Calculation of atomic integrals between relativistic functions by means of algebraic methods

Abstract

We propose the use of Sturmian basis set for relativistic atomic structure calculations. We describe a numerically stable algebraic calculation of one- and two-particle radial integrals. The method is illustrated on the basis set independent calculation of energies, electric dipole moments, hyperfine integrals and parity non-conserving (PNC) amplitude for Cs in Dirac-Hartree-Fock approximation with frozen core orbitals. The previously reported results for electric dipole moments and PNC amplitude are found to be strongly basis dependent. Program summaryProgram title: PASCCPC Library link to program files:https://doi.org/10.17632/xycmhhcr5h.1Licensing provisions: MITProgramming language: Fortran 2008Nature of problem: Precise atomic measurements require reliable and highly accurate atomic structure calculations. Here we deal with the problem of numerical stability of the atomic integrals and basis set independence of the calculations.Solution method: The radial parts of the electronic orbitals are expanded in a discrete Sturmian functions that are eigenfunctions of one of the generators of the so(2,1) Lie algebra. This algebraic structure is used to deduce algebraic relations between the radial parts of the atomic integrals. This leads to numerically stable calculation, which in turn allows to achieve basis set independence.Additional comments including restrictions and unusual features: The method is currently restricted to the Dirac-Hartree-Fock method. However, this limitation will be lifted in future versions, which will be extended with the coupled clusters method.