A proximal gradient method for ensemble density functional theory

Michael Ulbrich, Zaiwen Wen, Chao Yang, Dennis Klöckner, Zhaosong Lu

Research output: Contribution to journalReview articlepeer-review

14 Scopus citations


The ensemble density functional theory (E-DFT) is valuable for simulations of metallic systems due to the absence of a gap in the spectrum of the Hamiltonian matrices. Although the widely used self-consistent field (SCF) iteration method can be extended to solve the minimization of the total energy functional with respect to orthogonality constraints, there is no theoretical guarantee on the convergence of these algorithms. In this paper, we consider an equivalent model with a single variable and a single spherical constraint by eliminating the dependence on the fractional occupancies. A proximal gradient method is developed by keeping the entropy term but linearizing all other terms in the total energy functional. Convergence to the stationary point is established. Numerical results using the MATLAB toolbox KSSOLV can outperform SCF consistently on many metallic systems.

Original languageEnglish (US)
Pages (from-to)A1975-A2002
JournalSIAM Journal on Scientific Computing
Issue number4
StatePublished - 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.


  • Ensemble density functional theory
  • Kohn-Sham total energy minimization
  • Orthogonality/spherical constraints
  • Proximal gradient method


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