Ligand Field Theory: An ever-modern theory

The Ligand Field (LF) model in molecular science or the Crystal Field model in condensed matter science has been introduced more than eighty years ago. Since then, this theory plays a central role each time that molecules containing d- and/or f-elements with open shells are adressed. No doubt, this fact is related to the dominant localisation of the frontier orbitals within the metal-sphere. This common feature enables us to describe approximately the electronic structure of these molecules using orbitals that are centred on a single atom and to treat their interaction with the chemical environment essentially as a perturbation. Another reason for the success of this simple theory is the fact that the more accurate molecular orbital theory does generally over-estimate covalence of transition metal atoms and thus yields wave functions that are too delocalized.

We give here a survey of the development of LF theory since its introduction simultaneously by Hans Bethe and John Hasbrouck van Vleck more than eighty years ago. Over the years, LF theory was a semi-empirical model with adjustable parameter until the end of last century when we introduced non-empirical LF theory that is based on DFT calculations. The results of this first-principle prediction are in very good agreement with the experimental observations. Sample calculations of tetrahedral and octahedral Cr-complexes and hexa-acquo Ni(II)-complexes are used to validate the new model and to analyse the calculated parameters