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

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.