qp2/src/functionals/pbe.irp.f

 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