4.5 Article

A mathematical perspective on density functional perturbation theory

Journal

NONLINEARITY
Volume 27, Issue 9, Pages 1999-2033

Publisher

IOP Publishing Ltd
DOI: 10.1088/0951-7715/27/9/1999

Keywords

density functional theory; perturbation theory; quantum chemistry

Funding

  1. IPAM
  2. ANR

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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.

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