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

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.

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References in corpus (2)

• Electron shielding of the nuclear magnetic moment in hydrogen-like atom
• Addendum to "The Dirac-Coulomb Sturmians and the series expansion of the Dirac-Coulomb Green function: application to the relativistic polarizability of the hydrogen-like atom" [J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 825-61, (E) 30 (1997) 2747]

Cited by in corpus (5)

• Magnetic field-induced electric quadrupole moment in the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
• Electric and magnetic dipole shielding constants for the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
• Magnetizabilities of relativistic hydrogenlike atoms in some arbitrary discrete energy eigenstates
• Static electric multipole susceptibilities of the relativistic hydrogen-like atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
• Magnetic-dipole-to-electric-quadrupole cross-susceptibilities for relativistic hydrogenlike atoms in some low-lying discrete energy eigenstates