Going beyond the Computational Tool: Fermi Potential from DFT as an Electron (De)Localization Descriptor for Correlated Wave Functions

The Fermi potential, appearing in the basic equations of density functional theory (DFT), has been found to be an indispensable tool for the measurement of electron localization intensity in molecules and crystals. The regions of the most intensive electron localization appear there as negative wells, while the positive barriers of the Fermi potential prevent the electron concentration there to some extent. The shape of the Fermi potential distribution in covalent bonds reflects the bond order, while the structure of its components is able to provide valuable information about the bonding nature, e.g., helping to draw the line between covalent and noncovalent bonds. The accuracy of the Fermi potential's estimates of electron (de)localization stems from the ability of its components to preserve all the main features of the exchange-correlation hole behavior within the one-electron functions, while other popular descriptors can easily fail in this task. Such analysis is not restricted to DFT calculations; when applied to post-Hartree-Fock wave functions, it unravels details of how instantaneous Coulomb correlation prevents the overestimation of electron localization intensity 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.