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

In the paper commented on [J. Chem. Phys. 130 (2009) 144102], Cheng et al. derived a formula for the magnetic dipole shielding constant $σ$ 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.

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