On the importance of relativistic corrections to the vibrational averaging of molecular properties: A zeroth-order regular approximation study on selected mercury compounds.

Relativistic effects play a crucial role in the accurate prediction of spectroscopic properties of heavy-element compounds, yet their impact on vibrational corrections remains insufficiently explored. In this work, we assess the influence of scalar and spin-orbit relativistic treatments on vibrational corrections to electric field gradients (EFGs), nuclear magnetic resonance (NMR) shielding constants, chemical shifts, and spin-spin coupling constants (SSCCs) for seven mercury(II) compounds: HgCl2, HgBr2, HgI2, Hg(SH)2, H3CHgCl, H3CHgBr, and H3CHgI. Calculations were performed within density functional theory using the BHandHLYP functional for EFGs and PBE0 for NMR parameters, combined with the Zeroth-Order Regular Approximation (ZORA) scalar and spin-orbit relativistic approaches. Vibrational averaging employed the QZ4P basis set primarily, with QZ4P-J used for SSCCs, and additional basis-set tests were carried out for HgCl2. Our results demonstrate that relativistic effects substantially modify vibrational corrections for all investigated properties and that scalar relativistic treatments alone are generally insufficient. While replacing QZ4P with TZ2P for cubic force constants or property derivatives yields only minor absolute deviations, the relative changes can be significant due to the small magnitude of the corrections. The inclusion of zero-point vibrational effects at the spin-orbit ZORA level consistently improves agreement with experimental data. Methodological investigations further reveal that accurate numerical derivatives require larger step lengths for these compounds than typically assumed, with an optimal value near 0.5 for HgCl2. Overall, this study highlights the necessity of incorporating spin-orbit relativistic effects in vibrational corrections for heavy-element spectroscopic properties and provides guidance for robust computational protocols.