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* fixed laplacian of aos * corrected the laplacians of aos * added dft_one_e * added new feature for new dft functionals * changed the configure to add new functionals * changed the configure * added dft_one_e/README.rst * added README.rst in new_functionals * added source/programmers_guide/new_ks.rst * Thesis Yann * Added gmp installation in configure * improved qp_e_conv_fci * Doc * Typos * Added variance_max * Fixed completion in qp_create * modif TODO * fixed DFT potential for n_states gt 1 * improved pot pbe * trying to improve sr PBE * fixed potential pbe * fixed the vxc smashed for pbe sr and normal * Comments in selection * bug fixed by peter * Fixed bug with zero beta electrons * Update README.rst * Update e_xc_new_func.irp.f * Update links.rst * Update quickstart.rst * Update quickstart.rst * updated cipsi * Fixed energies of non-expected s2 (#9) * Moved diag_algorithm in Davdison * Add print_ci_vector in tools (#11) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Merge develop-toto and manus (#12) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Frozen core for heavy atoms * Improved molden module * In sync with manus * Fixed some of the documentation errors * Develop toto (#13) * Fixed energies of non-expected s2 * Moved diag_algorithm in Davdison * Fixed travis * Added print_ci_vector * Documentation * Cleaned qp_set_mo_class.ml * Removed Core in taskserver * Frozen core for heavy atoms * Improved molden module * In sync with manus * Fixed some of the documentation errors * Develop manus (#14) * modified printing for rpt2 * Comment * Fixed plugins * Scripting for functionals * Documentation * Develop (#10) * fixed laplacian of aos * corrected the laplacians of aos * added dft_one_e * added new feature for new dft functionals * changed the configure to add new functionals * changed the configure * added dft_one_e/README.rst * added README.rst in new_functionals * added source/programmers_guide/new_ks.rst * Thesis Yann * Added gmp installation in configure * improved qp_e_conv_fci * Doc * Typos * Added variance_max * Fixed completion in qp_create * modif TODO * fixed DFT potential for n_states gt 1 * improved pot pbe * trying to improve sr PBE * fixed potential pbe * fixed the vxc smashed for pbe sr and normal * Comments in selection * bug fixed by peter * Fixed bug with zero beta electrons * Update README.rst * Update e_xc_new_func.irp.f * Update links.rst * Update quickstart.rst * Update quickstart.rst * updated cipsi * Fixed energies of non-expected s2 (#9) * Moved diag_algorithm in Davdison * some modifs * modified gfortran_debug.cfg * fixed automatization of functionals * modified e_xc_general.irp.f * minor modifs in ref_bitmask.irp.f * modifying functionals * rs_ks_scf and ks_scf compiles with the automatic handling of functionals * removed prints * fixed configure * fixed the new functionals * Merge toto * modified automatic functionals * Changed python into python2 * from_xyz suppressed * Cleaning repo * Update README.md * Update README.md * Contributors * Update GITHUB.md * bibtex
901 lines
24 KiB
ReStructuredText
901 lines
24 KiB
ReStructuredText
.. _module_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 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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EZFIO parameters
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----------------
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.. option:: grid_type_sgn
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Type of grid used for the Becke's numerical grid. Can be, by increasing accuracy: [ 0 | 1 | 2 | 3 ]
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Default: 2
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.. option:: n_points_final_grid
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Total number of grid points
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Providers
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---------
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.. c:var:: alpha_knowles
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File : :file:`becke_numerical_grid/integration_radial.irp.f`
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.. code:: fortran
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double precision, allocatable :: alpha_knowles (100)
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Recommended values for the alpha parameters according to the paper of Knowles (JCP, 104, 1996)
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as a function of the nuclear charge
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`final_weight_at_r`
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* :c:data:`grid_points_per_atom`
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.. c:var:: angular_quadrature_points
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File : :file:`becke_numerical_grid/grid_becke.irp.f`
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.. code:: fortran
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double precision, allocatable :: angular_quadrature_points (n_points_integration_angular,3)
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double precision, allocatable :: weights_angular_points (n_points_integration_angular)
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weights and grid points for the integration on the angular variables on
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the unit sphere centered on (0,0,0)
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According to the LEBEDEV scheme
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_points_radial_grid`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`final_weight_at_r`
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* :c:data:`grid_points_per_atom`
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.. c:var:: dr_radial_integral
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File : :file:`becke_numerical_grid/grid_becke.irp.f`
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.. code:: fortran
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double precision, allocatable :: grid_points_radial (n_points_radial_grid)
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double precision :: dr_radial_integral
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points in [0,1] to map the radial integral [0,\infty]
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_points_radial_grid`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`final_weight_at_r`
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* :c:data:`grid_points_per_atom`
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.. c:var:: final_grid_points
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File : :file:`becke_numerical_grid/grid_becke_vector.irp.f`
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.. code:: fortran
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double precision, allocatable :: final_grid_points (3,n_points_final_grid)
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double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
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integer, allocatable :: index_final_points (3,n_points_final_grid)
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integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
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final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
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final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
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index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
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index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`final_weight_at_r`
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* :c:data:`grid_points_per_atom`
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* :c:data:`n_points_final_grid`
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* :c:data:`n_points_radial_grid`
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* :c:data:`nucl_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`aos_grad_in_r_array`
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* :c:data:`aos_grad_in_r_array_transp`
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* :c:data:`aos_grad_in_r_array_transp_xyz`
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* :c:data:`aos_in_r_array`
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* :c:data:`aos_lapl_in_r_array`
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* :c:data:`aos_sr_vc_alpha_lda_w`
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* :c:data:`aos_sr_vc_alpha_pbe_w`
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* :c:data:`aos_sr_vxc_alpha_lda_w`
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* :c:data:`aos_sr_vxc_alpha_pbe_w`
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* :c:data:`aos_vc_alpha_lda_w`
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* :c:data:`aos_vc_alpha_pbe_w`
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* :c:data:`aos_vxc_alpha_lda_w`
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* :c:data:`aos_vxc_alpha_pbe_w`
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* :c:data:`energy_c_lda`
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* :c:data:`energy_c_pbe`
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* :c:data:`energy_c_sr_lda`
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* :c:data:`energy_sr_x_lda`
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* :c:data:`energy_sr_x_pbe`
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* :c:data:`energy_x_lda`
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* :c:data:`energy_x_pbe`
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* :c:data:`energy_x_sr_lda`
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* :c:data:`energy_x_sr_pbe`
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* :c:data:`mos_in_r_array`
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* :c:data:`one_e_dm_alpha_at_r`
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* :c:data:`one_e_dm_and_grad_alpha_in_r`
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.. c:var:: final_weight_at_r
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File : :file:`becke_numerical_grid/grid_becke.irp.f`
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.. code:: fortran
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double precision, allocatable :: final_weight_at_r (n_points_integration_angular,n_points_radial_grid,nucl_num)
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Total weight on each grid point which takes into account all Lebedev, Voronoi and radial weights.
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`alpha_knowles`
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* :c:data:`angular_quadrature_points`
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* :c:data:`grid_points_radial`
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* :c:data:`m_knowles`
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* :c:data:`n_points_radial_grid`
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* :c:data:`nucl_charge`
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* :c:data:`nucl_num`
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* :c:data:`weight_at_r`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`final_grid_points`
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.. c:var:: final_weight_at_r_vector
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File : :file:`becke_numerical_grid/grid_becke_vector.irp.f`
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.. code:: fortran
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double precision, allocatable :: final_grid_points (3,n_points_final_grid)
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double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
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integer, allocatable :: index_final_points (3,n_points_final_grid)
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integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
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final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
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final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
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index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
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index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`final_weight_at_r`
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* :c:data:`grid_points_per_atom`
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* :c:data:`n_points_final_grid`
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* :c:data:`n_points_radial_grid`
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* :c:data:`nucl_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`aos_grad_in_r_array`
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* :c:data:`aos_grad_in_r_array_transp`
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* :c:data:`aos_grad_in_r_array_transp_xyz`
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* :c:data:`aos_in_r_array`
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* :c:data:`aos_lapl_in_r_array`
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* :c:data:`aos_sr_vc_alpha_lda_w`
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* :c:data:`aos_sr_vc_alpha_pbe_w`
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* :c:data:`aos_sr_vxc_alpha_lda_w`
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* :c:data:`aos_sr_vxc_alpha_pbe_w`
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* :c:data:`aos_vc_alpha_lda_w`
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* :c:data:`aos_vc_alpha_pbe_w`
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* :c:data:`aos_vxc_alpha_lda_w`
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* :c:data:`aos_vxc_alpha_pbe_w`
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* :c:data:`energy_c_lda`
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* :c:data:`energy_c_pbe`
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* :c:data:`energy_c_sr_lda`
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* :c:data:`energy_sr_x_lda`
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* :c:data:`energy_sr_x_pbe`
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* :c:data:`energy_x_lda`
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* :c:data:`energy_x_pbe`
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* :c:data:`energy_x_sr_lda`
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* :c:data:`energy_x_sr_pbe`
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* :c:data:`mos_in_r_array`
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* :c:data:`one_e_dm_alpha_at_r`
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* :c:data:`one_e_dm_and_grad_alpha_in_r`
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.. c:var:: grid_points_per_atom
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File : :file:`becke_numerical_grid/grid_becke.irp.f`
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.. code:: fortran
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double precision, allocatable :: grid_points_per_atom (3,n_points_integration_angular,n_points_radial_grid,nucl_num)
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x,y,z coordinates of grid points used for integration in 3d space
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`alpha_knowles`
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* :c:data:`angular_quadrature_points`
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* :c:data:`grid_points_radial`
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* :c:data:`m_knowles`
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* :c:data:`n_points_radial_grid`
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* :c:data:`nucl_charge`
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* :c:data:`nucl_coord`
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* :c:data:`nucl_num`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`final_grid_points`
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* :c:data:`one_e_dm_alpha_in_r`
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* :c:data:`weight_at_r`
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.. c:var:: grid_points_radial
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File : :file:`becke_numerical_grid/grid_becke.irp.f`
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.. code:: fortran
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double precision, allocatable :: grid_points_radial (n_points_radial_grid)
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double precision :: dr_radial_integral
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points in [0,1] to map the radial integral [0,\infty]
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`n_points_radial_grid`
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Needed by:
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.. hlist::
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:columns: 3
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* :c:data:`final_weight_at_r`
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* :c:data:`grid_points_per_atom`
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.. c:var:: index_final_points
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File : :file:`becke_numerical_grid/grid_becke_vector.irp.f`
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.. code:: fortran
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double precision, allocatable :: final_grid_points (3,n_points_final_grid)
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double precision, allocatable :: final_weight_at_r_vector (n_points_final_grid)
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integer, allocatable :: index_final_points (3,n_points_final_grid)
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integer, allocatable :: index_final_points_reverse (n_points_integration_angular,n_points_radial_grid,nucl_num)
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final_grid_points(1:3,j) = (/ x, y, z /) of the jth grid point
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final_weight_at_r_vector(i) = Total weight function of the ith grid point which contains the Lebedev, Voronoi and radial weights contributions
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index_final_points(1:3,i) = gives the angular, radial and atomic indices associated to the ith grid point
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index_final_points_reverse(i,j,k) = index of the grid point having i as angular, j as radial and l as atomic indices
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Needs:
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.. hlist::
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:columns: 3
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* :c:data:`final_weight_at_r`
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* :c:data:`grid_points_per_atom`
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* :c:data:`n_points_final_grid`
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* :c:data:`n_points_radial_grid`
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* :c:data:`nucl_num`
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Needed by:
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.. hlist::
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|
:columns: 3
|
|
|
|
* :c:data:`aos_grad_in_r_array`
|
|
* :c:data:`aos_grad_in_r_array_transp`
|
|
* :c:data:`aos_grad_in_r_array_transp_xyz`
|
|
* :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_vc_alpha_pbe_w`
|
|
* :c:data:`aos_sr_vxc_alpha_lda_w`
|
|
* :c:data:`aos_sr_vxc_alpha_pbe_w`
|
|
* :c:data:`aos_vc_alpha_lda_w`
|
|
* :c:data:`aos_vc_alpha_pbe_w`
|
|
* :c:data:`aos_vxc_alpha_lda_w`
|
|
* :c:data:`aos_vxc_alpha_pbe_w`
|
|
* :c:data:`energy_c_lda`
|
|
* :c:data:`energy_c_pbe`
|
|
* :c:data:`energy_c_sr_lda`
|
|
* :c:data:`energy_sr_x_lda`
|
|
* :c:data:`energy_sr_x_pbe`
|
|
* :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`
|
|
* :c:data:`one_e_dm_alpha_at_r`
|
|
* :c:data:`one_e_dm_and_grad_alpha_in_r`
|
|
|
|
|
|
.. 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`
|
|
|
|
Needed by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`aos_grad_in_r_array`
|
|
* :c:data:`aos_grad_in_r_array_transp`
|
|
* :c:data:`aos_grad_in_r_array_transp_xyz`
|
|
* :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_vc_alpha_pbe_w`
|
|
* :c:data:`aos_sr_vxc_alpha_lda_w`
|
|
* :c:data:`aos_sr_vxc_alpha_pbe_w`
|
|
* :c:data:`aos_vc_alpha_lda_w`
|
|
* :c:data:`aos_vc_alpha_pbe_w`
|
|
* :c:data:`aos_vxc_alpha_lda_w`
|
|
* :c:data:`aos_vxc_alpha_pbe_w`
|
|
* :c:data:`energy_c_lda`
|
|
* :c:data:`energy_c_pbe`
|
|
* :c:data:`energy_c_sr_lda`
|
|
* :c:data:`energy_sr_x_lda`
|
|
* :c:data:`energy_sr_x_pbe`
|
|
* :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`
|
|
* :c:data:`one_e_dm_alpha_at_r`
|
|
* :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
|
|
|
|
* :c:data:`n_points_radial_grid`
|
|
* :c:data:`nucl_num`
|
|
|
|
Needed by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`aos_grad_in_r_array`
|
|
* :c:data:`aos_grad_in_r_array_transp`
|
|
* :c:data:`aos_grad_in_r_array_transp_xyz`
|
|
* :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_vc_alpha_pbe_w`
|
|
* :c:data:`aos_sr_vxc_alpha_lda_w`
|
|
* :c:data:`aos_sr_vxc_alpha_pbe_w`
|
|
* :c:data:`aos_vc_alpha_lda_w`
|
|
* :c:data:`aos_vc_alpha_pbe_w`
|
|
* :c:data:`aos_vxc_alpha_lda_w`
|
|
* :c:data:`aos_vxc_alpha_pbe_w`
|
|
* :c:data:`energy_c_lda`
|
|
* :c:data:`energy_c_pbe`
|
|
* :c:data:`energy_c_sr_lda`
|
|
* :c:data:`energy_sr_x_lda`
|
|
* :c:data:`energy_sr_x_pbe`
|
|
* :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`
|
|
* :c:data:`mos_grad_in_r_array`
|
|
* :c:data:`mos_in_r_array`
|
|
* :c:data:`mos_lapl_in_r_array`
|
|
* :c:data:`one_e_dm_alpha_at_r`
|
|
* :c:data:`one_e_dm_and_grad_alpha_in_r`
|
|
* :c:data:`pot_grad_x_alpha_ao_pbe`
|
|
* :c:data:`pot_grad_xc_alpha_ao_pbe`
|
|
* :c:data:`pot_scal_x_alpha_ao_pbe`
|
|
* :c:data:`pot_scal_xc_alpha_ao_pbe`
|
|
* :c:data:`pot_sr_grad_x_alpha_ao_pbe`
|
|
* :c:data:`pot_sr_grad_xc_alpha_ao_pbe`
|
|
* :c:data:`pot_sr_scal_x_alpha_ao_pbe`
|
|
* :c:data:`pot_sr_scal_xc_alpha_ao_pbe`
|
|
* :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
|
|
|
|
|
|
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
integer :: n_points_grid_per_atom
|
|
|
|
|
|
Number of grid points per atom
|
|
|
|
Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`n_points_radial_grid`
|
|
|
|
|
|
|
|
.. c:var:: n_points_integration_angular
|
|
|
|
|
|
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
integer :: n_points_radial_grid
|
|
integer :: n_points_integration_angular
|
|
|
|
|
|
n_points_radial_grid = number of radial grid points per atom
|
|
|
|
n_points_integration_angular = number of angular grid points per atom
|
|
|
|
These numbers are automatically set by setting the grid_type_sgn parameter
|
|
|
|
Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`grid_type_sgn`
|
|
|
|
Needed by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`angular_quadrature_points`
|
|
* :c:data:`final_grid_points`
|
|
* :c:data:`final_weight_at_r`
|
|
* :c:data:`grid_points_per_atom`
|
|
* :c:data:`grid_points_radial`
|
|
* :c:data:`n_points_final_grid`
|
|
* :c:data:`n_points_grid_per_atom`
|
|
* :c:data:`one_e_dm_alpha_in_r`
|
|
* :c:data:`weight_at_r`
|
|
|
|
|
|
.. c:var:: n_points_radial_grid
|
|
|
|
|
|
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
integer :: n_points_radial_grid
|
|
integer :: n_points_integration_angular
|
|
|
|
|
|
n_points_radial_grid = number of radial grid points per atom
|
|
|
|
n_points_integration_angular = number of angular grid points per atom
|
|
|
|
These numbers are automatically set by setting the grid_type_sgn parameter
|
|
|
|
Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`grid_type_sgn`
|
|
|
|
Needed by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`angular_quadrature_points`
|
|
* :c:data:`final_grid_points`
|
|
* :c:data:`final_weight_at_r`
|
|
* :c:data:`grid_points_per_atom`
|
|
* :c:data:`grid_points_radial`
|
|
* :c:data:`n_points_final_grid`
|
|
* :c:data:`n_points_grid_per_atom`
|
|
* :c:data:`one_e_dm_alpha_in_r`
|
|
* :c:data:`weight_at_r`
|
|
|
|
|
|
.. c:var:: weight_at_r
|
|
|
|
|
|
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision, allocatable :: weight_at_r (n_points_integration_angular,n_points_radial_grid,nucl_num)
|
|
|
|
|
|
Weight function at grid points : w_n(r) according to the equation (22)
|
|
of Becke original paper (JCP, 88, 1988)
|
|
|
|
The "n" discrete variable represents the nucleis which in this array is
|
|
represented by the last dimension and the points are labelled by the
|
|
other dimensions.
|
|
|
|
Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`grid_points_per_atom`
|
|
* :c:data:`n_points_radial_grid`
|
|
* :c:data:`nucl_coord_transp`
|
|
* :c:data:`nucl_dist_inv`
|
|
* :c:data:`nucl_num`
|
|
* :c:data:`slater_bragg_type_inter_distance_ua`
|
|
|
|
Needed by:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`final_weight_at_r`
|
|
|
|
|
|
.. c:var:: weights_angular_points
|
|
|
|
|
|
File : :file:`becke_numerical_grid/grid_becke.irp.f`
|
|
|
|
.. 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`
|
|
|
|
|
|
|
|
Subroutines / functions
|
|
-----------------------
|
|
|
|
.. c:function:: cell_function_becke:
|
|
|
|
|
|
File : :file:`becke_numerical_grid/step_function_becke.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function cell_function_becke(r,atom_number)
|
|
|
|
|
|
atom_number :: atom on which the cell function of Becke (1988, JCP,88(4))
|
|
r(1:3) :: x,y,z coordinantes of the current point
|
|
|
|
Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`nucl_dist_inv`
|
|
* :c:data:`slater_bragg_type_inter_distance_ua`
|
|
* :c:data:`nucl_coord_transp`
|
|
* :c:data:`nucl_num`
|
|
|
|
|
|
.. c:function:: derivative_knowles_function:
|
|
|
|
|
|
File : :file:`becke_numerical_grid/integration_radial.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function derivative_knowles_function(alpha,m,x)
|
|
|
|
|
|
Derivative of the function proposed by Knowles (JCP, 104, 1996) for distributing the radial points
|
|
|
|
|
|
.. c:function:: example_becke_numerical_grid:
|
|
|
|
|
|
File : :file:`becke_numerical_grid/example.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
subroutine example_becke_numerical_grid
|
|
|
|
|
|
subroutine that illustrates the main features available in becke_numerical_grid
|
|
|
|
Needs:
|
|
|
|
.. hlist::
|
|
:columns: 3
|
|
|
|
* :c:data:`n_points_final_grid`
|
|
* :c:data:`final_weight_at_r`
|
|
* :c:data:`n_points_radial_grid`
|
|
* :c:data:`grid_points_per_atom`
|
|
* :c:data:`final_grid_points`
|
|
* :c:data:`nucl_coord`
|
|
* :c:data:`nucl_num`
|
|
|
|
|
|
.. c:function:: f_function_becke:
|
|
|
|
|
|
File : :file:`becke_numerical_grid/step_function_becke.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function f_function_becke(x)
|
|
|
|
|
|
|
|
|
|
.. c:function:: knowles_function:
|
|
|
|
|
|
File : :file:`becke_numerical_grid/integration_radial.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function knowles_function(alpha,m,x)
|
|
|
|
|
|
Function proposed by Knowles (JCP, 104, 1996) for distributing the radial points :
|
|
the Log "m" function ( equation (7) in the paper )
|
|
|
|
|
|
.. c:function:: step_function_becke:
|
|
|
|
|
|
File : :file:`becke_numerical_grid/step_function_becke.irp.f`
|
|
|
|
.. code:: fortran
|
|
|
|
double precision function step_function_becke(x)
|
|
|
|
|
|
Step function of the Becke paper (1988, JCP,88(4))
|
|
|