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QuantumPackage/docs/source/modules/dft_utils_in_r.rst

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.. _module_dft_utils_in_r:
.. program:: dft_utils_in_r
.. default-role:: option
==============
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
---------
.. c:var:: aos_grad_in_r_array
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
double precision, allocatable :: aos_grad_in_r_array (ao_num,n_points_final_grid,3)
aos_grad_in_r_array(i,j,k) = value of the kth component of the gradient of ith ao on the jth grid point
k = 1 : x, k= 2, y, k 3, z
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`mos_grad_in_r_array`
.. c:var:: aos_grad_in_r_array_transp
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
double precision, allocatable :: aos_grad_in_r_array_transp (n_points_final_grid,ao_num,3)
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:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
.. c:var:: aos_grad_in_r_array_transp_xyz
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
double precision, allocatable :: aos_grad_in_r_array_transp_xyz (3,ao_num,n_points_final_grid)
aos_grad_in_r_array_transp_xyz(k,i,j) = 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:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_pbe_w`
* :c:data:`aos_sr_vxc_alpha_pbe_w`
* :c:data:`aos_vc_alpha_pbe_w`
* :c:data:`aos_vxc_alpha_pbe_w`
.. c:var:: aos_in_r_array
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_lda_w`
* :c:data:`aos_sr_vc_alpha_pbe_w`
* :c:data:`aos_sr_vxc_alpha_lda_w`
* :c:data:`aos_sr_vxc_alpha_pbe_w`
* :c:data:`aos_vc_alpha_lda_w`
* :c:data:`aos_vc_alpha_pbe_w`
* :c:data:`aos_vxc_alpha_lda_w`
* :c:data:`aos_vxc_alpha_pbe_w`
* :c:data:`pot_grad_x_alpha_ao_pbe`
* :c:data:`pot_grad_xc_alpha_ao_pbe`
* :c:data:`pot_scal_x_alpha_ao_pbe`
* :c:data:`pot_scal_xc_alpha_ao_pbe`
* :c:data:`pot_sr_grad_x_alpha_ao_pbe`
* :c:data:`pot_sr_grad_xc_alpha_ao_pbe`
* :c:data:`pot_sr_scal_x_alpha_ao_pbe`
* :c:data:`pot_sr_scal_xc_alpha_ao_pbe`
* :c:data:`potential_c_alpha_ao_lda`
* :c:data:`potential_c_alpha_ao_sr_lda`
* :c:data:`potential_x_alpha_ao_lda`
* :c:data:`potential_x_alpha_ao_sr_lda`
* :c:data:`potential_xc_alpha_ao_lda`
* :c:data:`potential_xc_alpha_ao_sr_lda`
.. c:var:: aos_in_r_array_per_atom
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
double precision, allocatable :: aos_in_r_array_per_atom (ao_num,n_pts_max_per_atom,nucl_num)
double precision, allocatable :: aos_in_r_array_per_atom_transp (n_pts_max_per_atom,ao_num,nucl_num)
aos_in_r_array_per_atom(i,j,k) = value of the ith ao on the jth grid point attached on the kth atom
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points_per_atom`
* :c:data:`n_pts_per_atom`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
.. c:var:: aos_in_r_array_per_atom_transp
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
double precision, allocatable :: aos_in_r_array_per_atom (ao_num,n_pts_max_per_atom,nucl_num)
double precision, allocatable :: aos_in_r_array_per_atom_transp (n_pts_max_per_atom,ao_num,nucl_num)
aos_in_r_array_per_atom(i,j,k) = value of the ith ao on the jth grid point attached on the kth atom
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points_per_atom`
* :c:data:`n_pts_per_atom`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
.. c:var:: aos_in_r_array_transp
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_lda_w`
* :c:data:`aos_sr_vc_alpha_pbe_w`
* :c:data:`aos_sr_vxc_alpha_lda_w`
* :c:data:`aos_sr_vxc_alpha_pbe_w`
* :c:data:`aos_vc_alpha_lda_w`
* :c:data:`aos_vc_alpha_pbe_w`
* :c:data:`aos_vxc_alpha_lda_w`
* :c:data:`aos_vxc_alpha_pbe_w`
* :c:data:`pot_grad_x_alpha_ao_pbe`
* :c:data:`pot_grad_xc_alpha_ao_pbe`
* :c:data:`pot_scal_x_alpha_ao_pbe`
* :c:data:`pot_scal_xc_alpha_ao_pbe`
* :c:data:`pot_sr_grad_x_alpha_ao_pbe`
* :c:data:`pot_sr_grad_xc_alpha_ao_pbe`
* :c:data:`pot_sr_scal_x_alpha_ao_pbe`
* :c:data:`pot_sr_scal_xc_alpha_ao_pbe`
* :c:data:`potential_c_alpha_ao_lda`
* :c:data:`potential_c_alpha_ao_sr_lda`
* :c:data:`potential_x_alpha_ao_lda`
* :c:data:`potential_x_alpha_ao_sr_lda`
* :c:data:`potential_xc_alpha_ao_lda`
* :c:data:`potential_xc_alpha_ao_sr_lda`
.. c:var:: aos_lapl_in_r_array
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`mos_lapl_in_r_array`
.. c:var:: aos_lapl_in_r_array_transp
File : :file:`dft_utils_in_r/ao_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_coef_normalized_ordered_transp_per_nucl`
* :c:data:`ao_expo_ordered_transp_per_nucl`
* :c:data:`ao_num`
* :c:data:`ao_power_ordered_transp_per_nucl`
* :c:data:`ao_prim_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`nucl_aos_transposed`
* :c:data:`nucl_coord`
* :c:data:`nucl_n_aos`
* :c:data:`nucl_num`
Needed by:
.. hlist::
:columns: 3
* :c:data:`mos_lapl_in_r_array`
.. c:var:: elec_alpha_num_grid_becke
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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)
double precision, allocatable :: elec_beta_num_grid_becke (N_states)
double precision, allocatable :: elec_alpha_num_grid_becke (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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_lda_w`
* :c:data:`aos_sr_vxc_alpha_lda_w`
* :c:data:`aos_vc_alpha_lda_w`
* :c:data:`aos_vxc_alpha_lda_w`
* :c:data:`energy_c_lda`
* :c:data:`energy_c_sr_lda`
* :c:data:`energy_sr_x_lda`
* :c:data:`energy_x_lda`
* :c:data:`energy_x_sr_lda`
.. c:var:: elec_beta_num_grid_becke
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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)
double precision, allocatable :: elec_beta_num_grid_becke (N_states)
double precision, allocatable :: elec_alpha_num_grid_becke (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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_lda_w`
* :c:data:`aos_sr_vxc_alpha_lda_w`
* :c:data:`aos_vc_alpha_lda_w`
* :c:data:`aos_vxc_alpha_lda_w`
* :c:data:`energy_c_lda`
* :c:data:`energy_c_sr_lda`
* :c:data:`energy_sr_x_lda`
* :c:data:`energy_x_lda`
* :c:data:`energy_x_sr_lda`
.. c:var:: mos_grad_in_r_array
File : :file:`dft_utils_in_r/mo_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`aos_grad_in_r_array`
* :c:data:`mo_coef_transp`
* :c:data:`mo_num`
* :c:data:`n_points_final_grid`
.. c:var:: mos_in_r_array
File : :file:`dft_utils_in_r/mo_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`mo_coef_transp`
* :c:data:`mo_num`
* :c:data:`n_points_final_grid`
.. c:var:: mos_in_r_array_transp
File : :file:`dft_utils_in_r/mo_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`mo_coef_transp`
* :c:data:`mo_num`
* :c:data:`n_points_final_grid`
.. c:var:: mos_lapl_in_r_array
File : :file:`dft_utils_in_r/mo_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`aos_lapl_in_r_array`
* :c:data:`mo_coef_transp`
* :c:data:`mo_num`
* :c:data:`n_points_final_grid`
.. c:var:: one_e_dm_alpha_at_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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)
double precision, allocatable :: elec_beta_num_grid_becke (N_states)
double precision, allocatable :: elec_alpha_num_grid_becke (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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_lda_w`
* :c:data:`aos_sr_vxc_alpha_lda_w`
* :c:data:`aos_vc_alpha_lda_w`
* :c:data:`aos_vxc_alpha_lda_w`
* :c:data:`energy_c_lda`
* :c:data:`energy_c_sr_lda`
* :c:data:`energy_sr_x_lda`
* :c:data:`energy_x_lda`
* :c:data:`energy_x_sr_lda`
.. c:var:: one_e_dm_alpha_in_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`grid_points_per_atom`
* :c:data:`mo_num`
* :c:data:`n_points_radial_grid`
* :c:data:`n_states`
* :c:data:`nucl_num`
* :c:data:`one_e_dm_alpha_ao_for_dft`
.. c:var:: one_e_dm_and_grad_alpha_in_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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) = d\dx n_alpha(r_i,istate)
one_e_dm_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate)
one_e_dm_and_grad_alpha_in_r(3,i,i_state) = d\dz 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) = d\dx n_alpha(r_i,istate)^2 + d\dy n_alpha(r_i,istate)^2 + d\dz n_alpha(r_i,istate)^2
where r_i is the ith point of the grid and istate is the state number
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_pbe_w`
* :c:data:`aos_sr_vxc_alpha_pbe_w`
* :c:data:`aos_vc_alpha_pbe_w`
* :c:data:`aos_vxc_alpha_pbe_w`
* :c:data:`energy_c_pbe`
* :c:data:`energy_sr_x_pbe`
* :c:data:`energy_x_pbe`
* :c:data:`energy_x_sr_pbe`
.. c:var:: one_e_dm_and_grad_beta_in_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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) = d\dx n_alpha(r_i,istate)
one_e_dm_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate)
one_e_dm_and_grad_alpha_in_r(3,i,i_state) = d\dz 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) = d\dx n_alpha(r_i,istate)^2 + d\dy n_alpha(r_i,istate)^2 + d\dz n_alpha(r_i,istate)^2
where r_i is the ith point of the grid and istate is the state number
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_pbe_w`
* :c:data:`aos_sr_vxc_alpha_pbe_w`
* :c:data:`aos_vc_alpha_pbe_w`
* :c:data:`aos_vxc_alpha_pbe_w`
* :c:data:`energy_c_pbe`
* :c:data:`energy_sr_x_pbe`
* :c:data:`energy_x_pbe`
* :c:data:`energy_x_sr_pbe`
.. c:var:: one_e_dm_beta_at_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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)
double precision, allocatable :: elec_beta_num_grid_becke (N_states)
double precision, allocatable :: elec_alpha_num_grid_becke (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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_lda_w`
* :c:data:`aos_sr_vxc_alpha_lda_w`
* :c:data:`aos_vc_alpha_lda_w`
* :c:data:`aos_vxc_alpha_lda_w`
* :c:data:`energy_c_lda`
* :c:data:`energy_c_sr_lda`
* :c:data:`energy_sr_x_lda`
* :c:data:`energy_x_lda`
* :c:data:`energy_x_sr_lda`
.. c:var:: one_e_dm_beta_in_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`grid_points_per_atom`
* :c:data:`mo_num`
* :c:data:`n_points_radial_grid`
* :c:data:`n_states`
* :c:data:`nucl_num`
* :c:data:`one_e_dm_alpha_ao_for_dft`
.. c:var:: one_e_dm_no_core_and_grad_alpha_in_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
double precision, allocatable :: one_e_dm_no_core_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
double precision, allocatable :: one_e_dm_no_core_and_grad_beta_in_r (4,n_points_final_grid,N_states)
one_e_dm_no_core_and_grad_alpha_in_r(1,i,i_state) = d\dx n_alpha(r_i,istate) without core orbitals
one_e_dm_no_core_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate) without core orbitals
one_e_dm_no_core_and_grad_alpha_in_r(3,i,i_state) = d\dz n_alpha(r_i,istate) without core orbitals
one_e_dm_no_core_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) without core orbitals
where r_i is the ith point of the grid and istate is the state number
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft_no_core`
.. c:var:: one_e_dm_no_core_and_grad_beta_in_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
double precision, allocatable :: one_e_dm_no_core_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
double precision, allocatable :: one_e_dm_no_core_and_grad_beta_in_r (4,n_points_final_grid,N_states)
one_e_dm_no_core_and_grad_alpha_in_r(1,i,i_state) = d\dx n_alpha(r_i,istate) without core orbitals
one_e_dm_no_core_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate) without core orbitals
one_e_dm_no_core_and_grad_alpha_in_r(3,i,i_state) = d\dz n_alpha(r_i,istate) without core orbitals
one_e_dm_no_core_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) without core orbitals
where r_i is the ith point of the grid and istate is the state number
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft_no_core`
.. c:var:: one_e_grad_2_dm_alpha_at_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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) = d\dx n_alpha(r_i,istate)
one_e_dm_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate)
one_e_dm_and_grad_alpha_in_r(3,i,i_state) = d\dz 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) = d\dx n_alpha(r_i,istate)^2 + d\dy n_alpha(r_i,istate)^2 + d\dz n_alpha(r_i,istate)^2
where r_i is the ith point of the grid and istate is the state number
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_pbe_w`
* :c:data:`aos_sr_vxc_alpha_pbe_w`
* :c:data:`aos_vc_alpha_pbe_w`
* :c:data:`aos_vxc_alpha_pbe_w`
* :c:data:`energy_c_pbe`
* :c:data:`energy_sr_x_pbe`
* :c:data:`energy_x_pbe`
* :c:data:`energy_x_sr_pbe`
.. c:var:: one_e_grad_2_dm_beta_at_r
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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) = d\dx n_alpha(r_i,istate)
one_e_dm_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate)
one_e_dm_and_grad_alpha_in_r(3,i,i_state) = d\dz 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) = d\dx n_alpha(r_i,istate)^2 + d\dy n_alpha(r_i,istate)^2 + d\dz n_alpha(r_i,istate)^2
where r_i is the ith point of the grid and istate is the state number
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`final_grid_points`
* :c:data:`n_points_final_grid`
* :c:data:`n_states`
* :c:data:`one_e_dm_alpha_ao_for_dft`
Needed by:
.. hlist::
:columns: 3
* :c:data:`aos_sr_vc_alpha_pbe_w`
* :c:data:`aos_sr_vxc_alpha_pbe_w`
* :c:data:`aos_vc_alpha_pbe_w`
* :c:data:`aos_vxc_alpha_pbe_w`
* :c:data:`energy_c_pbe`
* :c:data:`energy_sr_x_pbe`
* :c:data:`energy_x_pbe`
* :c:data:`energy_x_sr_pbe`
Subroutines / functions
-----------------------
.. c:function:: dens_grad_a_b_no_core_and_aos_grad_aos_at_r:
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
subroutine dens_grad_a_b_no_core_and_aos_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 without the core orbitals
* dm_b = beta density evaluated at r without the core orbitals
* aos_array(i) = ao(i) evaluated at r without the core orbitals
* grad_dm_a(1) = X gradient of the alpha density evaluated in r without the core orbitals
* grad_dm_a(1) = X gradient of the beta density evaluated in r without the core orbitals
* grad_aos_array(1) = X gradient of the aos(i) evaluated at r
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`one_e_dm_alpha_ao_for_dft_no_core`
* :c:data:`n_states`
Called by:
.. hlist::
:columns: 3
* :c:data:`one_e_dm_no_core_and_grad_alpha_in_r`
Calls:
.. hlist::
:columns: 3
* :c:func:`dsymv`
* :c:func:`give_all_aos_and_grad_at_r`
.. c:function:: density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r:
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`one_e_dm_alpha_ao_for_dft`
* :c:data:`n_states`
Called by:
.. hlist::
:columns: 3
* :c:data:`one_e_dm_and_grad_alpha_in_r`
Calls:
.. hlist::
:columns: 3
* :c:func:`dsymv`
* :c:func:`give_all_aos_and_grad_at_r`
.. c:function:: dm_dft_alpha_beta_and_all_aos_at_r:
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`one_e_dm_alpha_ao_for_dft`
* :c:data:`n_states`
Calls:
.. hlist::
:columns: 3
* :c:func:`dsymv`
* :c:func:`give_all_aos_at_r`
.. c:function:: dm_dft_alpha_beta_at_r:
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
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:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`one_e_dm_alpha_ao_for_dft`
* :c:data:`n_states`
Called by:
.. hlist::
:columns: 3
* :c:data:`one_e_dm_alpha_at_r`
* :c:data:`one_e_dm_alpha_in_r`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemv`
* :c:func:`give_all_aos_at_r`
.. c:function:: dm_dft_alpha_beta_no_core_at_r:
File : :file:`dft_utils_in_r/dm_in_r.irp.f`
.. code:: fortran
subroutine dm_dft_alpha_beta_no_core_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) without the core orbitals
output : dm_b = beta density evaluated at r(3) without the core orbitals
Needs:
.. hlist::
:columns: 3
* :c:data:`ao_num`
* :c:data:`one_e_dm_alpha_ao_for_dft_no_core`
* :c:data:`n_states`
Calls:
.. hlist::
:columns: 3
* :c:func:`dgemv`
* :c:func:`give_all_aos_at_r`
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