The use of Slater-type spinor orbitals in algebraic solution of two-center Dirac equation

TL;DR

This paper explores the application of Slater-type spinor orbitals in solving the two-center Dirac equation, providing a numerical method for accurate relativistic electronic structure calculations of atoms and molecules.

Contribution

It introduces a numerical approach for evaluating two-center integrals over Slater-type spinor orbitals using ellipsoidal coordinates and adaptive integration methods.

Findings

Accurate evaluation of relativistic two-center integrals achieved.

Method applicable to ground and excited states of atoms and molecules.

Results compare favorably with existing literature.

Abstract

The use of Slater-type spinor orbitals in algebraic solution of the Dirac equation is investigated. The one- and two-center integrals constitute the matrix elements arising in generalized eigenvalue equation for one-electron atoms and molecules are evaluated over Slater-type spinor orbitals via ellipsoidal coordinates. These integrals are calculated through numerical global-adaptive method with Gauss-Kronrod numerical integration extension. The calculations are performed for electronic structure of ground and excited states of one-electron atoms and diatomic molecules. The screening constants are allowed to be variationally optimum values for given nuclear separation. The obtained results are compaired with the results those found in the literature. The procedures discussed in this work are capable of yielding highly accurate relativistic two-center one-electron integrals for all ranges of orbital parameters. Besides provides an efficient way to overcome the problems that arise in relativistic calculations.