Charge-Potential Model of Ligand Field in Lanthanide Complexes in the Single-Electron Space

The ligand field interactions in lanthanide-based magnetic molecular complexes are crucial for their magnetic properties, and simple models for rationalizing the ligand field effects are much desired. In this work, a charge-potential model is formulated in detail, which describes the ligand field interactions as an electrostatic interaction between a generalized single-electron charge density representing the 4f electrons and an electrostatic potential representing the ligands. The model is equivalent to a quantum mechanical effective spin Hamiltonian in the space of the electron f orbitals. Furthermore, the relation with the generalized many-electron charge density and familiar effective spin Hamiltonian in the space of the ground J multiplet is discussed. This permits us to translate the results of any model of the ligand field splittings in the J multiplet, which includes high-level ab initio techniques, into the single-electron domain, and vice versa. Models based on f orbitals are often well suited for rationalization, and it can be hoped that the results in this work will help us better understand the effects of ligand field in lanthanide complexes.