Communications in Mathematical Sciences

Volume 14 (2016)

Number 5

Existence of a type of optimal norm-conserving pseudopotentials for Kohn–Sham models

Pages: 1315 – 1352



Eric Cancès (Université Paris-Est, CERMICS, Ecole des Ponts and INRIA, Marne-la-Vallée, France)

Nahia Mourad (Université Paris-Est, CERMICS, Ecole des Ponts, Marne-la-Vallée, France)


In this article, we clarify the mathematical framework underlying the construction of norm-conserving semilocal pseudopotentials for Kohn–Sham models, and prove the existence of optimal pseudopotentials for a family of optimality criteria. Most of our results are proved for the Hartree (also called reduced Hartree–Fock) model, obtained by setting the exchange-correlation energy to zero in the Kohn–Sham energy functional. Extensions to the Kohn–Sham LDA (local density approximation) model are discussed.


density functional theory, self-consistent-field methods, Kohn–Sham model, pseudopotential, perturbation theory

2010 Mathematics Subject Classification

35Q40, 35Q55, 47H14, 81Q15

Published 18 May 2016