Calculation of Arbitrary Overlap Integrals over Slater Type Orbitals Using Basic Overlap Integrals

Abstract

The recurrence relations are presented for the calculation of basic overlap integrals, by making use of which other overlap integrals are calculated analytically. These recurrence relations are especially useful for the calculation of any overlap integral for large quantum numbers. For the arbitrary values of screening constants of atomic orbitals and internuclear distances an accuracy of the computer results is satisfactory for the values of principal quantum numbers of Slater functions up to 50.

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“…Also, by analyzing the function f m (N, N ) it is seen that this function converges at maximum m = 50 for overlap integrals with very high quantum numbers. [11] During calculations, the generalized binomial coefficients, f m (N, N ), and the functions A k and B k are stored in the memory of the computer for the rapid evaluation. The generalized binomial coefficients are put into or got back from the memory using Eq.…”

“…(6) should be equated to zero. [11,14] Recently, we have constructed an algorithm for the evaluation of two-center overlap integrals over STOs and NISTOs in aligned coordinate systems [11] in terms of the well-known auxiliary functions A k (p) and B k (p t), [15,16] as discussed in Appendix, as in the following form.…”

“…In our previous papers, [11] we have given different algorithms for the evaluation of two-center overlap integrals over STOs and NISTOs in aligned coordinate systems. The aim of this study is to evaluate two-center overlap integrals over STOs and NISTOs in unaligned coordinate systems.…”

Symbolic Calculation of Two‐Center Overlap Integrals Over Slater‐Type Orbitals

“…2,3 A va ri ety of ap proaches on the eval u a tion of two-center over lap integrals over STOs ex ists in the lit er a ture, for ex ample, ex pan sion of STOs, 4-8 el lip ti cal co or di nates method, 9 inte gral trans for ma tion meth ods, 10,11 and re cur rence schemes and other meth ods. [12][13][14] It is well known from the lit er a ture that in the cal cu lation of two-center over lap integrals some dis crep an cies oc cur for smaller quan tum num bers, higher quan tum num bers, higher or lower internuclear dis tances and, equal or nearly equal or bital ex po nents. There fore, the sym bolic cal cu la tion of two-center over lap integrals and also other multicenter integrals are needed to com pare with the val ues in the lit er ature.…”

“…Re cently, we have pre sented re cur rence re la tions 13 and a se ries ex pan sion for mula 15 for the eval u a tion of two-center over lap integrals over STOs. In or der to test the ef fi ciency of our re cent work and for mula in the lit er a ture, the sym bolic cal cu la tion of two-center over lap integrals over STOs con stitutes the aim of this work.…”