Density Functional Theory systematically underestimates electronic bandgaps due to derivative discontinuity errors
Density Functional Theory systematically underestimates electronic bandgaps because standard exchange-correlation functionals lack the explicit derivative discontinuity required at integer particle numbers.
The claim addresses a well-established theoretical limitation of standard Density Functional Theory (DFT), where standard approximations miss the derivative discontinuity of the exchange-correlation energy, leading to systematic underestimation of fundamental bandgaps. Papers [0] and [3] explicitly discuss this derivative discontinuity and its role in bandgap prediction.
Weitao Yang, Aron J. Cohen, Paula Mori-Sánchez. Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory. 2012. https://doi.org/10.1063/1.3702391
Paper 0 establishes that the exact Kohn-Sham energy gap differs from the fundamental bandgap due to the functional derivative discontinuity of the exchange-correlation energy.
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Johannes Gedeon, Jonathan Schmidt, Matthew Hodgson, Jack Wetherel, Carlos Benavides-Riveros, Miguel Marques. Machine learning the derivative discontinuity of density-functional theory. 2021. https://doi.org/10.21203/rs.3.rs-677067/v1
Paper 3 explains that standard functionals fail to reproduce the fundamental derivative discontinuity at integer particle numbers, which is essential for accurate bandgap descriptions.
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