Identifying a real space measure of charge-shift bonding with probability density analysis

Charge-shift bonds have been hypothesized as a third type of chemical bonds in addition to covalent and ionic bonds. They have first been described with valence bond theory where they are identified by the resonance energy resulting from ionic contributions. While other indicators have been described, a clear real space fingerprint for charge-shift bonding is still lacking. Probability density analysis has been developed as a real space method, allowing chemical bonding to be identified from the many-electron probability density |Ψ|² where the wave function Ψ can be obtained from any quantum chemical method. Recently, barriers of a probability potential, which depends on this density, have proven to be good measures for delocalization and covalent bonding. In this work, we employ many examples to demonstrate that a well-suited measure for charge-shift bonding can be defined within the framework of probability density analysis. This measure correlates well with the charge-shift resonance energy from valence bond theory and thus strongly supports the charge-shift bonding concept. It is, unlike the charge-shift resonance energy, not dependent on a reference state. Moreover, it is independent of the polarity of the bond, suggesting to characterize bonds in molecules by both their polarity and their charge-shift character.