Negative Band Gap for Crystalline Silicon from PBE0

[Jian Cheng Wong]

Dear BerkeleyGW Developers,

I performed a G0W0 test calculation on crystalline silicon from PBE and PBE0 using BerkeleyGW-3.0.1. While the G0W0 calculation from PBE turned out fine, I obtained a negative band gap from the G0W0 calculation from PBE0. The DFT hybrid functional calculation is performed using Quantum Espresso version 6.8. I used the kgrid.x script to generated both the unshifted and shifted 4x4x4 k-point grid for the SCF runs since 'nscf' and 'bands' for hybrid functionals are not allowed by Quantum Espresso.

I am not sure what is going on as I have tried the following steps:

• Using vxc.dat obtained as vxc_hybrid.dat instead of kih.dat generated via pw2bgw.x but this does not change the results.
• The bare_exchange_fraction parameter is set to 0.75 as indicated in the manual. I did a test run where I set the bare_exchange_fraction to 1 and managed to obtain a band gap of ~1.6 eV, which is still far from the experimental band gap of crystalline silicon.

I have attached the input files that I used for the DFT and G0W0 runs for reference. Any help is greatly appreciated!

Thank you!

Sincerely,

Jian Cheng Wong 

[Mauro Del Ben]

Hi Jian Cheng Wong,

If I remember right, if you use the combination:

dont_use_vxcdat

use_kihdat

You don't need to specify the bare_exchange_fraction since the bare exchange and self energy correlation will be just added to the KIH term (kinetic, ion and Hartree term) without need to subtract the vxc term.

Regarding the GW gap being too large, it seems your PBE0 starting point also has a large gap, just after a quick run it seems to be ~2.5 eV. 

One other thing, since silicon is not a direct gap material, it might be that you are not using a k-grid fine enough to include the proper CBM.

Best

-M

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[Jian Cheng Wong]

Thank you for your response!

It was not clear to me from the manual that the bare_exchange_fraction parameter is not needed for kih.dat when using hybrid functional as starting point for GW calculation in BerkeleyGW-3.0.1.

I did further testing for PBE0 calculations as starting point of GW using Quantum Espresso version 6.1. I noticed that bare_exchange_fraction 0.75 is needed in sigma.inp since the version 6.1 of pw2bgw.x cannot print out kih.dat but instead uses the VXC file printed from vxcg_flag.

Meanwhile for Quantum Espresso version 6.8, pw2bgw.x requires that kih.dat to be printed out when using hybrid functional. Also I noticed that using the vxc.dat file printed from vxc_hybrid_flag in sigma.inp gives me the same results as using kih.dat without setting the bare_exchange_fraction parameter for both calculations (at least for PBE0).

It seems to me that there is a significant change in the way pw2bgw.x converts pw.x output files for hybrid functional calculations in newer versions of Quantum Espresso that affects the setup of sigma.inp in BerkeleyGW-3.0.1.

Sincerely,

Jian Cheng Wong

[Mauro Del Ben]

Hi Jian Cheng Wong,

Yes, there have been quite some improvements on the pw2bgw side. Thanks for pointing out the inconsistency. 

Best

-M