dft_utils_in_r

This module contains most of the fundamental quantities (AOs, MOs or density derivatives) evaluated in real-space representation that are needed for the various DFT modules.

As these quantities might be used and re-used, the values at each point of the grid are stored (see becke_numerical_grid for more information on the grid).

The main providers for this module are:

• aos_in_r_array: values of the AO basis on the grid point.
• mos_in_r_array: values of the MO basis on the grid point.
• one_e_dm_and_grad_alpha_in_r: values of the density and its gradienst on the grid points.

Providers

aos_grad_in_r_array

File : dft_utils_in_r/ao_in_r.irp.f

double precision, allocatable   :: aos_grad_in_r_array  (ao_num,n_points_final_grid,3)
double precision, allocatable   :: aos_grad_in_r_array_transp   (n_points_final_grid,ao_num,3)
double precision, allocatable   :: aos_grad_in_r_array_transp_xyz       (3,n_points_final_grid,ao_num)

aos_grad_in_r_array(i,j,k) = value of the kth component of the gradient of ith ao on the jth grid point

aos_grad_in_r_array_transp(i,j,k) = value of the kth component of the gradient of jth ao on the ith grid point

k = 1 : x, k= 2, y, k 3, z

Needs:

ao_coef_normalized_ordered_transp_per_nucl ao_expo_ordered_transp_per_nucl ao_num ao_power_ordered_transp_per_nucl

ao_prim_num final_grid_points n_points_final_grid nucl_aos_transposed

nucl_coord nucl_n_aos nucl_num

Needed by:

aos_sr_vc_alpha_pbe_w aos_vc_alpha_pbe_w

mos_grad_in_r_array potential_sr_x_alpha_ao_pbe

potential_x_alpha_ao_pbe

aos_grad_in_r_array_transp

File : dft_utils_in_r/ao_in_r.irp.f

double precision, allocatable   :: aos_grad_in_r_array  (ao_num,n_points_final_grid,3)
double precision, allocatable   :: aos_grad_in_r_array_transp   (n_points_final_grid,ao_num,3)
double precision, allocatable   :: aos_grad_in_r_array_transp_xyz       (3,n_points_final_grid,ao_num)

aos_grad_in_r_array(i,j,k) = value of the kth component of the gradient of ith ao on the jth grid point

aos_grad_in_r_array_transp(i,j,k) = value of the kth component of the gradient of jth ao on the ith grid point

k = 1 : x, k= 2, y, k 3, z

Needs:

ao_coef_normalized_ordered_transp_per_nucl ao_expo_ordered_transp_per_nucl ao_num ao_power_ordered_transp_per_nucl

ao_prim_num final_grid_points n_points_final_grid nucl_aos_transposed

nucl_coord nucl_n_aos nucl_num

Needed by:

aos_sr_vc_alpha_pbe_w aos_vc_alpha_pbe_w

mos_grad_in_r_array potential_sr_x_alpha_ao_pbe

potential_x_alpha_ao_pbe

aos_grad_in_r_array_transp_xyz

File : dft_utils_in_r/ao_in_r.irp.f

double precision, allocatable   :: aos_grad_in_r_array  (ao_num,n_points_final_grid,3)
double precision, allocatable   :: aos_grad_in_r_array_transp   (n_points_final_grid,ao_num,3)
double precision, allocatable   :: aos_grad_in_r_array_transp_xyz       (3,n_points_final_grid,ao_num)

aos_grad_in_r_array(i,j,k) = value of the kth component of the gradient of ith ao on the jth grid point

aos_grad_in_r_array_transp(i,j,k) = value of the kth component of the gradient of jth ao on the ith grid point

k = 1 : x, k= 2, y, k 3, z

Needs:

ao_coef_normalized_ordered_transp_per_nucl ao_expo_ordered_transp_per_nucl ao_num ao_power_ordered_transp_per_nucl

ao_prim_num final_grid_points n_points_final_grid nucl_aos_transposed

nucl_coord nucl_n_aos nucl_num

Needed by:

aos_sr_vc_alpha_pbe_w aos_vc_alpha_pbe_w

mos_grad_in_r_array potential_sr_x_alpha_ao_pbe

potential_x_alpha_ao_pbe

aos_in_r_array

File : dft_utils_in_r/ao_in_r.irp.f

double precision, allocatable   :: aos_in_r_array       (ao_num,n_points_final_grid)
double precision, allocatable   :: aos_in_r_array_transp        (n_points_final_grid,ao_num)

aos_in_r_array(i,j) = value of the ith ao on the jth grid point

aos_in_r_array_transp(i,j) = value of the jth ao on the ith grid point

Needs:

ao_coef_normalized_ordered_transp_per_nucl ao_expo_ordered_transp_per_nucl ao_num ao_power_ordered_transp_per_nucl

ao_prim_num final_grid_points n_points_final_grid nucl_aos_transposed

nucl_coord nucl_n_aos nucl_num

Needed by:

aos_sr_vc_alpha_lda_w aos_sr_vc_alpha_pbe_w aos_vc_alpha_lda_w

aos_vc_alpha_pbe_w potential_sr_c_alpha_ao_lda potential_sr_x_alpha_ao_lda

potential_sr_x_alpha_ao_pbe potential_x_alpha_ao_lda potential_x_alpha_ao_pbe

aos_in_r_array_transp

File : dft_utils_in_r/ao_in_r.irp.f

double precision, allocatable   :: aos_in_r_array       (ao_num,n_points_final_grid)
double precision, allocatable   :: aos_in_r_array_transp        (n_points_final_grid,ao_num)

aos_in_r_array(i,j) = value of the ith ao on the jth grid point

aos_in_r_array_transp(i,j) = value of the jth ao on the ith grid point

Needs:

ao_coef_normalized_ordered_transp_per_nucl ao_expo_ordered_transp_per_nucl ao_num ao_power_ordered_transp_per_nucl

ao_prim_num final_grid_points n_points_final_grid nucl_aos_transposed

nucl_coord nucl_n_aos nucl_num

Needed by:

aos_sr_vc_alpha_lda_w aos_sr_vc_alpha_pbe_w aos_vc_alpha_lda_w

aos_vc_alpha_pbe_w potential_sr_c_alpha_ao_lda potential_sr_x_alpha_ao_lda

potential_sr_x_alpha_ao_pbe potential_x_alpha_ao_lda potential_x_alpha_ao_pbe

aos_lapl_in_r_array

File : dft_utils_in_r/ao_in_r.irp.f

double precision, allocatable   :: aos_lapl_in_r_array  (ao_num,n_points_final_grid,3)
double precision, allocatable   :: aos_lapl_in_r_array_transp   (n_points_final_grid,ao_num,3)

aos_lapl_in_r_array(i,j,k) = value of the kth component of the laplacian of ith ao on the jth grid point

aos_lapl_in_r_array_transp(i,j,k) = value of the kth component of the laplacian of jth ao on the ith grid point

k = 1 : x, k= 2, y, k 3, z

Needs:

ao_coef_normalized_ordered_transp_per_nucl ao_expo_ordered_transp_per_nucl ao_num ao_power_ordered_transp_per_nucl

ao_prim_num final_grid_points n_points_final_grid nucl_aos_transposed

nucl_coord nucl_n_aos nucl_num

Needed by:

mos_lapl_in_r_array

aos_lapl_in_r_array_transp

File : dft_utils_in_r/ao_in_r.irp.f

double precision, allocatable   :: aos_lapl_in_r_array  (ao_num,n_points_final_grid,3)
double precision, allocatable   :: aos_lapl_in_r_array_transp   (n_points_final_grid,ao_num,3)

aos_lapl_in_r_array(i,j,k) = value of the kth component of the laplacian of ith ao on the jth grid point

aos_lapl_in_r_array_transp(i,j,k) = value of the kth component of the laplacian of jth ao on the ith grid point

k = 1 : x, k= 2, y, k 3, z

Needs:

ao_coef_normalized_ordered_transp_per_nucl ao_expo_ordered_transp_per_nucl ao_num ao_power_ordered_transp_per_nucl

ao_prim_num final_grid_points n_points_final_grid nucl_aos_transposed

nucl_coord nucl_n_aos nucl_num

Needed by:

mos_lapl_in_r_array

mos_grad_in_r_array

File : dft_utils_in_r/mo_in_r.irp.f

double precision, allocatable   :: mos_grad_in_r_array  (mo_num,n_points_final_grid,3)

mos_grad_in_r_array(i,j,k) = value of the kth component of the gradient of ith mo on the jth grid point

mos_grad_in_r_array_transp(i,j,k) = value of the kth component of the gradient of jth mo on the ith grid point

k = 1 : x, k= 2, y, k 3, z

Needs:

ao_num aos_grad_in_r_array

mo_coef_transp mo_num

n_points_final_grid

mos_in_r_array

File : dft_utils_in_r/mo_in_r.irp.f

double precision, allocatable   :: mos_in_r_array       (mo_num,n_points_final_grid)
double precision, allocatable   :: mos_in_r_array_transp        (n_points_final_grid,mo_num)

mos_in_r_array(i,j) = value of the ith mo on the jth grid point

mos_in_r_array_transp(i,j) = value of the jth mo on the ith grid point

Needs:

ao_num final_grid_points

mo_coef_transp mo_num

n_points_final_grid

mos_in_r_array_transp

File : dft_utils_in_r/mo_in_r.irp.f

double precision, allocatable   :: mos_in_r_array       (mo_num,n_points_final_grid)
double precision, allocatable   :: mos_in_r_array_transp        (n_points_final_grid,mo_num)

mos_in_r_array(i,j) = value of the ith mo on the jth grid point

mos_in_r_array_transp(i,j) = value of the jth mo on the ith grid point

Needs:

ao_num final_grid_points

mo_coef_transp mo_num

n_points_final_grid

mos_lapl_in_r_array

File : dft_utils_in_r/mo_in_r.irp.f

double precision, allocatable   :: mos_lapl_in_r_array  (mo_num,n_points_final_grid,3)

mos_lapl_in_r_array(i,j,k) = value of the kth component of the laplacian of ith mo on the jth grid point

mos_lapl_in_r_array_transp(i,j,k) = value of the kth component of the laplacian of jth mo on the ith grid point

k = 1 : x, k= 2, y, k 3, z

Needs:

ao_num aos_lapl_in_r_array

mo_coef_transp mo_num

n_points_final_grid

one_e_dm_alpha_at_r

File : dft_utils_in_r/dm_in_r.irp.f

double precision, allocatable   :: one_e_dm_alpha_at_r  (n_points_final_grid,N_states)
double precision, allocatable   :: one_e_dm_beta_at_r   (n_points_final_grid,N_states)

one_e_dm_alpha_at_r(i,istate) = n_alpha(r_i,istate) one_e_dm_beta_at_r(i,istate) = n_beta(r_i,istate) where r_i is the ith point of the grid and istate is the state number

Needs:

ao_num final_grid_points

n_points_final_grid n_states

one_e_dm_alpha_ao_for_dft

Needed by:

aos_sr_vc_alpha_lda_w aos_vc_alpha_lda_w

energy_sr_x_lda

energy_x_lda

one_e_dm_alpha_in_r

File : dft_utils_in_r/dm_in_r.irp.f

double precision, allocatable   :: one_e_dm_alpha_in_r  (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
double precision, allocatable   :: one_e_dm_beta_in_r   (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)

Needs:

ao_num grid_points_per_atom mo_num

n_points_radial_grid n_states

nucl_num one_e_dm_alpha_ao_for_dft

one_e_dm_and_grad_alpha_in_r

File : dft_utils_in_r/dm_in_r.irp.f

double precision, allocatable   :: one_e_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
double precision, allocatable   :: one_e_dm_and_grad_beta_in_r  (4,n_points_final_grid,N_states)
double precision, allocatable   :: one_e_grad_2_dm_alpha_at_r   (n_points_final_grid,N_states)
double precision, allocatable   :: one_e_grad_2_dm_beta_at_r    (n_points_final_grid,N_states)

one_e_dm_and_grad_alpha_in_r(1,i,i_state) = ddx n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(2,i,i_state) = ddy n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(3,i,i_state) = ddz n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) one_e_grad_2_dm_alpha_at_r(i,istate) = ddx n_alpha(r_i,istate)^2 + ddy n_alpha(r_i,istate)^2 + ddz n_alpha(r_i,istate)^2 where r_i is the ith point of the grid and istate is the state number

Needs:

ao_num final_grid_points

n_points_final_grid n_states

one_e_dm_alpha_ao_for_dft

Needed by:

aos_sr_vc_alpha_pbe_w aos_vc_alpha_pbe_w

energy_sr_x_pbe

energy_x_pbe

one_e_dm_and_grad_beta_in_r

File : dft_utils_in_r/dm_in_r.irp.f

double precision, allocatable   :: one_e_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
double precision, allocatable   :: one_e_dm_and_grad_beta_in_r  (4,n_points_final_grid,N_states)
double precision, allocatable   :: one_e_grad_2_dm_alpha_at_r   (n_points_final_grid,N_states)
double precision, allocatable   :: one_e_grad_2_dm_beta_at_r    (n_points_final_grid,N_states)

one_e_dm_and_grad_alpha_in_r(1,i,i_state) = ddx n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(2,i,i_state) = ddy n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(3,i,i_state) = ddz n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) one_e_grad_2_dm_alpha_at_r(i,istate) = ddx n_alpha(r_i,istate)^2 + ddy n_alpha(r_i,istate)^2 + ddz n_alpha(r_i,istate)^2 where r_i is the ith point of the grid and istate is the state number

Needs:

ao_num final_grid_points

n_points_final_grid n_states

one_e_dm_alpha_ao_for_dft

Needed by:

aos_sr_vc_alpha_pbe_w aos_vc_alpha_pbe_w

energy_sr_x_pbe

energy_x_pbe

one_e_dm_beta_at_r

File : dft_utils_in_r/dm_in_r.irp.f

double precision, allocatable   :: one_e_dm_alpha_at_r  (n_points_final_grid,N_states)
double precision, allocatable   :: one_e_dm_beta_at_r   (n_points_final_grid,N_states)

one_e_dm_alpha_at_r(i,istate) = n_alpha(r_i,istate) one_e_dm_beta_at_r(i,istate) = n_beta(r_i,istate) where r_i is the ith point of the grid and istate is the state number

Needs:

ao_num final_grid_points

n_points_final_grid n_states

one_e_dm_alpha_ao_for_dft

Needed by:

aos_sr_vc_alpha_lda_w aos_vc_alpha_lda_w

energy_sr_x_lda

energy_x_lda

one_e_dm_beta_in_r

File : dft_utils_in_r/dm_in_r.irp.f

double precision, allocatable   :: one_e_dm_alpha_in_r  (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
double precision, allocatable   :: one_e_dm_beta_in_r   (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)

Needs:

ao_num grid_points_per_atom mo_num

n_points_radial_grid n_states

nucl_num one_e_dm_alpha_ao_for_dft

one_e_grad_2_dm_alpha_at_r

File : dft_utils_in_r/dm_in_r.irp.f

double precision, allocatable   :: one_e_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
double precision, allocatable   :: one_e_dm_and_grad_beta_in_r  (4,n_points_final_grid,N_states)
double precision, allocatable   :: one_e_grad_2_dm_alpha_at_r   (n_points_final_grid,N_states)
double precision, allocatable   :: one_e_grad_2_dm_beta_at_r    (n_points_final_grid,N_states)

one_e_dm_and_grad_alpha_in_r(1,i,i_state) = ddx n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(2,i,i_state) = ddy n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(3,i,i_state) = ddz n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) one_e_grad_2_dm_alpha_at_r(i,istate) = ddx n_alpha(r_i,istate)^2 + ddy n_alpha(r_i,istate)^2 + ddz n_alpha(r_i,istate)^2 where r_i is the ith point of the grid and istate is the state number

Needs:

ao_num final_grid_points

n_points_final_grid n_states

one_e_dm_alpha_ao_for_dft

Needed by:

aos_sr_vc_alpha_pbe_w aos_vc_alpha_pbe_w

energy_sr_x_pbe

energy_x_pbe

one_e_grad_2_dm_beta_at_r

File : dft_utils_in_r/dm_in_r.irp.f

double precision, allocatable   :: one_e_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
double precision, allocatable   :: one_e_dm_and_grad_beta_in_r  (4,n_points_final_grid,N_states)
double precision, allocatable   :: one_e_grad_2_dm_alpha_at_r   (n_points_final_grid,N_states)
double precision, allocatable   :: one_e_grad_2_dm_beta_at_r    (n_points_final_grid,N_states)

one_e_dm_and_grad_alpha_in_r(1,i,i_state) = ddx n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(2,i,i_state) = ddy n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(3,i,i_state) = ddz n_alpha(r_i,istate) one_e_dm_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) one_e_grad_2_dm_alpha_at_r(i,istate) = ddx n_alpha(r_i,istate)^2 + ddy n_alpha(r_i,istate)^2 + ddz n_alpha(r_i,istate)^2 where r_i is the ith point of the grid and istate is the state number

Needs:

ao_num final_grid_points

n_points_final_grid n_states

one_e_dm_alpha_ao_for_dft

Needed by:

aos_sr_vc_alpha_pbe_w aos_vc_alpha_pbe_w

energy_sr_x_pbe

energy_x_pbe

Subroutines / functions

density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r:()

File : dft_utils_in_r/dm_in_r.irp.f

subroutine density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r(r,dm_a,dm_b, grad_dm_a, grad_dm_b, aos_array, grad_aos_array)

input : r(1) ==> r(1) = x, r(2) = y, r(3) = z output : dm_a = alpha density evaluated at r

: dm_b = beta density evaluated at r : aos_array(i) = ao(i) evaluated at r : grad_dm_a(1) = X gradient of the alpha density evaluated in r : grad_dm_a(1) = X gradient of the beta density evaluated in r : grad_aos_array(1) = X gradient of the aos(i) evaluated at r

Needs:

ao_num

one_e_dm_alpha_ao_for_dft

n_states

Called by:

one_e_dm_and_grad_alpha_in_r

Calls:

dsymv()

give_all_aos_and_grad_at_r()

dm_dft_alpha_beta_and_all_aos_at_r:()

File : dft_utils_in_r/dm_in_r.irp.f

subroutine dm_dft_alpha_beta_and_all_aos_at_r(r,dm_a,dm_b,aos_array)

input: r(1) ==> r(1) = x, r(2) = y, r(3) = z output : dm_a = alpha density evaluated at r output : dm_b = beta density evaluated at r output : aos_array(i) = ao(i) evaluated at r

Needs:

ao_num

one_e_dm_alpha_ao_for_dft

n_states

Calls:

dsymv()

give_all_aos_at_r()

dm_dft_alpha_beta_at_r:()

File : dft_utils_in_r/dm_in_r.irp.f

subroutine dm_dft_alpha_beta_at_r(r,dm_a,dm_b)

input: r(1) ==> r(1) = x, r(2) = y, r(3) = z output : dm_a = alpha density evaluated at r(3) output : dm_b = beta density evaluated at r(3)

Needs:

ao_num

one_e_dm_alpha_ao_for_dft

n_states

Called by:

one_e_dm_alpha_at_r

one_e_dm_alpha_in_r

Calls:

dgemv()

give_all_aos_at_r()