Probing electron localization by means of coalescent pairs: A simple DFT-based approach

The Electron Localization Function (ELF) proposed by Becke and Edgecombe is routinely adopted as a simple descriptor of atomic shells and covalent bonds. Its construction entails the information on electrons with parallel spins in single reference states and, thus, it is not a good indicator when dealing with systems as the paradigmatic case of the Hydrogen molecule. The interest in improved descriptors for the localization is also linked to the quest of improving density functional approximations. Here, we show that the ELF can be usefully complemented with the information extracted from opposite-spin correlated electron pairs by means of a procedure which, remarkably, only requires occupied Kohn-Sham orbitals. In addition to the improvements for the exemplary case of the H$_2$ molecule, we show that our approach yields appealing trends in atoms and organic molecules.