The angular overlap model of the ligand field theory and applications

Abstract

The Angular Overlap Model, AOM, is historically reviewed. Solid and surface harmonics are discussed in relation to the model and chosen as real basis functions for the two-dimensional as well as the three-dimensional rotation group. The concepts of angular overlap integrals and group angular overlap integrals are described. Further the angular overlap operators and the surface angular overlap operators are developed. The AOM endeavours to parametrize the non-spherical part of the ligand field. The assumptions which are necessary for this parametrization are enumerated by considering it (1) as a perturbation model (2) as an overlap model. The two points of view give identical results, and for linearly ligating ligands the AOM is, in a formal parametrical sense, equivalent to the point charge electrostatic model, when all parameters of both models are taken into account. The expanded radial function model for parametrizing the interelectronic repulsion is discussed and the field strength series described. Finally the two-dimensional spectrochemical series is used as an illustration of the application of AOM to experiment. © 1970, Walter de Gruyter. All rights reserved.