Spin Purity and Spin Mixing in Lanthanide–Cyclooctatetraene Complexes: SO-MCQDPT2 and Axial-Field Analysis

Abstract

Despite strong relativistic effects in organolanthanide systems, the origin and extent of spin-state mixing within the resulting electronic manifolds remain not fully resolved. In this article, we present a systematic analysis of Ln(COT) (Ln = Ce, Pr, Nd; COT = cyclooctatetraene) by mapping second-order spin–orbit multiconfiguration quasi-degenerate perturbation theory (SO-MCQDPT2)-calculated energies onto the Stevens operator formalism. The approximately axial C8v ligand field imposes symmetry constraints that govern spin–orbit interactions. We demonstrate that direct spin mixing is restricted to states sharing the same J and Ω, whereas indirect mixing arises from ligand-field-induced J-mixing followed by spin–orbit coupling. J is the total electronic angular momentum quantum number associated with the lanthanide ion, and Ω is the unsigned projection of J onto the principal molecular C8 symmetry axis. This analysis accounts for the coexistence of spin-pure and spin-mixed states. By combining multiconfigurational relativistic theory with axial-field analysis, this work provides a framework for understanding spin-state character in organometallic f-block systems. The computed results are in close quantitative agreement with available high-resolution spectroscopic measurements.