How exponential type orbitals recently became a viable basis set choice in molecular electronic structure work and when to use them

Abstract

This paper advocates the use of the atomic orbitals which have direct physical interpretation, i.e. Coulomb Sturmians and hydrogen-like orbitals. They are exponential type orbitals (ETOs). Their radial nodes are shown to be essential in obtaining accurate nuclear shielding tensors for NMR work. Until 2008, their products on different atoms were difficult to manipulate for the evaluation of two-electron integrals. The difficulty was mostly due to somewhat cumbersome orbital translations involving slowly convergent infinite sums. These are eliminated using Coulomb resolutions. Coulomb resolutions 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 co-ordinates. They are thus readily evaluated. Only these integrals need to be re-evaluated to change basis functions. In this paper, a review of the translation procedures for Slater type orbitals (STO) and for Coulomb Sturmians follows that of the more recent application to ETOs of a particularly convenient Coulomb resolution. © 2009 Springer Science + Business Media B.V.