mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-08-16 17:28:32 +02:00
73 lines
3.5 KiB
ReStructuredText
73 lines
3.5 KiB
ReStructuredText
|
====================
|
||
|
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` which is the number of angular integration points. WARNING: it obeys to specific rules so it cannot be any integer number. Some of the possible values are [ 50 | 74 | 170 | 194 | 266 | 302 | 590 | 1202 | 2030 | 5810 ] for instance. See :file:`angular.f` for more details.
|
||
|
* `n_points_radial_grid` which is the number of radial angular points. This can be any strictly positive integer. Nevertheless, a minimum of 50 is in general necessary.
|
||
|
* `final_grid_points` which are the (x,y,z) coordinates of the grid points.
|
||
|
* `final_weight_at_r_vector` which are the weights at each grid point
|
||
|
|
||
|
|
||
|
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.
|
||
|
|
||
|
|