How specific exponential type orbitals recently became a viable basis set choice in NMR shielding tensor calculation

TL;DR

This paper demonstrates that exponential type orbitals, specifically Coulomb Sturmians, are effective and practical basis functions for accurate NMR shielding tensor calculations, with improved evaluation methods for two-electron integrals.

Contribution

It introduces a new basis function choice for NMR calculations and presents efficient evaluation techniques for two-electron integrals using Coulomb resolutions.

Findings

Coulomb Sturmians improve NMR shielding tensor accuracy.

Two-electron integrals are efficiently computed using Coulomb resolutions.

Basis functions are easily adaptable through re-evaluation of two-center integrals.

Abstract

This paper advocates 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. The present work builds on a 2003 French PhD and many numerical results were published by 2007. The improvements in this paper are noteworthy, the key being the actual basis function choice. Until 2008, their products on different atoms were difficult to manipulate for the evaluation of two-electron integrals. 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.