A mathematical perspective on density functional perturbation theory

This article is concerned with the mathematical analysis of the perturbation method for extended Kohn-Sham models, in which fractional occupation numbers are allowed. All our results are established in the framework of the reduced Hartree-Fock (rHF) model, but our approach can be used to study other kinds of Kohn-Sham models, under some assumptions on the mathematical structure of the exchange-correlation functional. The classical results of density functional perturbation theory in the non-degenerate case (that is when the Fermi level is not a degenerate eigenvalue of the mean-field Hamiltonian) are formalized, and a proof of Wigner's (2n+1) rule is provided. We then focus on the situation when the Fermi level is a degenerate eigenvalue of the rHF Hamiltonian, which has not been considered so far.