Key Role of Point Group Symmetry: g-Factor Anisotropy in the Paramagnetic Two-Center-One-Electron Molecular System

The unique two-center-one-electron (2c-1e) metal-metal bond exhibits unique electronic structure and magnetic properties, giving birth to various candidates in the field of molecular spin devices (MSDs). Experimental characterization, theoretical researches, and device developments for these paramagnetic molecules highly rely on the key parameter of anisotropic Landé g-factor, while the relevance of geometric or electronic structure to g-factor anisotropy has remained unclear yet for species encapsulating such 2c-1e bond (denoted by the symbol {2c-1e}). To remove the barrier to in-depth study and further applications, here we develop a theoretical framework describing the g-factor anisotropy in S = 1/2 {2c-1e} systems. Taking the anion Y2@C80- as exemplar, we integrate theoretical derivations with ab initio computations to elucidate how point group symmetry determines the spin-orbit coupling interactions between electronic states in a {2c-1e} system, thereby consequently governing the anisotropy of the g-factor. On such basis, explicit formulations describing the g-factor anisotropy are derived, on which we conduct mathematical analyses, identifying and summarizing several general rules about the variation patterns of g-tensor. The analytical methodology and the resulting conclusions in this work are universally applicable for various {2c-1e} systems, offering direct guidance for the spectroscopic analysis and supports future development of related MSDs.