Curvature and frontier orbital energies in density functional theory

Tamar Stein, Jochen Autschbach, Niranjan Govind, Leeor Kronik*, Roi Baer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

145 Scopus citations


Perdew et al. discovered two different properties of exact Kohn-Sham density functional theory (DFT): (i) The exact total energy versus particle number is a series of linear segments between integer electron points. (ii) Across an integer number of electrons, the exchange-correlation potential "jumps" by a constant, known as the derivative discontinuity (DD). Here we show analytically that in both the original and the generalized Kohn-Sham formulation of DFT the two properties are two sides of the same coin. The absence of a DD dictates deviation from piecewise linearity, but the latter, appearing as curvature, can be used to correct for the former, thereby restoring the physical meaning of orbital energies. A simple correction scheme for any semilocal and hybrid functional, even Hartree-Fock theory, is shown to be effective on a set of small molecules, suggesting a practical correction for the infamous DFT gap problem. We show that optimally tuned range-separated hybrid functionals can inherently minimize both DD and curvature, thus requiring no correction, and that this can be used as a sound theoretical basis for novel tuning strategies.

Original languageAmerican English
Pages (from-to)3740-3744
Number of pages5
JournalJournal of Physical Chemistry Letters
Issue number24
StatePublished - 20 Dec 2012


  • General Theory
  • Molecular Structure
  • Quantum Chemistry


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