Calculation of overlap integrals over Slater-type spinor orbitals of arbitrary half-integral spin using auxiliary functions

Abstract

Analytical relations are derived for two-center overlap integrals over the basis set of 2(2s + 1)-component Slater-type spinor orbitals, which can be used for the solution of generalized Dirac equation, introduced by one of the authors, in the linear combination of atomic orbitals approach, where  . These relativistic integrals are reduced to the linear combinations of two-center non-relativistic overlap integrals of scalar Slater-type orbitals. The calculations for non-relativistic overlap integrals are performed with the arbitrary values of quantum numbers, screening constants and the location of orbitals. To obtain more accurate results from the calculations, the well-known auxiliary functions and are used. It is observed that the computer program carrying out these extended calculations, indeed, works without any restrictions and in all ranges of orbital parameters.

Keywords:

• generalized Dirac equation
• Slater-type spinor orbital
• overlap integral
• auxiliary function

Acknowledgments

This work was financially supported by the Research Fund of the Çanakkale Onsekiz Mart University, project numbers: 2010/184.