Link between Spin-Orbit Relativity and Magnetically Induced Current Densities in Heavy-Atom Hydrides: trans-Ligand...

Interactions between individual atoms underpin the structure and behavior of matter. These interactions govern atomic positions and dynamics, as well as the organization of electronsparticularly in the frontier region. Because electrons lie at the core of chemical phenomena, numerous theoretical frameworks have been developed to rationalize the molecular structure and properties. Electronic motion within molecules and the resulting induced currents provide powerful probes of the molecular or supramolecular structure, building on and going beyond molecular orbital and valence bond theories. In particular, current density offers a spatially-resolved description of the electronic response to external perturbations, enabling direct analysis of electron delocalization and magnetic response in molecular systems. In this work, the effect of relativistic spin-orbit (SO) coupling on the strength and topology of the magnetically induced current density (MICD) is analyzed in depth for a series of model heavy-atom hydrides at the four-component Dirac-Kohn-Sham level. For the most simple molecules, TlH, HAt, and AuH, we demonstrate a connection between the SO effects on the molecular geometry, strength and topology of MICDs, and ligand ¹H NMR shielding. For model HMX molecules, where M = Au^I, Hg^II; X = F, Cl, Ph, CH₃, H, SiH₃, BH₂, the hydride deshielding due to the slight elongation of the M-H bond upon increasing the trans-ligand influence (TLI) of X is shown to be marginal when compared to that originating from the electronic SO effect. In particular, the inclusion of SO effects gives rise to highly localized paratropic MICD vortices on the hydride position of those complexes bearing strong TLI ligands. Our results disprove the previously proposed governing role of the current around the metal atom (similar to the classical Buckingham-Stephens model for transition metal hydrides) associated with TLI-induced variations in the metal-hydrogen bond length in determining the characteristic ligand ¹H NMR shifts.