On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. IV. Use of recurrence relations for basic two‐center overlap and hybrid integrals

Abstract

ABSTRACT:Using expansion formula for the translation of Slater-type orbitals (STOs) obtained with the help of Coulomb Sturmian exponential-type functions (ETFs) (Guseinov, I. I. Int J Quantum Chem 2001, 81, 126) the multicenter electron-repulsion integrals are expressed in terms of the basic overlap integrals with the same screening parameters and the two-center basic hybrid integrals. For the calculation of basic hybrid integrals the recurrence relations are derived. These recurrence relations enable us to calculate some basic hybrid integrals by the use of which other basic integrals are calculated analytically from the formulas in terms of new auxiliary functions introduced recently by the authors. The recurrence relations obtained in this work for basic hybrid integrals are especially useful for the calculation of multicenter electron-repulsion integrals for large quantum numbers of STOs.

On the Exact Evaluation of Intermolecular Electrostatic Interaction Energy in a Molecular Coordinate System

“…The two-center Coulomb integrals occurring in the HFR equations evaluated in this study are defined as follows [48]:…”

“…Hence, fast and accurate analytical evaluations for basic two-center Coulomb integrals are very important in molecular structure calculations. In the literature, there are several calculation methods for basic two-center Coulomb integrals which have allowed other scientists to improve their studies in this field [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. When all the developments and different approximations are considered, the evaluation of the Coulomb interactions becomes more straightforward.…”