Spin–orbit effects on the molecular properties of Group 14 tetracoordinate compounds TX4 (T = Ge, Sn, and Pb; X = H, F, Cl, Br, and I): Natural electron configuration-based rationalization of structural variations

Abstract

The spin–orbit (SO) effects on the molecular properties of Group 14 tetracoordinate compounds TX4 (T = Ge, Sn, and Pb; X = H, F, Cl, Br, and I) were systematically investigated using two-component spin–orbit density functional theory with the PBE0 and MN15 functionals. The spin–orbit coupling (SOC)-induced changes in the T–X equilibrium bond lengths exhibit a non-monotonic pattern across the 15 TX4 compounds, governed by the competition between central-atom p1/2 contraction and ligand p3/2 elongation. The natural electron configuration-based spinor occupation inference (NSOI) framework, extended from diatomic to polyatomic systems, accounts for all observed structural variations, including the counterintuitive enhancement of bond contraction from TF4 to TCl4 and the crossover from contraction to elongation in PbI4. For the TX2 series, the NSOI framework consistently rationalizes not only the SOC-induced bond length changes but also the bond angle changes, which are interpreted as secondary geometric consequences of changes in bond lengths and X–X interactions. The robustness of the NSOI approach was confirmed with the MN15 functional. The reaction energies for TX4 → TX2 + X2 decrease systematically from Ge to Pb, consistent with the inert-pair effect. Time-dependent density functional theory calculations reveal that SOC activates singlet–triplet mixing, transforming the UV–Vis absorption spectra of heavy-atom TX4 and providing theoretical reference data for experimentally elusive species such as PbX4. In contrast to the structural SO effects, which are attenuated by partial cancellation between central-atom and ligand contributions, the spectral SO effects are more pronounced because singlet–triplet mixing introduces absorption features absent in the scalar-relativistic spectra.