Comment on "Four-component relativistic theory for NMR parameters: Unified formulation and numerical assessment of different approaches" [J. Chem. Phys. 130, 144102 (2009)]

TL;DR

This paper simplifies a complex infinite series formula for the magnetic dipole shielding constant in Dirac one-electron atoms into a closed-form expression using elementary functions, enhancing computational efficiency.

Contribution

It provides a simplified, closed-form expression for the magnetic dipole shielding constant, improving upon the original infinite series approach.

Findings

Series can be expressed with elementary functions

Closed-form formula derived for the shielding constant

Simplifies calculations for Dirac one-electron atoms

Abstract

In the paper commented on [J. Chem. Phys. 130 (2009) 144102], Cheng et al. derived a formula for the magnetic dipole shielding constant $\sigma$ for the Dirac one-electron atom in its ground state. That formula involves an infinite series of ratios of the Euler's gamma functions. We show that with some algebra the series may be expressed in terms of elementary functions. This leads to a simple closed-form expression for the shielding constant.