Extension of ligand-field theory to encompass bridged structures. Emphasis on the angular overlap model

The concepts of weak and strong exchange fields are defined as a way of introducing ligand-field theory into problems associated with bridging. Then the molecular orbital angular overlap model (MO-AOM) is used to illuminate the concept of nephelauxetism and contribute to the understanding of the complementarity between charge transfer and electron transfer in bonding and spectroscopy. Charge transfer is associated with orthogonalization, electronic density and diffraction experiments; electron transfer with covalency, transfer of unpaired electron spins and population numbers of predominantly central-ion-localized orbitals. This discussion lends further support to the idea that the chemical concept of oxidation states in ligand-field complexes has an important physical meaning independent from the degree of charge transfer. This is illustrated by a number of chemical examples. It emerges that the MO-AOM has a mutual character in that not only can ligand orbitals be conceived as perturbers of central ion orbitals, but also vice versa. The perturbations are in pairs and have the same values angularly. The importance of the orthogonality of the AOM operators in this context is illustrated. This is also used to extend the MO-AOM to cover nonlinear ligation and bridging. The concept of angular overlap (AO) is given wider scope. The usual chemical distinction between the two limiting cases of bonding, the covalent bond and the heteropolar bond, is exhibited in the model description. The d-electron ligand-field-theory contribution to the problem of bridging emphasizes the usefulness of the concept of the parametrical dq model for this theory. For a bicentric system, for example, the electronic dq⊗dq Hamiltonian of this model can be partitioned into AA and BB parts associated with the individual centers and a part, (AB+BA), associated with the (weak) coupling between the centers and its various symmetry/geometry-determined one-electron pathways, and this partition can be made at the orbital as well as at the dq-state level. The AA and BB parts can then be diagonalized and the (AB+BA) part rediagonalized, so as to follow the associated basis change. One is left with an almost diagonal description in cases of weak exchange coupling.