One-Center Nonrelativistic Integrals of Second Order for the NMR Shielding Tensor

TL;DR

This paper develops analytical formulas for one-center second-order nonrelativistic integrals related to NMR shielding tensors, addressing computational challenges posed by the $r^{-3}$ operator.

Contribution

It introduces compact, accurate analytical formulas for complex integrals crucial in NMR shielding tensor calculations, using Fourier transform formalism.

Findings

Formulas are computationally convenient.

Results can be computed to machine accuracy.

Addresses the difficulty of $r^{-3}$ operator in integrals.

Abstract

This work presents the analytical development of one-center nonrelativistic integrals of second order for the NMR (nuclear magnetic resonance) shielding tensor. The main difficulty in the analytical and numerical treatments of these integrals arise from the presence of $r^{-3}$ in the operator. Compact analytical formulae are obtained using the Fourier transform formalism. Moreover, the obtained formulae are computationally convenient and can be computed to machine accuracy.