JRAF.jl

This is a package for computation of relativistic molecular auxiliary functions
Author abagciphys
Github
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5 Stars
Updated Last
9 Months Ago
Started In
February 2021

JRAF

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This is a package for calculation of relativistic molecular auxiliary functions derived in a paper Phys Rev E 91:023303, 2015) by Bagci and Hoggan. These auxiliary functions provide efficient computation of integrals arising at the self-consistent field level for molecules using Slater-type bases with non-integer principal quantum numbers. It applies both in relativistic and non-relativistic electronic structure theory. Highly accurate results can be achieved for these auxiliary functions via the procedure described in papers:

  • Rendiconti Lincei. Scienze Fisiche e Naturali volume 29, pages191–197(2018) A. Bagci, P. E. Hoggan
  • Rendiconti Lincei. Scienze Fisiche e Naturali volume 29, pages765–775(2018) A. Bagci, P. E. Hoggam and M. Adak
  • Rendiconti Lincei. Scienze Fisiche e Naturali volume 31, pages1089–1103(2020) A. Bagci, P. E. Hoggan,
    and using Nemo Package developed by William Hart, Tommy Hofmann, Claus Fieker, Fredrik Johansson.
The JRAF package inludes a "math.jl" file. In this file the basic mathematical functions are defined with the notation used by Mathematica. It is written for those familiar with the Mathematica programming language.
For accuracy, both arbitrary-precision floating-point ball arithmetic which supports real and complex numbers and the MPFR library are used.

The list of special functions such as Legendre, Laguerre polynomials, spherical harmonics, spherical spinors, rotated-angular functions, hypergeometric functions ect. defined in the package can be found in "special_functions.jl" file. The mathematica notation is used for the definition of these functions too.

The radial part of Slater-type orbitals and Slater-type spinor orbitals can be found in "radial_coefficients.jl".

See "angular_coefficients.jl" file for the angular momentum coefficients related with product of two spherical harmonics located on different centers, the Clebsch-Gordan and Gaunt coefficients.

See "gaux_p12_bsrep.jl", "gaux_p123_bsrep.jl", "gaux_p123_rec.jl" and "cgaux_p123_num.jl" files finally for the details on the analytical and numerical evaluation through "Cuba" multidimensional numerical integration library for relativistic molecular auxiliary functions, respectively. The numerical integration approximation is just for comparison. Highly accurate calculation is possible for now only via the analytical method.

In the JRAF package we focused on computation of the non-relativsitic two-center one-electron overlap, nuclear attraction and kinetic energy integrals over the real spherical harmonics at the present. The details are in "sto_mol_integ_one_elect.jl". file.

The JRAF package will be updated periodically.

The documentation will be available soon.

Installation

The Legendre.jl package that used for tests must be installed separately.

Install the Nemo and JRAF packages via package manager as,

using Pkg
Pkg.add(path="https://github.com/Nemocas/Nemo.jl.git")
Pkg.add(path="https://github.com/abagciphys/JRAF.jl.git")