BEGIN_PROVIDER[double precision, energy_x_pbe, (N_states) ] &BEGIN_PROVIDER[double precision, energy_c_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_pbe = 0.d0 energy_c_pbe = 0.d0 mu = 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,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(istate) += ex * weight energy_c_pbe(istate) += 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 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_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_d_vc_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)] &BEGIN_PROVIDER[double precision, aos_d_vc_beta_pbe_w , (ao_num,n_points_final_grid,N_states)] &BEGIN_PROVIDER[double precision, aos_d_vx_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)] &BEGIN_PROVIDER[double precision, aos_d_vx_beta_pbe_w , (ao_num,n_points_final_grid,N_states)] implicit none BEGIN_DOC ! intermediates to compute the sr_pbe potentials ! ! 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 :: 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_pbe_w= 0.d0 aos_d_vc_beta_pbe_w = 0.d0 aos_d_vx_alpha_pbe_w= 0.d0 aos_d_vx_beta_pbe_w = 0.d0 mu = 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,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_pbe_w(j,i,istate) = vc_rho_a * aos_in_r_array(j,i) aos_vc_beta_pbe_w (j,i,istate) = vc_rho_b * aos_in_r_array(j,i) aos_vx_alpha_pbe_w(j,i,istate) = vx_rho_a * aos_in_r_array(j,i) aos_vx_beta_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_pbe_w(j,i,istate) += contrib_grad_ca(m) * aos_grad_in_r_array_transp(m,j,i) aos_d_vc_beta_pbe_w (j,i,istate) += contrib_grad_cb(m) * aos_grad_in_r_array_transp(m,j,i) aos_d_vx_alpha_pbe_w(j,i,istate) += contrib_grad_xa(m) * aos_grad_in_r_array_transp(m,j,i) aos_d_vx_beta_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_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 ! 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_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_d_vc_alpha_pbe_w(1,1,istate),size(aos_d_vc_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_d_vc_beta_pbe_w(1,1,istate),size(aos_d_vc_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_d_vx_alpha_pbe_w(1,1,istate),size(aos_d_vx_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_d_vx_beta_pbe_w(1,1,istate),size(aos_d_vx_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_d_vxc_alpha_pbe_w , (ao_num,n_points_final_grid,N_states)] &BEGIN_PROVIDER[double precision, aos_d_vxc_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 :: 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 mu = 0.d0 aos_d_vxc_alpha_pbe_w = 0.d0 aos_d_vxc_beta_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,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_pbe_w(j,i,istate) = ( vc_rho_a + vx_rho_a ) * aos_in_r_array(j,i) aos_vxc_beta_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_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_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_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 ! exchange - correlation alpha call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, & aos_d_vxc_alpha_pbe_w(1,1,istate),size(aos_d_vxc_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)) ! exchange - correlation beta call dgemm('N','N',ao_num,ao_num,n_points_final_grid,1.d0, & aos_d_vxc_beta_pbe_w(1,1,istate),size(aos_d_vxc_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