Interpretation and Automatic Generation of Fermi-Orbital Descriptors

We present an interpretation of Fermi-orbital descriptors (FODs) and argue that these descriptors carry chemical bonding information. We show that a bond order derived from these FODs agrees well with reference values, and highlight that optimized FOD positions used within the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) method correspond to expectations from Linnett's double-quartet theory, which is an extension of Lewis theory. This observation is independent of the underlying exchange-correlation functional, which is shown using the local spin density approximation, the Perdew–Burke–Ernzerhof generalized gradient approximation (GGA), and the strongly constrained and appropriately normed meta-GGA. To make FOD positions generally accessible, we propose and discuss four independent methods for the generation of Fermi-orbital descriptors, their implementation as well as their advantages and drawbacks. In particular, we introduce a re-implementation of the electron force field, an approach based on the centers of mass of orbital densities, a Monte Carlo-based algorithm, and a method based on Lewis-like bonding information. All results are summarized with respect to future developments of FLO-SIC and related methods.