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.. _module_becke_numerical_grid:
.. program :: becke_numerical_grid
.. default-role :: option
====================
becke_numerical_grid
====================
This module contains all quantities needed to build Becke's grid used in general for DFT integration. Note that it can be used for whatever integration in R^3 as long as the functions to be integrated are mostly concentrated near the atomic regions.
This grid is built as the reunion of a spherical grid around each atom. Each spherical grid contains
a certain number of radial and angular points. No pruning is done on the angular part of the grid.
The main keyword for that module is:
* :option: `becke_numerical_grid grid_type_sgn` which controls the precision of the grid according the standard **SG-n** grids. This keyword controls the two providers `n_points_integration_angular` `n_points_radial_grid`
The main providers of that module are:
* `n_points_integration_angular` :file: `angular.f` for more details.
* `n_points_radial_grid`
* `final_grid_points`
* `final_weight_at_r_vector`
For a simple example of how to use the grid, see :file: `example.irp.f` .
The spherical integration uses Lebedev-Laikov grids, which was used from the code distributed through CCL (http://www.ccl.net/).
See next section for explanations and citation policies.
.. code-block :: text
This subroutine is part of a set of subroutines that generate
Lebedev grids [1-6] for integration on a sphere. The original
C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
translated into fortran by Dr. Christoph van Wuellen.
This subroutine was translated using a C to fortran77 conversion
tool written by Dr. Christoph van Wuellen.
Users of this code are asked to include reference [1] in their
publications, and in the user- and programmers-manuals
describing their codes.
This code was distributed through CCL (http://www.ccl.net/).
[1] V.I. Lebedev, and D.N. Laikov
"A quadrature formula for the sphere of the 131st
algebraic order of accuracy"
Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
[2] V.I. Lebedev
"A quadrature formula for the sphere of 59th algebraic
order of accuracy"
Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
[3] V.I. Lebedev, and A.L. Skorokhodov
"Quadrature formulas of orders 41, 47, and 53 for the sphere"
Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
[4] V.I. Lebedev
"Spherical quadrature formulas exact to orders 25-29"
Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
[5] V.I. Lebedev
"Quadratures on a sphere"
Computational Mathematics and Mathematical Physics, Vol. 16,
1976, pp. 10-24.
[6] V.I. Lebedev
"Values of the nodes and weights of ninth to seventeenth
order Gauss-Markov quadrature formulae invariant under the
octahedron group with inversion"
Computational Mathematics and Mathematical Physics, Vol. 15,
1975, pp. 44-51.
EZFIO parameters
----------------
.. option :: grid_type_sgn
Type of grid used for the Becke's numerical grid. Can be, by increasing accuracy: [ 0 | 1 | 2 | 3 ]
Default: 2
.. option :: n_points_final_grid
Total number of grid points
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.. option :: thresh_grid
threshold on the weight of a given grid point
Default: 1.e-20
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Providers
---------
.. c:var :: alpha_knowles
File : :file: `becke_numerical_grid/integration_radial.irp.f`
.. code :: fortran
double precision, allocatable :: alpha_knowles (100)
Recommended values for the alpha parameters according to the paper of Knowles (JCP, 104, 1996)
as a function of the nuclear charge
Needed by:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
.. c:var :: angular_quadrature_points
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File : :file: `becke_numerical_grid/angular_grid_pts.irp.f`
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.. code :: fortran
double precision, allocatable :: angular_quadrature_points (n_points_integration_angular,3)
double precision, allocatable :: weights_angular_points (n_points_integration_angular)
weights and grid points for the integration on the angular variables on
the unit sphere centered on (0,0,0)
According to the LEBEDEV scheme
Needs:
.. hlist ::
:columns: 3
* :c:data: `n_points_radial_grid`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
.. c:var :: dr_radial_integral
File : :file: `becke_numerical_grid/grid_becke.irp.f`
.. code :: fortran
double precision, allocatable :: grid_points_radial (n_points_radial_grid)
double precision :: dr_radial_integral
points in [0,1] to map the radial integral [0,\infty]
Needs:
.. hlist ::
:columns: 3
* :c:data: `n_points_radial_grid`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
.. c:var :: final_grid_points
File : :file: `becke_numerical_grid/grid_becke_vector.irp.f`
.. code :: fortran
double precision, allocatable :: final_grid_points (3,n_points_final_grid)
double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
integer, allocatable :: index_final_points (3,n_points_final_grid)
integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
Needs:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
* :c:data: `n_points_final_grid`
* :c:data: `n_points_radial_grid`
* :c:data: `nucl_num`
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* :c:data: `thresh_grid`
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Needed by:
.. hlist ::
:columns: 3
* :c:data: `aos_grad_in_r_array`
* :c:data: `aos_in_r_array`
* :c:data: `aos_lapl_in_r_array`
* :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_vc_alpha_pbe_w`
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* :c:data: `aos_vc_alpha_sr_pbe_w`
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* :c:data: `aos_vxc_alpha_lda_w`
* :c:data: `aos_vxc_alpha_pbe_w`
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* :c:data: `aos_vxc_alpha_sr_pbe_w`
* :c:data: `elec_beta_num_grid_becke`
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* :c:data: `energy_c_lda`
* :c:data: `energy_c_sr_lda`
* :c:data: `energy_x_lda`
* :c:data: `energy_x_pbe`
* :c:data: `energy_x_sr_lda`
* :c:data: `energy_x_sr_pbe`
* :c:data: `mos_in_r_array`
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* :c:data: `mos_in_r_array_omp`
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* :c:data: `one_e_dm_and_grad_alpha_in_r`
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.. c:var :: final_grid_points_per_atom
File : :file: `becke_numerical_grid/grid_becke_per_atom.irp.f`
.. code :: fortran
double precision, allocatable :: final_grid_points_per_atom (3,n_pts_max_per_atom,nucl_num)
double precision, allocatable :: final_weight_at_r_vector_per_atom (n_pts_max_per_atom,nucl_num)
integer, allocatable :: index_final_points_per_atom (3,n_pts_max_per_atom,nucl_num)
integer, allocatable :: index_final_points_per_atom_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
Needs:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
* :c:data: `n_points_radial_grid`
* :c:data: `n_pts_per_atom`
* :c:data: `nucl_num`
* :c:data: `thresh_grid`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `aos_in_r_array_per_atom`
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.. c:var :: final_weight_at_r
File : :file: `becke_numerical_grid/grid_becke.irp.f`
.. code :: fortran
double precision, allocatable :: final_weight_at_r (n_points_integration_angular,n_points_radial_grid,nucl_num)
Total weight on each grid point which takes into account all Lebedev, Voronoi and radial weights.
Needs:
.. hlist ::
:columns: 3
* :c:data: `alpha_knowles`
* :c:data: `angular_quadrature_points`
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* :c:data: `grid_atomic_number`
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* :c:data: `grid_points_radial`
* :c:data: `m_knowles`
* :c:data: `n_points_radial_grid`
* :c:data: `nucl_num`
* :c:data: `weight_at_r`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `final_grid_points`
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* :c:data: `final_grid_points_per_atom`
* :c:data: `n_points_final_grid`
* :c:data: `n_pts_per_atom`
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.. c:var :: final_weight_at_r_vector
File : :file: `becke_numerical_grid/grid_becke_vector.irp.f`
.. code :: fortran
double precision, allocatable :: final_grid_points (3,n_points_final_grid)
double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
integer, allocatable :: index_final_points (3,n_points_final_grid)
integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
Needs:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
* :c:data: `n_points_final_grid`
* :c:data: `n_points_radial_grid`
* :c:data: `nucl_num`
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* :c:data: `thresh_grid`
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Needed by:
.. hlist ::
:columns: 3
* :c:data: `aos_grad_in_r_array`
* :c:data: `aos_in_r_array`
* :c:data: `aos_lapl_in_r_array`
* :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_vc_alpha_pbe_w`
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* :c:data: `aos_vc_alpha_sr_pbe_w`
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* :c:data: `aos_vxc_alpha_lda_w`
* :c:data: `aos_vxc_alpha_pbe_w`
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* :c:data: `aos_vxc_alpha_sr_pbe_w`
* :c:data: `elec_beta_num_grid_becke`
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* :c:data: `energy_c_lda`
* :c:data: `energy_c_sr_lda`
* :c:data: `energy_x_lda`
* :c:data: `energy_x_pbe`
* :c:data: `energy_x_sr_lda`
* :c:data: `energy_x_sr_pbe`
* :c:data: `mos_in_r_array`
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* :c:data: `mos_in_r_array_omp`
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* :c:data: `one_e_dm_and_grad_alpha_in_r`
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.. c:var :: final_weight_at_r_vector_per_atom
File : :file: `becke_numerical_grid/grid_becke_per_atom.irp.f`
.. code :: fortran
double precision, allocatable :: final_grid_points_per_atom (3,n_pts_max_per_atom,nucl_num)
double precision, allocatable :: final_weight_at_r_vector_per_atom (n_pts_max_per_atom,nucl_num)
integer, allocatable :: index_final_points_per_atom (3,n_pts_max_per_atom,nucl_num)
integer, allocatable :: index_final_points_per_atom_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
Needs:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
* :c:data: `n_points_radial_grid`
* :c:data: `n_pts_per_atom`
* :c:data: `nucl_num`
* :c:data: `thresh_grid`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `aos_in_r_array_per_atom`
.. c:var :: grid_atomic_number
File : :file: `becke_numerical_grid/atomic_number.irp.f`
.. code :: fortran
integer, allocatable :: grid_atomic_number (nucl_num)
Atomic number used to adjust the grid
Needs:
.. hlist ::
:columns: 3
* :c:data: `nucl_charge`
* :c:data: `nucl_num`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
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.. c:var :: grid_points_per_atom
File : :file: `becke_numerical_grid/grid_becke.irp.f`
.. code :: fortran
double precision, allocatable :: grid_points_per_atom (3,n_points_integration_angular,n_points_radial_grid,nucl_num)
x,y,z coordinates of grid points used for integration in 3d space
Needs:
.. hlist ::
:columns: 3
* :c:data: `alpha_knowles`
* :c:data: `angular_quadrature_points`
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* :c:data: `grid_atomic_number`
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* :c:data: `grid_points_radial`
* :c:data: `m_knowles`
* :c:data: `n_points_radial_grid`
* :c:data: `nucl_coord`
* :c:data: `nucl_num`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `final_grid_points`
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* :c:data: `final_grid_points_per_atom`
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* :c:data: `weight_at_r`
.. c:var :: grid_points_radial
File : :file: `becke_numerical_grid/grid_becke.irp.f`
.. code :: fortran
double precision, allocatable :: grid_points_radial (n_points_radial_grid)
double precision :: dr_radial_integral
points in [0,1] to map the radial integral [0,\infty]
Needs:
.. hlist ::
:columns: 3
* :c:data: `n_points_radial_grid`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
.. c:var :: index_final_points
File : :file: `becke_numerical_grid/grid_becke_vector.irp.f`
.. code :: fortran
double precision, allocatable :: final_grid_points (3,n_points_final_grid)
double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
integer, allocatable :: index_final_points (3,n_points_final_grid)
integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
Needs:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
* :c:data: `n_points_final_grid`
* :c:data: `n_points_radial_grid`
* :c:data: `nucl_num`
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* :c:data: `thresh_grid`
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Needed by:
.. hlist ::
:columns: 3
* :c:data: `aos_grad_in_r_array`
* :c:data: `aos_in_r_array`
* :c:data: `aos_lapl_in_r_array`
* :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_vc_alpha_pbe_w`
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* :c:data: `aos_vc_alpha_sr_pbe_w`
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* :c:data: `aos_vxc_alpha_lda_w`
* :c:data: `aos_vxc_alpha_pbe_w`
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* :c:data: `aos_vxc_alpha_sr_pbe_w`
* :c:data: `elec_beta_num_grid_becke`
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* :c:data: `energy_c_lda`
* :c:data: `energy_c_sr_lda`
* :c:data: `energy_x_lda`
* :c:data: `energy_x_pbe`
* :c:data: `energy_x_sr_lda`
* :c:data: `energy_x_sr_pbe`
* :c:data: `mos_in_r_array`
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* :c:data: `mos_in_r_array_omp`
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* :c:data: `one_e_dm_and_grad_alpha_in_r`
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.. c:var :: index_final_points_per_atom
File : :file: `becke_numerical_grid/grid_becke_per_atom.irp.f`
.. code :: fortran
double precision, allocatable :: final_grid_points_per_atom (3,n_pts_max_per_atom,nucl_num)
double precision, allocatable :: final_weight_at_r_vector_per_atom (n_pts_max_per_atom,nucl_num)
integer, allocatable :: index_final_points_per_atom (3,n_pts_max_per_atom,nucl_num)
integer, allocatable :: index_final_points_per_atom_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
Needs:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
* :c:data: `n_points_radial_grid`
* :c:data: `n_pts_per_atom`
* :c:data: `nucl_num`
* :c:data: `thresh_grid`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `aos_in_r_array_per_atom`
.. c:var :: index_final_points_per_atom_reverse
File : :file: `becke_numerical_grid/grid_becke_per_atom.irp.f`
.. code :: fortran
double precision, allocatable :: final_grid_points_per_atom (3,n_pts_max_per_atom,nucl_num)
double precision, allocatable :: final_weight_at_r_vector_per_atom (n_pts_max_per_atom,nucl_num)
integer, allocatable :: index_final_points_per_atom (3,n_pts_max_per_atom,nucl_num)
integer, allocatable :: index_final_points_per_atom_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
Needs:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
* :c:data: `n_points_radial_grid`
* :c:data: `n_pts_per_atom`
* :c:data: `nucl_num`
* :c:data: `thresh_grid`
Needed by:
.. hlist ::
:columns: 3
* :c:data: `aos_in_r_array_per_atom`
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.. c:var :: index_final_points_reverse
File : :file: `becke_numerical_grid/grid_becke_vector.irp.f`
.. code :: fortran
double precision, allocatable :: final_grid_points (3,n_points_final_grid)
double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
integer, allocatable :: index_final_points (3,n_points_final_grid)
integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
Needs:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
* :c:data: `n_points_final_grid`
* :c:data: `n_points_radial_grid`
* :c:data: `nucl_num`
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* :c:data: `thresh_grid`
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Needed by:
.. hlist ::
:columns: 3
* :c:data: `aos_grad_in_r_array`
* :c:data: `aos_in_r_array`
* :c:data: `aos_lapl_in_r_array`
* :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_vc_alpha_pbe_w`
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* :c:data: `aos_vc_alpha_sr_pbe_w`
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* :c:data: `aos_vxc_alpha_lda_w`
* :c:data: `aos_vxc_alpha_pbe_w`
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* :c:data: `aos_vxc_alpha_sr_pbe_w`
* :c:data: `elec_beta_num_grid_becke`
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* :c:data: `energy_c_lda`
* :c:data: `energy_c_sr_lda`
* :c:data: `energy_x_lda`
* :c:data: `energy_x_pbe`
* :c:data: `energy_x_sr_lda`
* :c:data: `energy_x_sr_pbe`
* :c:data: `mos_in_r_array`
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* :c:data: `mos_in_r_array_omp`
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* :c:data: `one_e_dm_and_grad_alpha_in_r`
.. c:var :: m_knowles
File : :file: `becke_numerical_grid/grid_becke.irp.f`
.. code :: fortran
integer :: m_knowles
value of the "m" parameter in the equation (7) of the paper of Knowles (JCP, 104, 1996)
Needed by:
.. hlist ::
:columns: 3
* :c:data: `final_weight_at_r`
* :c:data: `grid_points_per_atom`
.. c:var :: n_points_final_grid
File : :file: `becke_numerical_grid/grid_becke_vector.irp.f`
.. code :: fortran
integer :: n_points_final_grid
Number of points which are non zero
Needs:
.. hlist ::
:columns: 3
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* :c:data: `final_weight_at_r`
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* :c:data: `n_points_radial_grid`
* :c:data: `nucl_num`
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* :c:data: `thresh_grid`
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Needed by:
.. hlist ::
:columns: 3
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* :c:data: `alpha_dens_kin_in_r`
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* :c:data: `aos_grad_in_r_array`
* :c:data: `aos_grad_in_r_array_transp`
* :c:data: `aos_in_r_array`
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* :c:data: `aos_in_r_array_transp`
2019-03-07 16:29:06 +01:00
* :c:data: `aos_lapl_in_r_array`
2020-12-06 22:58:30 +01:00
* :c:data: `aos_lapl_in_r_array_transp`
2019-03-07 16:29:06 +01:00
* :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_vc_alpha_pbe_w`
2020-12-06 22:58:30 +01:00
* :c:data: `aos_vc_alpha_sr_pbe_w`
2019-03-07 16:29:06 +01:00
* :c:data: `aos_vxc_alpha_lda_w`
* :c:data: `aos_vxc_alpha_pbe_w`
2020-12-06 22:58:30 +01:00
* :c:data: `aos_vxc_alpha_sr_pbe_w`
* :c:data: `elec_beta_num_grid_becke`
2019-03-07 16:29:06 +01:00
* :c:data: `energy_c_lda`
* :c:data: `energy_c_sr_lda`
* :c:data: `energy_x_lda`
* :c:data: `energy_x_pbe`
* :c:data: `energy_x_sr_lda`
* :c:data: `energy_x_sr_pbe`
* :c:data: `final_grid_points`
2020-12-06 22:58:30 +01:00
* :c:data: `kinetic_density_generalized`
2019-03-07 16:29:06 +01:00
* :c:data: `mos_grad_in_r_array`
2020-12-06 22:58:30 +01:00
* :c:data: `mos_grad_in_r_array_tranp`
2019-03-07 16:29:06 +01:00
* :c:data: `mos_in_r_array`
2020-12-06 22:58:30 +01:00
* :c:data: `mos_in_r_array_omp`
* :c:data: `mos_in_r_array_transp`
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* :c:data: `mos_lapl_in_r_array`
* :c:data: `one_e_dm_and_grad_alpha_in_r`
* :c:data: `pot_grad_x_alpha_ao_pbe`
2020-12-06 22:58:30 +01:00
* :c:data: `pot_grad_x_alpha_ao_sr_pbe`
2019-03-07 16:29:06 +01:00
* :c:data: `pot_grad_xc_alpha_ao_pbe`
2020-12-06 22:58:30 +01:00
* :c:data: `pot_grad_xc_alpha_ao_sr_pbe`
2019-03-07 16:29:06 +01:00
* :c:data: `pot_scal_x_alpha_ao_pbe`
2020-12-06 22:58:30 +01:00
* :c:data: `pot_scal_x_alpha_ao_sr_pbe`
2019-03-07 16:29:06 +01:00
* :c:data: `pot_scal_xc_alpha_ao_pbe`
2020-12-06 22:58:30 +01:00
* :c:data: `pot_scal_xc_alpha_ao_sr_pbe`
2019-03-07 16:29:06 +01:00
* :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 :: n_points_grid_per_atom
