Ligand-Field and Spin–Orbit Coupling Competition in a Pb−π Model

Abstract

There has been a strong recent interest in the large spin–orbit coupling (SOC), a relativistic effect, in Pb moieties adsorbed on graphene and related 2D materials. Since the SOC mainly originates from the strong nuclear potential of heavy atoms, a conceptually simple approach is adopted to relate the underlying physical/chemical origin of the large spin–orbit splitting to the lead atom’s outermost valence 6p atomic level. To examine this possible origin at the most fundamental level, we investigated a minimal heavy-adatom−π model system consisting of a single Pb atom positioned at various distances above the center of a benzene (C6H6) molecule. In order to analyze the evolution of the electronic structure of this model system, fully relativistic four-component Dirac–Hartree–Fock (4c-DHF) calculations, which took account of the angular momentum coupling of the open shell, Pb 6p, electrons, as well as quasi-relativistic approaches are used. Our results show that the ligand field effects exerted by benzene on the excited states of Pb are comparable in magnitude to the intrinsic 6p SOC of the Pb atom when it is at short distances above the C6H6. Indeed, in this regime, the SOC and ligand-field interactions cannot be cleanly separated. In addition, single-determinant and quasi-relativistic SOC treatments are shown to overestimate the Pb–benzene interaction and the associated SOC transfer to the π system, whereas the inclusion of multiconfigurational effects significantly reduces SOC within the open-shell space. A key result of our findings is that the SOC in heavy-adatom−π systems is not a simple projection of atomic SOC, but rather a consequence of hybridization, which depends critically on the correlated description of the heavy-atom valence shell.