The role of electronic delocalization in transition metal complexes from the electron localization function and the quantum theory of atoms in molecules viewpoints

Electronic delocalization is invoked in many textbooks as the driving force of several fundamental phenomena such as conjugation, hyperconjugation, and aromaticity. These phenomena are important to explain structure, stability, and reactivity not only of classical organic compounds but also of many inorganic, organometallic, and all-metal cluster species. There are a number of available theoretical methods to quantify the electron localization/delocalization in molecules. In this review, we concentrate our efforts in the description of those studies that analyze electron delocalization in transition metal complexes employing the two most widespread techniques to measure delocalization: the electron localization function and the electron sharing indices obtained in the framework of the quantum theory of atoms in molecules. While the former enables the localization of regions in the molecular space where electrons concentrate leading to chemically significant regions such as bonds or lone pairs, the latter provides an atomic subdivision of the molecular space where each atom localizes a certain number of electrons. The joint effort of these techniques has already been proven as one of the most powerful methods to understand the chemical bonding. We show that theoretical studies of electron delocalization improve significantly our understanding of the bonding mechanism, structural properties, and reactivity of transition metal species.