DFT potentials from a chemical perspective: Anatomy of electron (de)localization in molecules and crystals.

We introduce a fermionic potential, v f $$ {v}_f $$ , as a comprehensive measure of electron (de)localization in atomic-molecular systems. Unlike other common descriptors as ELF, LOL, etc., it characterizes all physical effects responsible for (de)localization of electrons, namely: an exchange hole depth, its tendency to change, a sensitivity of an exchange correlation hidden in a pair density and kinetic potential to local variations in electron density. Wells in the v f $$ {v}_f $$ distribution correspond to the domains of maximum electron localization, while the potential's barriers prevent delocalization of electrons through them. It also estimates bond orders and successfully reveals the impact of chemical modifications or environmental effects on the delocalization of electrons in molecules and crystals. The v f $$ {v}_f $$ components provide a unique opportunity to compare the influence of the mentioned physical effects on electron (de)localization. This merges physical and chemical views of electron delocalization using functions appearing in density functional theory.