Relativistic and QED corrections to one-bond indirect nuclear spin–spin couplings in X22+ and X32+ ions (X = Zn, Cd, Hg)

Abstract

The indirect spin–spin coupling tensor, J, between mercury nuclei in systems containing this element can be of the order of a few kHz and one of the largest measured. We analyzed the physics behind the electronic mechanisms that contribute to the one- and two-bond couplings n JHg–Hg ( n = 1, 2). For doing so, we performed calculations for J-couplings in the ionized [Formula: see text] and [Formula: see text] linear molecules ( X = Zn, Cd, Hg) within polarization propagator theory using the random phase approximation and the pure zeroth-order approximation with Dirac–Hartree–Fock and Dirac–Kohn–Sham orbitals, both at four-component and zeroth-order regular approximation levels. We show that the “paramagnetic-like” mechanism contributes more than 99.98% to the total isotropic value of the coupling tensor. By analyzing the molecular and atomic orbitals involved in the total value of the response function, we find that the s-type valence atomic orbitals have a predominant role in the description of the coupling. This fact allows us to develop an effective model from which quantum electrodynamics (QED) effects on J-couplings in the aforementioned ions can be estimated. Those effects were found to be within the interval (0.7; 1.7)% of the total relativistic effect on isotropic one-bond 1 J coupling, though ranging those corrections between the interval (−0.4; −0.2)% in Zn-containing ions, to (−1.2; −0.8)% in Hg-containing ions, of the total isotropic coupling constant in the studied systems. The estimated QED corrections show a visible dependence on the nuclear charge Z of each atom X in the form of a power-law proportional to [Formula: see text].