Fractional charge perspective on the band gap in density-functional theory
By A. Cohen, Paula Mori-S'anchez, Weitao Yang. 2007
452 citations recorded by the source corpus.
The calculation of the band gap by density-functional theory (DFT) is examined by considering the behavior of the energy as a function of number of electrons. It is explained that the incorrect band-gap prediction with most approximate functionals originates mainly from errors in describing systems with fractional charges. Formulas for the energy derivatives with respect to number of electrons are derived, which clarify the role of optimized effective potentials in prediction of the band gap. Calculations with a recent functional that has much improved behavior for fractional charges give a good prediction of the energy gap and also ${\ensuremath{\epsilon}}_{\mathrm{HOMO}}\ensuremath{\simeq}\ensuremath{-}I$ for finite systems. Our results indicate that it is possible, within DFT, to have a functional whose eigenvalues or derivatives accurately predict the band gap.
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/b442ea14defa0668a16c3a071e450c457de82981
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In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations (2017, background): “[10] Despite the success of GSC, it does not offer any cure to the size-dependent discrepancy ∆I, because it gives zero correction to energies at integers.”
- Density functional theory: Its origins, rise to prominence, and future (2015, background): “This has proved to be valuable in the context of many-electron self-interaction (Mori-Sánchez, Cohen, and Yang, 2006) and band gap errors (Cohen, Mori-Sánchez, and Yang, 2008a).”