Energy Continuity in Degenerate Density Functional Perturbation Theory
  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. 
Mark C. Palenik and Brett I. Dunlap
cond-mat.mtrl-sci physics.chem-ph quant-ph