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.. | ||
angular_extra_grid.irp.f | ||
angular_grid_pts.irp.f | ||
angular.f | ||
atomic_number.irp.f | ||
example.irp.f | ||
extra_grid_vector.irp.f | ||
extra_grid.irp.f | ||
EZFIO.cfg | ||
grid_becke_per_atom.irp.f | ||
grid_becke_vector.irp.f | ||
grid_becke.irp.f | ||
integration_radial.irp.f | ||
list_angular_grid | ||
NEED | ||
README.rst | ||
step_function_becke.irp.f |
==================== 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.