[Pw_forum] Band gap hybrid functionals

Mostafa Youssef myoussef at mit.edu
Wed Nov 11 18:03:16 CET 2015

Dear Phil and all,

Note that for a functional with exact exchange, the difference between ionization potential and electron affinity (I-A) is not the same as the Kohn-Sham single particle states  gap.  The consensus, as far as I know, is that I-A is more physical and relevant to comparison with experimental band gaps.  Calculating I-A  requires 3 scf calculations (neutral cell, +electorn, -electron).  The cases of +/- e require high smearing similar to that of metals (or you could use the tetrahedron method but I doubt it is implemented for hybrids). Also +/-  calculations require large cells and correction for a charged cell (Makov-Payne for example).  See section III-A in this paper for elaboration on computational details:

PHYSICAL REVIEW B 78, 235104 ?2008?

For PBE, LDA, ...  I-A is the same as  Kohn-Sham gap.

For elaboration on the theoretical aspects and why I-A is not the same as K-S band gap for the exact exchange, consult the work of A. J. Cohen and collaborators .

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