Energy Continuity in Degenerate Density Functional Perturbation Theory

TL;DR

This paper develops a perturbation theory for degenerate states in density functional theory with fractional occupations, linking initial and perturbed states through a differentiable map and analyzing occupation number behavior.

Contribution

It introduces a novel perturbation approach for degenerate density functional theory states using differentiable mappings and explores occupation number behavior in a model system.

Findings

First-order occupation numbers can have counterintuitive signs.

Eigenvalues of the electron-electron interaction Hessian explain occupation number signs.

The theory connects degenerate and perturbed states through energy extremization.

Abstract

Fractional occupation numbers can produce open-shell degeneracy in density functional theory. We develop the corresponding perturbation theory by requiring that a differentiable map connects the initial and perturbed states. The degenerate state connects to a single perturbed state which extremizes, but does not necessarily minimize or maximize, the energy with respect to occupation numbers. Using a system of three electrons in a harmonic oscillator potential, we relate the counterintuitive sign of first-order occupation numbers to eigenvalues of the electron-electron interaction Hessian.