Convergence properties of the S(D)over-bar transformation and a fast and accurate numerical evaluation of molecular integrals

摘要

The present work concerns the study of the convergence properties of the nonlinear S (D) over bar transformation. A fast and accurate numerical evaluation of highly oscillatory semi-infinite integrals involved in the analytic expressions of molecular integrals over Slater-type orbitals is obtained using the S (D) over bar transformation. These semi-infinite integrals involve spherical and reduced Bessel functions. The convergence properties are analysed and they show that the approximations obtained using the S (D) over bar approach converge to the exact values of the semi-infinite integrals without any constraint. The numerical tables show that the S (D) over bar method gives unprecedented accuracy with speed-up by a factor 2 over the H (D) over bar method and a factor 10 over the (D) over bar transformation. This illustrates the superiority of this new approach. [References: 43]