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Despite the fact that DFT is a ground state theory, researchers often extract band gaps (the energy difference between the VBM and the CBM) directly from DFT, even though the CBM/VBM eigenvalue difference in fact does not correspond to a measurable quantity such as the optical band gap. LDA or GGA XC functionals usually badly underestimate band gaps compared to measured values.
Perdew and Levy proved that the underestimation of band gaps in pure DFT is due in part to the lack of derivative discontinuities in XC density functionals.

New concepts and modeling strategies to design and evaluate photo-electro-catalysts based on transition metal oxides
Peilin Liao and Emily A. Carter
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