Relation between Electrostatic Charge Density and Spin Hamiltonian Models of Ligand Field in Lanthanide Complexes

Understanding the ligand field interactions in lanthanide-containing magnetic molecular complexes is of paramount importance for understanding their magnetic properties, and simple models for rationalizing their effects are much desired. In this work, the equivalence between electrostatic models, which derive their results from calculating the electrostatic interaction energy of the charge density of the 4f electrons in an electrostatic potential representing the ligands, and the common quantum mechanical effective spin Hamiltonian in the space of the ground J multiplet is formulated in detail. This enables the construction of an electrostatic potential for any given ligand field Hamiltonian and discusses the effects of the ligand field interactions in terms of an interaction of a generalized 4f charge density with the electrostatic potential. Such models often allow for an easier rationalization of the ligand field interactions, and it can be hoped that the results in this work will help us to better understand the effects of ligand field in lanthanide complexes.