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73 lines
3.5 KiB
ReStructuredText
73 lines
3.5 KiB
ReStructuredText
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====================
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becke_numerical_grid
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====================
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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.
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This grid is built as the reunion of a spherical grid around each atom. Each spherical grid contains
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a certain number of radial and angular points. No pruning is done on the angular part of the grid.
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The main keyword for that module is:
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* :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`.
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The main providers of that module are:
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* `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.
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* `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.
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* `final_grid_points` which are the (x,y,z) coordinates of the grid points.
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* `final_weight_at_r_vector` which are the weights at each grid point
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For a simple example of how to use the grid, see :file:`example.irp.f`.
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The spherical integration uses Lebedev-Laikov grids, which was used from the code distributed through CCL (http://www.ccl.net/).
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See next section for explanations and citation policies.
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.. code-block:: text
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This subroutine is part of a set of subroutines that generate
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Lebedev grids [1-6] for integration on a sphere. The original
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C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
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translated into fortran by Dr. Christoph van Wuellen.
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This subroutine was translated using a C to fortran77 conversion
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tool written by Dr. Christoph van Wuellen.
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Users of this code are asked to include reference [1] in their
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publications, and in the user- and programmers-manuals
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describing their codes.
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This code was distributed through CCL (http://www.ccl.net/).
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[1] V.I. Lebedev, and D.N. Laikov
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"A quadrature formula for the sphere of the 131st
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algebraic order of accuracy"
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Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
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[2] V.I. Lebedev
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"A quadrature formula for the sphere of 59th algebraic
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order of accuracy"
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Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
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[3] V.I. Lebedev, and A.L. Skorokhodov
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"Quadrature formulas of orders 41, 47, and 53 for the sphere"
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Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
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[4] V.I. Lebedev
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"Spherical quadrature formulas exact to orders 25-29"
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Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
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[5] V.I. Lebedev
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"Quadratures on a sphere"
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Computational Mathematics and Mathematical Physics, Vol. 16,
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1976, pp. 10-24.
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[6] V.I. Lebedev
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"Values of the nodes and weights of ninth to seventeenth
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order Gauss-Markov quadrature formulae invariant under the
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octahedron group with inversion"
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Computational Mathematics and Mathematical Physics, Vol. 15,
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1975, pp. 44-51.
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