An extremely efficient and rapid algorithm for numerical evaluation of three-centre nuclear attraction integrals over Slater-type functions

Abstract

The present work concerns the development of an extremely accurate and rapid algorithm for the numerical evaluation of the three-centre nuclear attraction integrals over Slater-type functions. These integrals are numerous, they occur in many millions of terms, even for small molecules and they require rapid and accurate evaluation. The new algorithm is based on nonlinear transformation methods, on numerical quadrature and on properties of the sine and Bessel functions. The section with numerical results shows the high accuracy and the substantial gain in calculation time realized using the new algorithm. The complete expressions of the three-centre nuclear attraction integrals over B functions and over Slater-type functions are evaluated for different values of the quantum numbers to show the efficiency of the new approach. Numerical results obtained with linear and nonlinear systems and comparisons with numerical results from the literature are listed.