New translation method for STOs and its application to calculation of overlap integrals

Abstract

A new translation method for Slater-type orbitals STOs is proposed involving exact translation of the regular solid harmonic part of the orbital followed by the series expansion of the residual spherical part in powers of the radial variable. The method is positively tested in the case of the overlap integral, showing good rate of convergence and great numerical stability under wide changes in the relevant molecular parameters.

International Year of Chemistry— A European Journal

“…In a recent study 3, we have proposed a new translation method for STOs based on the exact translation of the regular solid harmonic part of the orbital 4, 5 followed by the series expansion of the residual spherical part in powers of the radial variable. All many‐center integrals over STOs can be reduced in this way to the calculation of a certain number of one‐center integrals.…”

“…All many‐center integrals over STOs can be reduced in this way to the calculation of a certain number of one‐center integrals. The method was successfully applied to the calculation of the overlap integral, showing remarkable properties of convergence and stability under wide changes in the molecular parameters (orbital exponents and internuclear distances), provided the auxiliary functions entering the radial part of the integral were carefully calculated using both analytical methods and Gaussian integration techniques fully described elsewhere 3.…”

“…After a short review of the basic expansion formulas described in more detail elsewhere 3, we present here (i) the treatment of the angular part of the integration, common to all types of two‐center two‐electron integrals (hybrid, Coulomb, exchange), (ii) the evaluation of the one‐electron one‐center potentials needed for hybrid and Coulomb integrals, (iii) the calculation of the integrals themselves, followed by (iv) a rather extended set of numerical results covering different ranges of internuclear distances and orbital exponents. The appropriate treatment of the auxiliary functions needed in the calculations is fully described in Appendix .…”

On the calculation of arbitrary multielectron molecular integrals over Slater‐type orbitals using recurrence relations for overlap integrals. III. Auxiliary functions \documentclass{article}\pagestyle{empty}\begin{document}$Q_{nn'}^{q}$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$G_{-nn'}^{q}$\end{document}

“…One of the most important methods for the evaluation of multicenter molecular integrals is based upon the use of auxiliary functions. Different approaches, now available for solving multicenter integrals with STOs, have introduced a rather large number of diverse auxiliary functions 1–12. There is a long history, starting with Kotani et al 13, Mulliken et al 14, Barnett and Coulson 15, Roothaan 16, Ruedenberg 17, Löwdin 18, Harris and Mitchel 19, of systematic attempts to obtain accurate and fast evaluations of molecular integrals using auxiliary functions.…”

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

“…It is well known that the difficulties in calculation of multicenter integrals has restricted the use of STOs in molecular quantum mechanics. In the literature there is renewed interest in developing efficient methods for calculation of multicenter integrals by employing STOs as basis set 14–22. In Ref.…”