Bonding and antibonding characters of the first order reduced density matrix. A new look at two charge-shift bonds.

This article presents a novel approach to chemical bond analysis using the gradient of the first-order reduced density matrix (1-RDM) map, which partitions bonds into atomic core, valence, and dorsal regions with bonding or antibonding characterizations linked to molecular orbital concepts. Applying this method to various diatomic molecules and the charge-shift bonds in F₂ and the bridge bond of [1.1.1] propellane reveals distinct bonding features undetected by traditional density-based or valence bond theories, such as local interference critical points (LICPs) that indicate complex orbital interactions. The study demonstrates that bonding and antibonding interactions arise from multiple atomic regions, including the area behind nuclei, and that the gradient of the 1-RDM provides a detailed, phase-sensitive visualization of these interactions. This approach offers a valuable complement to existing bonding analyses by capturing qualitative distinctions in chemical bonds that other methods do not reveal.