New development in evaluation of three-center nuclear attraction integrals over Slater type orbitals

TL;DR

This paper introduces a new method for evaluating three-center nuclear attraction integrals over Slater type orbitals using one-range addition theorems, improving convergence and accuracy for molecular calculations.

Contribution

It extends previous methods by applying complete orthonormal sets of exponential type orbitals to evaluate these integrals with enhanced convergence and general applicability.

Findings

Optimal series expansion parameters identified for best convergence.

The method is valid for arbitrary quantum numbers and orbital positions.

Convergence and accuracy confirmed through concrete numerical cases.

Abstract

Three-center nuclear attraction integrals with Slater type orbitals (STOs) appearing in the Hartree-Fock-Roothaan (HFR) equations for molecules are evaluated using one-range addition theorems of STOs obtained from the use of complete orthonormal sets of -exponential type orbitals (-ETOs), where . These integrals are investigated for the determination of the best with respect to the convergence and accuracy of series expansion relations. It is shown that the best values are obtained for . The convergence of three-center nuclear attraction integrals with respect to the indices for is presented. The final results are expressed through the overlap integrals of STOs containing . The hermitian properties of three-center nuclear attraction integrals are also investigated. The algorithm described in this work is valid for the arbitrary values of, and quantum numbers, screening constants and location of orbitals. The convergence and accuracy of series are tested by calculating concrete cases. It should be noted that the theory of three-center nuclear attraction integrals presented in this work is the extension of method described in our previous paper for to the case of (I.I. Guseinov, N. Seckin Gorgun and N. Zaim, Chin. Phys. B 19 (2010) 043101-1-043101-5).