Quantum-chemical insights into mixed-valence systems: within and beyond the Robin-Day scheme.

In mixed-valence (MV) systems essentially identical, more or less electronically coupled, redox centres are brought into formally different oxidation states by removal or addition of an electron. Depending on the strength of electronic coupling, an electron or a hole is either concentrated on one of the redox centres, or it is symmetrically delocalised onto several sites, or the situation is somewhere in between, which leads to the classification system for MV systems introduced by Melvin Robin and Peter Day. These different characteristics are of fundamental importance for the understanding of electron transfer processes. Applications of quantum-chemical methods to aid the classification and to unravel the nature of the electronic structure and spectroscopic data of both organic and transition-metal MV systems, have gained tremendous importance over the last two decades. In this review, we emphasise the prerequisites the quantum-chemical methods need to fulfill to successfully describe MV systems close to the borderline between Robin-Day classes II and III. These are, in particular, a balanced treatment of exchange, dynamical and non-dynamical correlation effects, as well as consideration of the crucial influence of the (solvent or solid-state) environment on the partial localisation of charge. A large variety of applications of quantum-chemical methods to both organic and inorganic MV systems are critically appraised here in view of these prerequisites. Practical protocols based on a combination of suitable density functional methods with continuum or non-continuum solvent models provided good agreement with experimental data for the ground states and the electronic excitations of a large range of MV systems close to the borderline. Recent applications of such methods have highlighted the crucial importance of conformational effects on electronic coupling, all the way to systems where conformational motion may cause a thermal mixing of class II and class III situations in one system.