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)) 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, 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