TY - JOUR

T1 - Curvature and frontier orbital energies in density functional theory

AU - Stein, Tamar

AU - Autschbach, Jochen

AU - Govind, Niranjan

AU - Kronik, Leeor

AU - Baer, Roi

PY - 2012/12/20

Y1 - 2012/12/20

N2 - 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.

AB - 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.

KW - General Theory

KW - Molecular Structure

KW - Quantum Chemistry

UR - http://www.scopus.com/inward/record.url?scp=84871580727&partnerID=8YFLogxK

U2 - 10.1021/jz3015937

DO - 10.1021/jz3015937

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AN - SCOPUS:84871580727

SN - 1948-7185

VL - 3

SP - 3740

EP - 3744

JO - Journal of Physical Chemistry Letters

JF - Journal of Physical Chemistry Letters

IS - 24

ER -