Formulas and numerical table for the radial part of overlap integrals with the same screening parameters of Slater-type orbitals

Abstract

The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = nR over Slater-type orbitals have been studied and obtained by using three dierent methods. For that purpose, the characteristics of auxiliary functions were used ®rst, then Fourier transform convolution theorem, and recurrence relations for the basic coecients of A s nlk;n H l H k were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 £ n £ 75, 1 £ n¢ £ 75, and 10 )6 £ p.

Fast and stable algorithm for analytical evaluation of two‐center overlap integrals over Slater‐type orbitals with integer and noninteger principal quantum numbers

“…Also, some pilot calculations were placed in Table I to test whether this procedure can be used in translational methods. In spite of the fact that agreements are best with the prior literature, striking results have been obtained with the more recent works of Barnett 3h] and Öztekin et al 23 (Table III). Whereas good agreement is obtained with the values of Barnett and Öztekin et al for low quantum numbers, such as n , n ′ < 55, some discrepancies occurred with the values of Öztekin et al for very high quantum numbers.…”

Closed formulae for (1s|1s), Slater two‐center integrals, using the three‐center nuclear attraction integral program in spherical coordinates

“…Elaborate precautions must be taken to delineate the range of validity of each procedure. Similarly, Barnett 7 has shown, using Mathematica, that gross errors have occurred in an overlap integral table given by Oztekin and colleagues 8. The moral is clear: All procedures must be validated by computer algebra.…”