A mathematical perspective on density functional perturbation theory

Eric Cancès (1, 2) , Nahia Mourad (2)

1 MATHERIALS - MATHematics for MatERIALS
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

In this article, we provide a 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 extended 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 had not been considered so far.

Mots clés: degenerate Fermi level; Wigner (2n+1) rule; fractional occupation number; density functional perturbation theory

Domaines: Physique mathématique [math-ph]

Eric Cancès, Nahia Mourad. A mathematical perspective on density functional perturbation theory. Nonlinearity, 2014, 27 (9), pp.1999-2033. ⟨10.1088/09517715⟩. ⟨hal-00952732v1⟩