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Dear all,

In some cases, HSE and +U methods gives similar results on many band gap problems.
We usually control their parameters mixing parameter alpha in HSE and on-site Coulomb energy U in plus-U method, to find band gap or other physical properties.

Q. What happened if we use HSE with alpha and plus-U together?

Q. Usually in HSE methods we set alpha so that the calculated band gap is matched with experimental value. In plus-U method, we also take appropriate U value so that the calculated physical properties (ex. band gap) are similar to the experimental observations.
If I want to turn on U in HSE with certain alpha, what should we do first? Should I vary alpha first? or U first? Is it physically non-sense to take both methodology at once?

Thank you.
Kim.

Both approaches "plus U" and hybrid functionals are procedures with well defined theoretical background.
When mixed together all theoretical background is lost. I would not recommend such a mixing.

We have recently explored the idea of employing the hybrid functional scheme and the DFT+U method as complementary approaches in our paper [J. Chem. Phys. 141, 044106 (2014); http://dx.doi.org/10.1063/1.4890458], and found that combining a hybrid functional with the Hubbard U is not only valid but also extremely useful approach (in spite of apparent prejudice against it), provided that the U terms are used only for localized states; consult Ref. 42.

This is particularly so for the band gap correction. The band gap is underestimated in the hybrid (HSE) calculations in proportionality with 1/eps (see Appendix of the foregoing paper). This is cured by the band gap correction thanks to the Hubbard term, which is proportional to U/eps (see Fig. 4 and Eq. 4). Here eps denotes the high-frequency dielectric constant. It is thus advisable to employ a single universal value for the exchange mixing coefficient together with the U values (for localized states) that are calibrated to match the band gap.