JRAF: A Julia package for computation of relativistic molecular auxiliary functions

The evaluation of relativistic molecular integrals over exponential−type spinor orbitals requires the use auxiliary functions in prolate spheroidal coordinates, and has been recently achieved (Bağcı Hoggan (2015) [14]). This process is used solution Dirac equation for electrons moving a Coulomb potential. A series papers on method fully analytical published [2, 3, 4] From perspective computational physics, these studies demonstrate how to deal with product power non−integer exponents incomplete gamma functions. computer program package calculate high accuracy presented. It designed using Julia programming language yields highly accurate results wide range orbital parameters quantum numbers. Additionally, facilitates efficient calculation angular momentum coefficients that arise from two normalized Legendre centered at different atomic positions, determination rotation both complex real spherical harmonics. Sample calculations are performed two−center one−electron Slater−type orbitals, prove robustness package. Program Title: JRAF CPC Library link files: https://doi.org/10.17632/942xsbvfdf.1 Developer's repository link: https://github.com/abagciphys/JRAF.jl Licensing provisions: MIT Programming language: Supplementary material: An experimental version written Mathematica [5]. External routines/libraries: Nemo algebra [6], Cuba multidimensional numerical integration algorithms [7]. Nature problem: Relativistic function result expression two−electron energy associated charge density. transformed into kinetic Poisson's single−center potential, considering Laplace expansion interactions expressed terms [1]. Using resulting integrals, derived ellipsoidal coordinates. These generalized entire set physical potential operators case. integral have no closed−form solutions except their integers. As such, challenging. They matrix form representation Dirac−Fock self−consistent field (SCF) equation. Solution method: criterion considers symmetry properties initially proposed [2]. obviates need computation complementary functions, utilizes sum (P+Q=1). convergent beta Recurrence relationships then each sub−functions [3]. algorithm based vectorization procedure defined [4]. A. Bağcı, P.E. Hoggan, Phys. Rev. E 91 (2) 023303, https://link.aps.org/doi/10.1103/PhysRevE.91.023303. Rend. Fis. Accad. Lincei 29 (1) (2018) 191–197, https://doi.org/10.1007/s12210-018-0669-8. M. Adak, (4) 765–775, https://doi.org/10.1007/s12210-018-0734-3. 31 (2020) 1089–1103, https://doi.org/10.1007/s12210-020-00953-3. https://www.wolfram.com/mathematica/. C. Fieker, W. Hart, T. Hofmann, F. Johansson, in: Proceedings ISSAC '17, New York, ACM, 2017, pp. 157–164. Hahn, Comput. Commun. 176 (11) (2007) 712–713, https://doi.org/10.1016/j.cpc.2007.03.006.