How to calculate scissor operator

For Bethe-Salpeter calculations, they set a scissor operator of 0.8 eV in the tutorial. The scissor operator is the difference between the GGA band gap and experimental band gap. Is there a way to calculate the scissor operator theoretically with ABINIT?

Hi, essentially you’d want to do a GW (or at least a G0W0) calculation, to get an estimate for the correction to the band gap. You could then use this value for scissors in a BSE calculation. There are detailed tutorials on GW in the abinit set, just preceding the BSE tutorial.

Thank you! I appreciate it.

I have done GW calculations. Unfornuately, I do not know what k-point I should use to for the correction in the band-gap. My understanding is that GW calculates the band-gap at one specific k-point, is there a way to calculate the minimum direct band gap or fundamental band gap instead?

I do not know what k-point I should use to for the correction in the band-gap.

This is normal as the scissor operator approximates the QP corrections \Delta_{nk}
with a rigid constant shift \Delta that is applied to the conduction states only.

In other words, the scissors approximation does not take into account the renormalization of the QP states at the level of the group velocity and effective masses. You are just rigidly shifting the conduction states by \Delta.
Despite all these approximations, the scissors operator is commonly used in BSE calculations since BSE spectra converge slowly wrt the k-sampling and the computation of the quasi-particle states for all these kpoints at the GW level would be extremely expensive.
In a nutshell, the scissors operator is supposed to emulate the effect of a GW calculation but only in a average way.

My understanding is that GW calculates the band-gap at one specific k-point

The Abinit GW code can compute QP corrections only for the k points included in the WFK file.
This is a limitation common to other GW codes.

One usually computes the QP corrections for the fundamental/direct gaps predicted by the KS calculation but there’s no guarantee that these are the “true” fundamental/direct QP gaps.

As a matter of fact, the value of what Abinit calls fundamental/direct gap depends on the k-point sampling used in the calculation.
This is the reason why, before performing GW calculations, one should always compute the KS band structure along a high-symmetry k-path to locate the relevant k-points around the KS band edges.

is there a way to calculate the minimum direct band gap or fundamental band gap instead?

One can use the input variable https://docs.abinit.org/variables/gw/#gw_qprange
to compute the GW corrections for the fundamental/direct gap for the k-wave vectors and bands predicted by the KS Hamiltonian but, again, this does not mean that what you get is the true fundamental/direct gap. Everything depends on the input k-sampling.

Hi, thank you for your hasty response.

I’m still fairly new to GW calculations so bear with me if my questions may be a bit redundant.

I see that in the output file of my GW calculations, only 7 qpoints in the IBZ were tested, I can’t seem how to adjust this number to be very large like in KS calculations?

Additionally, is it possible to graph the band structure from GW calculations?

I think the input variable gw_qprange is what you want, as noted by gmatteo in his answer. This would allow you to compute the correction at every kpt in the IBZ you used. If you want to go beyond that, I think you have to use interpolation methods, which are described in the GW tutorials.

Hi,

I am trying to calculate BSE with GW correction. However, there are some questions when I doing the calculation.

For the BSE, one can gw.in file to read the GW correction.
However, the BSE usually requires dense k-sampling compare with GW as gmatteo said. So when I do the BSE using the dense grid, Can I still use the GW correction on the coarse grid to simulate the quasiparticle correction? Or in this situation, I should use the scissor to mimic the quasiparticle effect?

Also, Can I use the GW correction after interpolate band structure (Wannier for example) to execute the BSE calculation?

Regards,
Andy Hsu