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https://github.com/LCPQ/quantum_package
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482 lines
18 KiB
ReStructuredText
482 lines
18 KiB
ReStructuredText
.. _dft_utils_in_r:
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.. program:: dft_utils_in_r
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.. default-role:: option
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==============
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dft_utils_in_r
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==============
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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.
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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).
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The main providers for this module are:
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* `aos_in_r_array`: values of the |AO| basis on the grid point.
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* `mos_in_r_array`: values of the |MO| basis on the grid point.
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* `one_e_dm_and_grad_alpha_in_r`: values of the density and its gradienst on the grid points.
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Providers
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---------
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.. c:var:: aos_grad_in_r_array
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.. code:: text
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double precision, allocatable :: aos_grad_in_r_array (ao_num,n_points_final_grid,3)
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double precision, allocatable :: aos_grad_in_r_array_transp (n_points_final_grid,ao_num,3)
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File: :file:`ao_in_r.irp.f`
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aos_grad_in_r_array(i,j,k) = value of the kth component of the gradient of ith ao on the jth grid point
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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
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k = 1 : x, k= 2, y, k 3, z
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.. c:var:: aos_grad_in_r_array_transp
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.. code:: text
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double precision, allocatable :: aos_grad_in_r_array (ao_num,n_points_final_grid,3)
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double precision, allocatable :: aos_grad_in_r_array_transp (n_points_final_grid,ao_num,3)
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File: :file:`ao_in_r.irp.f`
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aos_grad_in_r_array(i,j,k) = value of the kth component of the gradient of ith ao on the jth grid point
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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
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k = 1 : x, k= 2, y, k 3, z
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.. c:var:: aos_in_r_array
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.. code:: text
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double precision, allocatable :: aos_in_r_array (ao_num,n_points_final_grid)
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double precision, allocatable :: aos_in_r_array_transp (n_points_final_grid,ao_num)
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File: :file:`ao_in_r.irp.f`
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aos_in_r_array(i,j) = value of the ith ao on the jth grid point
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aos_in_r_array_transp(i,j) = value of the jth ao on the ith grid point
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.. c:var:: aos_in_r_array_transp
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.. code:: text
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double precision, allocatable :: aos_in_r_array (ao_num,n_points_final_grid)
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double precision, allocatable :: aos_in_r_array_transp (n_points_final_grid,ao_num)
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File: :file:`ao_in_r.irp.f`
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aos_in_r_array(i,j) = value of the ith ao on the jth grid point
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aos_in_r_array_transp(i,j) = value of the jth ao on the ith grid point
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.. c:var:: aos_lapl_in_r_array
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.. code:: text
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double precision, allocatable :: aos_lapl_in_r_array (ao_num,n_points_final_grid,3)
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double precision, allocatable :: aos_lapl_in_r_array_transp (n_points_final_grid,ao_num,3)
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File: :file:`ao_in_r.irp.f`
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aos_lapl_in_r_array(i,j,k) = value of the kth component of the laplacian of ith ao on the jth grid point
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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
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k = 1 : x, k= 2, y, k 3, z
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.. c:var:: aos_lapl_in_r_array_transp
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.. code:: text
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double precision, allocatable :: aos_lapl_in_r_array (ao_num,n_points_final_grid,3)
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double precision, allocatable :: aos_lapl_in_r_array_transp (n_points_final_grid,ao_num,3)
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File: :file:`ao_in_r.irp.f`
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aos_lapl_in_r_array(i,j,k) = value of the kth component of the laplacian of ith ao on the jth grid point
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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
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k = 1 : x, k= 2, y, k 3, z
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.. c:var:: mos_grad_in_r_array
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.. code:: text
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double precision, allocatable :: mos_grad_in_r_array (mo_num,n_points_final_grid,3)
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File: :file:`mo_in_r.irp.f`
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mos_grad_in_r_array(i,j,k) = value of the kth component of the gradient of ith mo on the jth grid point
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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
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k = 1 : x, k= 2, y, k 3, z
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.. c:var:: mos_in_r_array
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.. code:: text
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double precision, allocatable :: mos_in_r_array (mo_num,n_points_final_grid)
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double precision, allocatable :: mos_in_r_array_transp (n_points_final_grid,mo_num)
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File: :file:`mo_in_r.irp.f`
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mos_in_r_array(i,j) = value of the ith mo on the jth grid point
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mos_in_r_array_transp(i,j) = value of the jth mo on the ith grid point
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.. c:var:: mos_in_r_array_transp
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.. code:: text
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double precision, allocatable :: mos_in_r_array (mo_num,n_points_final_grid)
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double precision, allocatable :: mos_in_r_array_transp (n_points_final_grid,mo_num)
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File: :file:`mo_in_r.irp.f`
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mos_in_r_array(i,j) = value of the ith mo on the jth grid point
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mos_in_r_array_transp(i,j) = value of the jth mo on the ith grid point
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.. c:var:: mos_lapl_in_r_array
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.. code:: text
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double precision, allocatable :: mos_lapl_in_r_array (mo_num,n_points_final_grid,3)
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File: :file:`mo_in_r.irp.f`
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mos_lapl_in_r_array(i,j,k) = value of the kth component of the laplacian of ith mo on the jth grid point
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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
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k = 1 : x, k= 2, y, k 3, z
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.. c:var:: one_body_dm_alpha_at_r
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.. code:: text
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double precision, allocatable :: one_body_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_body_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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one_body_dm_alpha_at_r(i,istate) = n_alpha(r_i,istate) one_body_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
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.. c:var:: one_body_dm_beta_at_r
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.. code:: text
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double precision, allocatable :: one_body_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_body_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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one_body_dm_alpha_at_r(i,istate) = n_alpha(r_i,istate) one_body_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
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.. c:var:: one_body_grad_2_dm_alpha_at_r
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.. code:: text
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double precision, allocatable :: one_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_dm_and_grad_beta_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_body_grad_2_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_body_grad_2_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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one_dm_and_grad_alpha_in_r(1,i,i_state) = d\dx n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(3,i,i_state) = d\dz n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) one_body_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
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.. c:var:: one_body_grad_2_dm_beta_at_r
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.. code:: text
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double precision, allocatable :: one_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_dm_and_grad_beta_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_body_grad_2_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_body_grad_2_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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one_dm_and_grad_alpha_in_r(1,i,i_state) = d\dx n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(3,i,i_state) = d\dz n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) one_body_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
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.. c:var:: one_dm_alpha_in_r
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.. code:: text
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double precision, allocatable :: one_dm_alpha_in_r (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
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double precision, allocatable :: one_dm_beta_in_r (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
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File: :file:`dm_in_r.irp.f`
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.. c:var:: one_dm_and_grad_alpha_in_r
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.. code:: text
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double precision, allocatable :: one_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_dm_and_grad_beta_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_body_grad_2_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_body_grad_2_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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one_dm_and_grad_alpha_in_r(1,i,i_state) = d\dx n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(3,i,i_state) = d\dz n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) one_body_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
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.. c:var:: one_dm_and_grad_beta_in_r
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.. code:: text
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double precision, allocatable :: one_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_dm_and_grad_beta_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_body_grad_2_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_body_grad_2_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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one_dm_and_grad_alpha_in_r(1,i,i_state) = d\dx n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(2,i,i_state) = d\dy n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(3,i,i_state) = d\dz n_alpha(r_i,istate) one_dm_and_grad_alpha_in_r(4,i,i_state) = n_alpha(r_i,istate) one_body_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
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.. c:var:: one_dm_beta_in_r
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.. code:: text
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double precision, allocatable :: one_dm_alpha_in_r (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
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double precision, allocatable :: one_dm_beta_in_r (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
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File: :file:`dm_in_r.irp.f`
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.. c:var:: one_e_dm_alpha_at_r
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.. code:: text
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double precision, allocatable :: one_e_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_e_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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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
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.. c:var:: one_e_dm_alpha_in_r
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.. code:: text
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double precision, allocatable :: one_e_dm_alpha_in_r (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
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double precision, allocatable :: one_e_dm_beta_in_r (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
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File: :file:`dm_in_r.irp.f`
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.. c:var:: one_e_dm_and_grad_alpha_in_r
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.. code:: text
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double precision, allocatable :: one_e_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_e_dm_and_grad_beta_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_e_grad_2_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_e_grad_2_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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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
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.. c:var:: one_e_dm_and_grad_beta_in_r
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.. code:: text
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double precision, allocatable :: one_e_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_e_dm_and_grad_beta_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_e_grad_2_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_e_grad_2_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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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
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.. c:var:: one_e_dm_beta_at_r
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.. code:: text
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double precision, allocatable :: one_e_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_e_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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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
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.. c:var:: one_e_dm_beta_in_r
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.. code:: text
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double precision, allocatable :: one_e_dm_alpha_in_r (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
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double precision, allocatable :: one_e_dm_beta_in_r (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states)
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File: :file:`dm_in_r.irp.f`
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.. c:var:: one_e_grad_2_dm_alpha_at_r
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.. code:: text
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double precision, allocatable :: one_e_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_e_dm_and_grad_beta_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_e_grad_2_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_e_grad_2_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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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
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.. c:var:: one_e_grad_2_dm_beta_at_r
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.. code:: text
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double precision, allocatable :: one_e_dm_and_grad_alpha_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_e_dm_and_grad_beta_in_r (4,n_points_final_grid,N_states)
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double precision, allocatable :: one_e_grad_2_dm_alpha_at_r (n_points_final_grid,N_states)
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double precision, allocatable :: one_e_grad_2_dm_beta_at_r (n_points_final_grid,N_states)
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File: :file:`dm_in_r.irp.f`
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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
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Subroutines / functions
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-----------------------
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.. c:function:: density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r
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.. code:: text
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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)
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File: :file:`dm_in_r.irp.f`
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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
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.. c:function:: dm_dft_alpha_beta_and_all_aos_at_r
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.. code:: text
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subroutine dm_dft_alpha_beta_and_all_aos_at_r(r,dm_a,dm_b,aos_array)
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File: :file:`dm_in_r.irp.f`
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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
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.. c:function:: dm_dft_alpha_beta_at_r
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.. code:: text
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subroutine dm_dft_alpha_beta_at_r(r,dm_a,dm_b)
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File: :file:`dm_in_r.irp.f`
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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)
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