Fractional charge perspective on the band gap in density-functional theory
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- 18 March 2008
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 77 (11), 115123
- https://doi.org/10.1103/physrevb.77.115123
Abstract
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 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.
Keywords
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