ABSTRACT
The nuclear-spin-dependent parity-violation contributions to the nuclear magnetic resonance shielding and nuclear spin-rotation tensors (σPV and MPV, respectively) are known to be formally related to one another in the non-relativistic regime. In this work, the polarization propagator formalism and the linear response within the elimination of small components model are used to show a new and more general relationship between them, which is valid within the relativistic framework. The full set of the zeroth- and first-order relativistic contributions to σPV and MPV are also given here for the first time, and these results are compared with previous findings. According to four-component relativistic calculations, the electronic spin-orbit effects are the most significant ones for the isotropic values of σPV and MPV in the H2X2 series of molecules (with X = O, S, Se, Te, and Po). When only scalar relativistic effects are taken into account, the non-relativistic relationship between σPV and MPV does hold. However, when the spin-orbit effects are taken into consideration, this old non-relativistic relationship breaks down, and therefore, the new one must be considered.
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 nJHg-Hg (n = 1, 2). For doing so, we performed calculations for J-couplings in the ionized X2 2+ and X3 2+ 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 1J 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 ZX 5.
