Hubbard effective parameter

[IBRAHIM]

Dear All,

When I try to tune the band gap of my system using the DFT+U functional, I find that the band gap decreases as Ueff​ increases.

Could you help me resolve this issue? I would like to obtain a value close to that calculated by HSE06, which is 1.32 eV.

Many thanks in advance,
Ibrahim

[michael_wolloch]

Dear Ibrahim,

You apply the Hubbard U to the 4d states of Silver, but those states do not contribute significantly to the bandgap.
Instead, the 5s and 5p states, which weakly hybridize with the 4d states, form the top of the valence- and the bottom of the conduction band.

Increasing the U parameter does shift the bulk of the d-states to lower energies and compresses the bandwidth. The small d-contributions near the Fermi level are nearly unchanged (examples with an effective U of 0, 4, and 6 eV):

Ag d states for 3 different effective U parameters.

The s and p states are only slightly affected by the U. The conduction band is lowered a bit:

Ag s and p states for 3 different effective U parameters.

Thus, you are getting a small reduction of the bandgap with increasing U.

This is also shown for Ag clusters in e.g.:
https://www.nature.com/articles/s41467-024-53428-6

Apparently PBE+U is not able to recover the HSE bandgap in this case.

Let me know if this solves your issue,
all the best, Michael