Generalized valences and oxidation scores for solids

Classically defined oxidation numbers (in addition to quantum-chemical population analyses) are regularly used to quantify or at least stick to the ionic notion of molecules and solid-state materials. As such, crystalline NaCl is understood as being composed of Na⁺ and Cl^-, without any necessity for quantum-chemical calculation. The convenient accessibility of tools such as wave function-based Mulliken and Löwdin as well as density-based Bader charges, however, paves the way towards understanding far more complex cases, at least in principle. While classical oxidation numbers are derived from likewise classical recipes, i.e., assigning bonding as well as non-bonding electrons to the more electronegative atom, one may do something similar given first-principles local wave functions for molecules and solids, thereby defining a convenient quantum-chemical scheme to arrive at ab initio valences and ab initio oxidation scores. Both concepts are calculated from wave function-based charges and bond orders as provided within the LOBSTER approach transforming plane waves into local-orbital wave functions. The applicability of such ab initio valences and ab initio oxidation scores is demonstrated from a large number of molecular and solid-state examples, and the prospects as well as challenges, both numerically and conceptionally, are critically discussed.