General degeneracy in density functional perturbation theory

TL;DR

This paper develops a comprehensive perturbation theory for degenerate systems in density functional theory, overcoming limitations of traditional methods by handling open-shell cases without symmetry assumptions, demonstrated on an iron atom example.

Contribution

It introduces a fully general perturbation theory for degenerate systems in Kohn-Sham DFT, applicable to open-shell and symmetry-unrelated degeneracies, expanding the theoretical framework.

Findings

Successfully applied to the iron atom with quadrupole perturbation

Handles both symmetry-required and accidental degeneracies

Provides a new method for perturbation analysis in DFT

Abstract

Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. Herein, we develop the fully general perturbation theory for open-shell, degenerate systems in Kohn-Sham DFT, without assuming the presence of symmetry or equal occupation of degenerate orbitals. To demonstrate the resulting methodology, we apply it to the iron atom in the central field approximation, perturbed by an electric quadrupole. This system was chosen because it displays both symmetry required degeneracy, between the five 3\textit{d} orbitals, as well as accidental degeneracy, between the 3\textit{d} and 4\textit{s} orbitals. The quadrupole potential couples the degenerate 3\textit{d} and 4\textit{s} states, serving as an example of the most general perturbation.