchange alpha
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_d_vx_alpha_sr_pbe_w(1,1,istate),size(aos_d_vx_alpha_sr_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_x_alpha_ao_sr_pbe(1,1,istate),size(pot_grad_x_alpha_ao_sr_pbe,1))
! exchange beta
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_d_vx_beta_sr_pbe_w(1,1,istate),size(aos_d_vx_beta_sr_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_x_beta_ao_sr_pbe(1,1,istate),size(pot_grad_x_beta_ao_sr_pbe,1))
enddo
call wall_time(wall_2)
END_PROVIDER
BEGIN_PROVIDER[double precision, aos_vxc_alpha_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_vxc_beta_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_d_vxc_alpha_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
&BEGIN_PROVIDER[double precision, aos_d_vxc_beta_sr_pbe_w , (ao_num,n_points_final_grid,N_states)]
implicit none
BEGIN_DOC
! aos_vxc_alpha_sr_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 :: mu,weight
double precision :: ex, ec
double precision :: rho_a,rho_b,grad_rho_a(3),grad_rho_b(3),grad_rho_a_2,grad_rho_b_2,grad_rho_a_b
double precision :: contrib_grad_xa(3),contrib_grad_xb(3),contrib_grad_ca(3),contrib_grad_cb(3)
double precision :: vc_rho_a, vc_rho_b, vx_rho_a, vx_rho_b
double precision :: 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
aos_d_vxc_alpha_sr_pbe_w = 0.d0
aos_d_vxc_beta_sr_pbe_w = 0.d0
do istate = 1, N_states
do i = 1, n_points_final_grid
weight = final_weight_at_r_vector(i)
rho_a = one_e_dm_and_grad_alpha_in_r(4,i,istate)
rho_b = one_e_dm_and_grad_beta_in_r(4,i,istate)
grad_rho_a(1:3) = one_e_dm_and_grad_alpha_in_r(1:3,i,istate)
grad_rho_b(1:3) = 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 += grad_rho_a(m) * grad_rho_a(m)
grad_rho_b_2 += grad_rho_b(m) * grad_rho_b(m)
grad_rho_a_b += grad_rho_a(m) * grad_rho_b(m)
enddo
! inputs
call GGA_sr_type_functionals(mu_erf_dft,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 *= weight
vc_rho_a *= weight
vx_rho_b *= weight
vc_rho_b *= weight
do m= 1,3
contrib_grad_ca(m) = weight * (2.d0 * vc_grad_rho_a_2 * grad_rho_a(m) + vc_grad_rho_a_b * grad_rho_b(m) )
contrib_grad_xa(m) = weight * (2.d0 * vx_grad_rho_a_2 * grad_rho_a(m) + vx_grad_rho_a_b * grad_rho_b(m) )
contrib_grad_cb(m) = weight * (2.d0 * vc_grad_rho_b_2 * grad_rho_b(m) + vc_grad_rho_a_b * grad_rho_a(m) )
contrib_grad_xb(m) = weight * (2.d0 * vx_grad_rho_b_2 * grad_rho_b(m) + vx_grad_rho_a_b * grad_rho_a(m) )
enddo
do j = 1, ao_num
aos_vxc_alpha_sr_pbe_w(j,i,istate) = ( vc_rho_a + vx_rho_a ) * aos_in_r_array(j,i)
aos_vxc_beta_sr_pbe_w (j,i,istate) = ( vc_rho_b + vx_rho_b ) * aos_in_r_array(j,i)
enddo
do j = 1, ao_num
do m = 1,3
aos_d_vxc_alpha_sr_pbe_w(j,i,istate) += ( contrib_grad_ca(m) + contrib_grad_xa(m) ) * aos_grad_in_r_array_transp(m,j,i)
aos_d_vxc_beta_sr_pbe_w (j,i,istate) += ( contrib_grad_cb(m) + contrib_grad_xb(m) ) * aos_grad_in_r_array_transp(m,j,i)
enddo
enddo
enddo
enddo
END_PROVIDER
BEGIN_PROVIDER [double precision, pot_scal_xc_alpha_ao_sr_pbe, (ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_scal_xc_beta_ao_sr_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_sr_pbe = 0.d0
pot_scal_xc_beta_ao_sr_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_sr_pbe_w(1,1,istate),size(aos_vxc_alpha_sr_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_xc_alpha_ao_sr_pbe(1,1,istate),size(pot_scal_xc_alpha_ao_sr_pbe,1))
! exchange - correlation beta
call dgemm('N','T',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_vxc_beta_sr_pbe_w(1,1,istate),size(aos_vxc_beta_sr_pbe_w,1), &
aos_in_r_array,size(aos_in_r_array,1),1.d0, &
pot_scal_xc_beta_ao_sr_pbe(1,1,istate),size(pot_scal_xc_beta_ao_sr_pbe,1))
enddo
call wall_time(wall_2)
END_PROVIDER
BEGIN_PROVIDER [double precision, pot_grad_xc_alpha_ao_sr_pbe,(ao_num,ao_num,N_states)]
&BEGIN_PROVIDER [double precision, pot_grad_xc_beta_ao_sr_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_sr_pbe = 0.d0
pot_grad_xc_beta_ao_sr_pbe = 0.d0
do istate = 1, N_states
! exchange - correlation alpha
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_d_vxc_alpha_sr_pbe_w(1,1,istate),size(aos_d_vxc_alpha_sr_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_xc_alpha_ao_sr_pbe(1,1,istate),size(pot_grad_xc_alpha_ao_sr_pbe,1))
! exchange - correlation beta
call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, &
aos_d_vxc_beta_sr_pbe_w(1,1,istate),size(aos_d_vxc_beta_sr_pbe_w,1), &
aos_in_r_array_transp,size(aos_in_r_array_transp,1),1.d0, &
pot_grad_xc_beta_ao_sr_pbe(1,1,istate),size(pot_grad_xc_beta_ao_sr_pbe,1))
enddo
call wall_time(wall_2)
END_PROVIDER
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