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83 lines
3.0 KiB
ReStructuredText
.. _becke_numerical_grid:
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.. program:: becke_numerical_grid
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.. default-role:: option
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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 the 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 a certain number of radial and angular points.
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For a simple example of how to use the grid, see 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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EZFIO parameters
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----------------
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.. option:: n_points_integration_angular
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Number of angular points per atom for 3d numerical integration, needed for DFT for example [ 50 | 74 | 266 | 590 | 1202 | 2030 | 5810 ]
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Default: 590
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.. option:: n_points_radial_grid
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Number of radial points per atom for 3d numerical integration, needed for DFT for example
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Default: 60
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