Curvature and Frontier Orbital Energies in Density Functional Theory.
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.
†Fritz Haber Center for Molecular Dynamics, The Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel.
Tamar
T
Stein
‡Department of Chemistry, University at Buffalo, Buffalo, New York 14260, United States.
Jochen
J
Autschbach
§William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States.
Niranjan
N
Govind
∥Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel.
Leeor
L
Kronik
†Fritz Haber Center for Molecular Dynamics, The Institute of Chemistry, The Hebrew University, Jerusalem 91904, Israel.
Roi
R
Baer
density functional theory; derivative discontinuity; frontier orbitals; ionization energy