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It is known that the nuclear-spin-dependent parity-violating contributions tothe NMR shielding and the nuclear spin-rotation tensors (${\bf \sigma}^{PV}$and ${\bf M}^{PV}$, respectively) are formally related each other within thenon-relativistic (NR) regime. Such a formal relationship is not any longervalid within the relativistic domain. A new more general formal relationship,that is valid within the relativistic framework is shown here, being developedthrough the use of the LRESC model. The formalism of polarization propagatorsis applied to write the different contributions to both properties within bothregimes, relativistic and NR. In the relativistic regime the Dirac-CoulombHamiltonian was selected as the unperturbed Hamiltonian. Theoreticaldevelopments 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 closerelationship between the parity-violation contributions to both properties. Inparticular, spin-dependent contributions are the most important in thefour-component calculations of electroweak effects on the isotropic values ofboth tensors, ${\bf \sigma}^{PV}$ and ${\bf M}^{PV}$, being also responsiblefor the breakdown of the previously mentioned NR relationship among them. Thislast relationship is still fulfilled when the scalar-relativistic effects areconsidered.

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