Elena Levina

The Fermi potential, vf, appearing in the basic equations of density functional theory (DFT), has been introduced as a comprehensive measure of electron (de)localization intensity in molecules and crystals. More specifically, it originates from the decomposition of the one-electron potential from the Euler-Lagrange equation for electron density in such a way that all quantum terms reflecting the effects of Fermi-Dirac statistics are enclosed within vf. Therefore, unlike popular descriptors such as ELF or LOL, it condenses all main information about physical effects responsible for (de)localization of electron pairs in one-electron function, simultaneously characterizing the average exchange-correlation hole depth, its tendency to change, and the sensitivity of electron correlation to local variations in electron density. The regions of the most intensive electron localization in atomic-molecular systems appear as negative wells in the vf distribution, while positive barriers mark areas where electron delocalization is hindered to some extent; the highest and widest barriers arise in interatomic and other non-bonded regions. The shape of the vf distribution discriminates between bond types: its domains are approximately cylindrical for single bonds, strongly elongated in the π-plane for double bonds, and torus-shaped for triple bonds. Despite originating from DFT, Fermi potential analysis is not restricted solely to the DFT results. When vf is computed for post-Hartree-Fock wave functions it unravels how the explicit account of instantaneous Coulomb correlation prevents the overestimation of electron localization produced by the exchange-only approximation. While the form of the potential’s domains and their connection with bond type are retained, intensity of electron localization is reduced through different mechanisms in strongly correlated and ordinary systems. Generally, the slight decrease in localization intensity is achieved by the intensified response of electron correlation to variations in electron density, while in systems where instantaneous Coulomb correlation is particularly important, it also comes from the growth in the exchange-correlation hole mobility; the average hole depth increases in all cases.