Chemical Bonding from the Statistics of the Electron Distribution

An introduction to the theory of chemical bonding from the point of view of the statistics of the electron distribution is presented. When atoms bind to form a molecule, their originally fixed number of electrons ceases to be a well-defined observable, and this implies that their in-the-molecule electron populations fluctuate. If a chemically meaningful definition of an atom in a molecule is assumed, the probabilities of finding a given number of electrons in each of the atoms comprising the molecule can be computed. We show in this review how the complete electron distribution function (EDF) can be used to reconstruct the basic concepts and quantities used in chemical bonding without recourse to the orbital paradigm. From the statistical point of view, which inherits Born's probabilistic interpretation of quantum mechanics, a set of atoms are bonded when their electron populations are mutually dependent. We quantify this statistical dependence by the cumulant moments of the EDF, which provide a consistent description of both two- and multi-center bonding. Particular attention is paid to building EDFs from model wavefunctions. With this, a simple bridge with orbital thinking is built. The statistical interpretation allows to easily classify all possible bonds of a given kind. We show that there are vast unexplored territories that should receive due consideration. Although building EDFs from models is easy and very instructive, the contrary is considerably more difficult. Recipes to extract chemical information from computed EDFs are also reviewed and, in all the cases, simple toy systems are used to show how the methodology works, allowing non-experts to follow easily the presentation.