Information Gain from Density-Based Reactivity Theory Reveals Charge-Shift Bonding in Real Space

Charge-shift bonding (CSB), in which stabilization arises primarily from resonance between covalent and ionic structures rather than simple electron sharing, challenges the traditional covalent-ionic paradigm of chemical bonding. However, its identification has so far relied on either the resonance-energy-based analysis within valence bond theory (VBT) or electron-density-based analysis in molecular orbital theory (MOT), with no unified approach that directly connects the two perspectives. Although real-space descriptors such as density topology and the Laplacian provide qualitative connections, a direct quantitative link between resonance energy and electron density remains lacking. Here, we introduce information gain (IG) from density-based reactivity theory of density functional theory (DFT), defined as the Kullback-Leibler divergence between the actual electron density and a reference density, as a real-space descriptor of resonance-driven density reorganization that connects resonance with electron density. Two simple rules emerge. With the pure Lewis covalent density as the reference, negative IG in the bonding region characterizes regular covalent bonds, whereas positive IG signals charge-shift character. More generally, a sign reversal ("flip") of IG upon switching between covalent and ionic reference densities reveals competition between resonance structures and provides the more robust diagnostic of charge-shift bonding. These features are consistently observed across homonuclear, heteronuclear, and geometrically constrained systems, and their evolution with bond length reveals a continuous transition between bonding regimes. IG thus provides a unified real-space measure of chemical bonding, establishing a direct link between resonance in VBT and the density-based descriptor in DFT.