General two‐electron exponential type orbital integrals in polyatomics without orbital translations

Abstract

ABSTRACT:This article advocates the use of atomic orbitals which have direct physical interpretation, i.e., hydrogen-like orbitals. They are exponential type orbitals (ETOs). Convenient nodeless linear combinations are used, namely Slater type orbitals (STOs) (with a product of a single power of r and an exponential as radial factor). Until 2008, such orbital products on different atoms were difficult to manipulate for the evaluation of two-electron integrals. The difficulty was mostly due to cumbersome orbital translations involving slowly convergent infinite sums. These are completely eliminated using Coulomb resolutions. They provide an excellent approximation that reduces these integrals to a sum of one-electron overlap-like integral products that each involve orbitals on at most two centers. Such two-center integrals are separable in prolate spheroidal coordinates. They are thus readily evaluated. Only these integrals need to be re-evaluated to change basis functions. The above is still valid or three-center integrals. In four-center integrals, the resolutions require translating one potential term per product. This is outlined here and detailed elsewhere. Numerical results are reported for the H 2 dimer and CH 3 F molecule.

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

“…Recent work by Gill has been used to speed up two‐electron, two‐center integral evaluation (regardless of basis) using the resolution of the Coulomb operator 9–11. The same approach is used here to reduce the three‐ and four‐center two‐electron integrals over Slater type orbitals to a sum of products of overlap‐like (one‐electron) integrals that is basically two‐centered.…”

“…A change of basis set requires relatively few simple new evaluations. A modular or object oriented program is being designed to do this more efficiently 11, 17, 18…”

“…Many exponential type functions exist 34. Preferential use of Sturmian and related functions with similar radial nodes is discussed 11…”

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. I. Coulomb and hybrid integrals

“…Gill et al [54,55] introduced the Coulomb resolution techniques where the interaction potential is expanded in terms of the so-called potential functions resulting from the the Poisson equation. This method has been recently pursued by Hoggan and coworkers [56,57] and included in their STOP program package [58].…”

Combining Slater-type orbitals and effective core potentials

“…Interestingly enough, there has been a significant progress on this issue in recent years. In fact, looking at only the past 15 years, there are many notable works of Bouferguene et al [10][11][12][13], Rico et al [14][15][16][17][18][19][20][21][22][23][24], Hoggan et al [25][26][27][28][29][30], Pachucki [31][32][33][34][35], and others [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. In particular, for the diatomic systems STOs can be now used routinely [51].…”