On the Computation of Overlap Integrals

over STOs using Computer Algebra

S. M. Mekelleche1*, H. Dib2, A. Baba-Ahmed1

a Département de Chimie, Faculté des Sciences, Université A. Belkaïd, B.P. 119, Tlemcen, 13000, Algeria

b Département de Mathématiques, Faculté des Sciences, Université A. Belkaïd, B.P. 119, Tlemcen, 13000, Algeria

* Corresponding author. E-mail: sidi_mekelleche@yahoo.fr

Received : 19 July 2004; revised version accepted : 14 April 2005

Abstract

An efficient algorithm for the calculation of two-center overlap integrals over Slater-type Orbitals (STOs) is presented. A general analytical formula is developed by means of the ellipsoidal coordinate method and programmed with Fortran and Mathematica languages. The elaborated programs are tested for a wide range of quantum numbers, scaling parameters, and internuclear distances. The integer arithmetic used in Mathematica software allows obtaining very accurate values of the overlap integrals even for critical regions, particularly, in the case of high quantum numbers and nearly equal scaling parameters. Moreover, the Mathematica code permits to overcome the problem of cancellation errors, which is unavoidable in Fortran programming. The Mathematica program is included and comparisons with other approaches are presented.

Keywords: Overlap integrals; Slater-Type Orbitals; Computer Algebra; Mathematica.

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