Relativistic relationship between nuclear-spin-dependent parity-violating NMR shielding and nuclear spin-rotation tensors

TL;DR

This paper develops a relativistic formalism linking parity-violating contributions to NMR shielding and spin-rotation tensors, revealing their relationship and the impact of relativistic effects on electroweak properties in molecules.

Contribution

It introduces a new relativistic formal relationship between parity-violating NMR properties using the LRESC model, extending beyond the non-relativistic approximation.

Findings

Relativistic effects alter the relationship between parity-violating NMR tensors.

Spin-dependent contributions dominate in relativistic calculations of electroweak effects.

Scalar-relativistic effects preserve the non-relativistic relationship between the tensors.

Abstract

It is known that the nuclear-spin-dependent parity-violating contributions to the NMR shielding and the nuclear spin-rotation tensors (${\bf \sigma}^{PV}$ and ${\bf M}^{PV}$, respectively) are formally related each other within the non-relativistic (NR) regime. Such a formal relationship is not any longer valid within the relativistic domain. A new more general formal relationship, that is valid within the relativistic framework is shown here, being developed through the use of the LRESC model. The formalism of polarization propagators is applied to write the different contributions to both properties within both regimes, relativistic and NR. In the relativistic regime the Dirac-Coulomb Hamiltonian was selected as the unperturbed Hamiltonian. Theoretical developments together with results of calculations performed on the H$_2X_2$ series of molecules ($X =$ $^{17}$O, $^{33}$S, $^{77}$Se, $^{125}$Te and $^{209}$Po) show that also within the relativistic regime there is a close relationship between the parity-violation contributions to both properties. In particular, spin-dependent contributions are the most important in the four-component calculations of electroweak effects on the isotropic values of both tensors, ${\bf \sigma}^{PV}$ and ${\bf M}^{PV}$, being also responsible for the breakdown of the previously mentioned NR relationship among them. This last relationship is still fulfilled when the scalar-relativistic effects are considered.