Numerical Evaluation of Two–Center Overlap Integrals Over Slater–Type Orbitals and Convergence Properties

Motivation. Among the molecular integrals, the two-center overlap integrals play a major role in any accurate molecular structure calculation. They are central to the calculation of multicenter overlap integrals when using the series expansion formulae for Slater type functions about a new center. Consequently, these integrals require an accurate and fast numerical evaluation. Recently, we showed that these integrals are suitable to apply the nonlinear D transformation of Sidi, which is shown to be highly efficient in improving convergence of highly oscillatory integrals. Method. In this work, we present an algorithm for a numerical evaluation of the molecular integrals under consideration over STOs. Convergence properties in the numerical evaluation of these molecular integrals are discussed. It is now shown that the approximation obtained using the nonlinear D transformation converges to the exact value of the integral without any constraint. Results. Numerical results are obtained for two-center overlap integrals over Slater type orbitals with HCN, C2H2, BH3 and CH4 molecules. Comparisons with results obtained using the ACJU code developed by Hommeier et al. are presented. Numerical results from the litterature were also reproduced using the algorithm described in the present work. Conclusions. The results obtained in this work illustrate the efficiency of the algorithm based on the nonlinear D transformation, which will lead to a highly accurate algorithm for the numerical evaluation of the integrals under consideration.