Zeroth order regular approximation approach to parity violating nuclear magnetic resonance shielding tensors

In this paper, a quasirelativistic two-component zeroth order regular approximation (ZORA) density functional theory (DFT) approach to the calculation of parity violating (PV) resonance frequency differences between the nuclear magnetic resonance (NMR) spectra of enantiomers is presented and the systematics of PV NMR shielding constants in C(2)-symmetric dihydrogen dichalcogenides (H(2)X(2) with X=(17)O, (33)S, (77)Se, (125)Te, (209)Po) are investigated. The typical sin(2alpha)-like dependence of the PV NMR frequency splittings on the dihedral angle alpha is observed for the entire series. As for the scaling behavior of the effect with the nuclear charge Z of X, the previously reported Z(2.5+/-0.5) scaling in the nonrelativistic limit is reproduced and a scaling of approximately Z(3) for the paramagnetic and Z(5) for the spin-orbit coupling contribution to the frequency splitting is observed in the relativistic framework. The paramagnetic and spin-orbit coupling contributions are typically of opposite sign for the molecular structures studied herein and the maximum scaling of the total ZORA frequency splitting (i.e., the sum of the two contributions) is Z(3.9) for H(2)Po(2). Thus, an earlier claim for a spin-orbit coupling contribution scaling with up to Z(7) for H(2)Po(2) and the erratic dihedral angle dependence obtained for this compound within a four-component Dirac-Hartree-Fock-Coulomb study is not confirmed at the DFT level. The maximum NMR frequency splitting reported here is of the order of 10 mHz for certain clamped conformations of H(2)Po(2) inside a static magnetic field with magnetic flux density of 11.7 T. Frequency splittings of this size have been estimated to be detectable with present day NMR spectrometers. Thus, a NMR route toward molecular PV appears promising once suitable compounds have been identified.