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 of relativistic auxiliary functions in prolate spheroidal coordinates, and has been recently achieved (Bağcı and Hoggan (2015) [14]). This process is used in the solution of the molecular Dirac equation for electrons moving in a Coulomb potential. A series of papers on a method for fully analytical evaluation of relativistic auxiliary functions has been published [2, 3, 4] From the perspective of computational physics, these studies demonstrate how to deal with the integrals of the product of power functions with non−integer exponents and incomplete gamma functions. The computer program package used to calculate these auxiliary functions with high accuracy is presented. It is designed using the Julia programming language and yields highly accurate results for molecular integrals over a wide range of orbital parameters and quantum numbers. Additionally, the program package facilitates the efficient calculation of the angular momentum coefficients that arise from the product of two normalized Legendre functions centered at different atomic positions, and the determination of the rotation angular functions used for both complex and real spherical harmonics. Sample calculations are performed for two−center one−electron integrals over non−integer Slater−type orbitals, and the results prove the robustness of the package.