Interpretation and Automatic Generation of Fermi‐Orbital Descriptors

Abstract

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. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Electronic Structure of Mononuclear Cu-based Molecule from Density-Functional Theory with Self-Interaction Correction

“…Another way is to alternate, such that one C-C bond in the ring has 2 spin-up FODs and 1 spindown FOD, and the next bond has 1 spin-up FOD and 2 spin-down FOD. The latter alternating picture is related to Linnett double-quartet theory and has been shown to achieve slightly lower energy than the former scheme 30 . Therefore, the alternating FOD pattern is used for the ligands.…”

Testing Self‐Interaction Correction for Molecules in Solution

“…Firstly, as the FODs are real-space vectors and it is possible to calculate an analytic FOD gradient, [14,15] the FOD optimization can be conducted with the help of gradientbased algorithms in a procedure that is similar to the optimization of nuclear positions. Second, it has clearly been demonstrated [30,32,33] that the locations of optimized FODs can be interpreted in terms of the semiclassical theories of chemical bonding by Lewis [34] and Linnett. [35][36][37][38][39] Simply put, the number of α-spin and β-spin FODs in a given system is equal to the number of α-spin and β-spin electrons in this system, and counting the optimized FODs that are located between two atoms reveals the respective bond order.…”

“…[35][36][37][38][39] Simply put, the number of α-spin and β-spin FODs in a given system is equal to the number of α-spin and β-spin electrons in this system, and counting the optimized FODs that are located between two atoms reveals the respective bond order. [33] Because concepts such as core electrons and lone electrons are likewise applicable to FOD arrangements, these arrangements can be described as electronic geometries. For further information on the interpretation of FODs, we refer the interested reader to the study by Schwalbe et al, [33] as the FLO-SIC analysis of chemical bonds is not the focus of this work.…”

“…[33] Because concepts such as core electrons and lone electrons are likewise applicable to FOD arrangements, these arrangements can be described as electronic geometries. For further information on the interpretation of FODs, we refer the interested reader to the study by Schwalbe et al, [33] as the FLO-SIC analysis of chemical bonds is not the focus of this work.…”

“…Moreover, the molecular FLO-SIC calculations were performed on electronic geometries corresponding to FOD gradients below 1.5 ⋅ 10 À4 E h =a 0 , which were obtained from an optimization procedure analogous to the one detailed earlier for the nuclear geometries. For this study, initial FOD geometries were generated via a pre-manuscriptpublication version of the fodMC code, a detailed description of which is presented in the study by Schwalbe et al [33] . In the context of this article, it is suffice to say that fodMC generates FODs based on nuclear geometry and bond order input by the user.…”