The electron localization function and the chemical interpretation of Fermi orbital descriptors in Fermi–Löwdin self-interaction correction calculations

A set of Fermi orbital descriptors (FODs), representing "semi-classical" electronic positions, is a crucial ingredient in the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method. The FODs are utilized to generate Fermi orbitals, which, in turn, are symmetrically orthogonalized to give the Fermi-Löwdin orbitals employed in FLOSIC calculations. It has been argued, based on empirical evidence, that FODs carry chemical bonding information and that FOD arrangements are reminiscent of electron distributions predicted by Lewis or Linnett theory. Here, we show that there is a formal connection between FODs and critical points of the electron localization function (ELF) and illustrate this fact for several cases where fully relaxed FODs from FLOSIC calculations closely resemble the structure of critical points (CPs). We also propose a new localization function, the SIC-ELF, based on the local mobility of the Fermi orbitals. In certain instances involving double and triple bonds, FLOSIC FODs offer a more precise interpretation of the chemical bonding structure suggested by Lewis theory than ELF or SIC-ELF. We suggest that the connection between FODs and CPs can be exploited to obtain initial FOD configurations for FLOSIC calculations.