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This is not an easy question. Please refer to this reference
Dmitrij Rappoport, Nathan R. M. Crawford, Filipp Furche and Kieron Burke "Approximate Density Functionals: Which Should I Choose?"
http://onlinelibrary.wiley.com/doi/10.1002/0470862106.ia615/pdf
On pg. 8
Perhaps the most useful property of an insulating solid to predict is its fundamental gap. This is I − A, the difference between ionization energy and electron affinity for a macroscopic chunk of that solid. This gap would be given exactly by adding and removing an electron from such a chunk, if we had the exact XC functional. On the other hand, the KS band gap, defined as the HOMO–LUMO difference, is not equal to the fundamental band gap, even with the exact XC.109 Although the HOMO energy computed with the exact XC functional is equal to the negative ionization potential I, the LUMO energy is not equal to the electron affinity A, even when the exact functional is used. In general, the KS band gap is smaller than the fundamental gap and, in an extreme case (Mott insulator), can vanish, while correlation effects still make the solid an insulator. |
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