Degenerate Density Perturbation Theory
  Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system of $N_d$ degenerate electrons in a harmonic oscillator potential. The order-by-order expansions of both the fractional occupation numbers and unitary transformations within the degenerate subspace are determined by the requirement that a differentiable map exists connecting the initial and perturbed states. Using the X$\alpha$ exchange-correlation (XC) functional, we find an analytic solution for the first-order density and first through third-order energies as a function of $\alpha$, with and without a self-interaction correction. The fact that the XC Hessian is not positive definite plays an important role in the behavior of the occupation numbers. 
Mark C. Palenik and Brett I. Dunlap
cond-mat.mtrl-sci physics.chem-ph quant-ph