## GW calculation for arbitrary K point

**Moderators:** gmatteo, bruneval, rigna

### GW calculation for arbitrary K point

Dear all Abinit users:

I'm studying the band structure of BC8 Carbon and want to get the band structure with GW correction.

For GW calculation, the kptgw must belong to the k-mesh generated for the KSS file. So, is there a good way to get GW correction for common k-points so that we can construct a band structure along the high symmetry lines?

Many thanks for your comments and advices.

Yu

I'm studying the band structure of BC8 Carbon and want to get the band structure with GW correction.

For GW calculation, the kptgw must belong to the k-mesh generated for the KSS file. So, is there a good way to get GW correction for common k-points so that we can construct a band structure along the high symmetry lines?

Many thanks for your comments and advices.

Yu

### Re: GW calculation for arbitrary K point

Due to the non-locality of the exact-exchange and of the self-energy operator, there is no possibility to avoid the use of a regular grid within GW.

My advice to obtain the GW band structure is to perform the GW corrections for all the the k-points in the full Brillouin Zone and then perform a Fourier interpolation to obtain the GW band structure along a given line.

This is not so straightforward. We should definitely provide a tool to do that operation...

Fabien

My advice to obtain the GW band structure is to perform the GW corrections for all the the k-points in the full Brillouin Zone and then perform a Fourier interpolation to obtain the GW band structure along a given line.

This is not so straightforward. We should definitely provide a tool to do that operation...

Fabien

### Re: GW calculation for arbitrary K point

At present one can use wannier90 to perform the Wannier interpolation of the

GW band structure produced by abinit. See test/wannier90/t03.in and

the test/wannier90/README.

I agree however that we should provide an automatic and painless way

for interpolating QP band structures.

Matteo

GW band structure produced by abinit. See test/wannier90/t03.in and

the test/wannier90/README.

I agree however that we should provide an automatic and painless way

for interpolating QP band structures.

Matteo

### Re: GW calculation for arbitrary K point

Dear Fabien and Matteo,

Thanks for your reply. That's helpful!

Best regards,

Yu

Thanks for your reply. That's helpful!

Best regards,

Yu

### Re: GW calculation for arbitrary K point

Dear all,

Can do it in the following way?:

1) First perform a self consistent LDA/GGA calculation using a conventional file with a regular k-grid.

2) Copy the values for keywords related to the generated k-point such as nkpt, kpt, and wtk, and explicitly add all desired k-points along high-symmetry lines of the BZ that are needed for the band structure plot. Add the them into the input file, but set the weights of these added k-points (i.e., the k-points for band structure plots) to 0. Correspondingly, set the number of k-points (i.e., the value of nkpt) in input file correctly (to the number of the k-points used in the standard mesh PLUS the number of the k-points along the lines), such that all k-points are used for the calculations.

3) Perform a second LDA/GGA calculation;

4) Perform a GW calculation with k points in the step 2);

5) The GW-eigenvalues of the states along the high-symmetry lines are written in output; cut the k-points required for the band structure from one of output file and proceed as usual.

I observed that such way is adopted in the VASP code for the hybrid functional calculation of band structure. I wondered whether this way is feasible to do the GW calculation of band structure with ABINIT code. Welcome to your comments.

Best regards

Hou

Can do it in the following way?:

1) First perform a self consistent LDA/GGA calculation using a conventional file with a regular k-grid.

2) Copy the values for keywords related to the generated k-point such as nkpt, kpt, and wtk, and explicitly add all desired k-points along high-symmetry lines of the BZ that are needed for the band structure plot. Add the them into the input file, but set the weights of these added k-points (i.e., the k-points for band structure plots) to 0. Correspondingly, set the number of k-points (i.e., the value of nkpt) in input file correctly (to the number of the k-points used in the standard mesh PLUS the number of the k-points along the lines), such that all k-points are used for the calculations.

3) Perform a second LDA/GGA calculation;

4) Perform a GW calculation with k points in the step 2);

5) The GW-eigenvalues of the states along the high-symmetry lines are written in output; cut the k-points required for the band structure from one of output file and proceed as usual.

I observed that such way is adopted in the VASP code for the hybrid functional calculation of band structure. I wondered whether this way is feasible to do the GW calculation of band structure with ABINIT code. Welcome to your comments.

Best regards

Hou

### Re: GW calculation for arbitrary K point

No, the k-points need to be regularly spaced in a GW calculation. The same is also true for the exact-exchange. So I don't know what VASP is doing for hybrid.

Fabien

Fabien

### Re: GW calculation for arbitrary K point

It sounds like it is integrating E, n, etc... only on the first kpt (with weights) but calculate all the eigenvalues so you get the BS at the same time.

I'm not sure this would work in abinit - there are a few places where the weights might not be used explicitly, and then you would get spurious kpt contributions. Interesting test though! Try it for a ground state run and tell us if it works.

cheers

Matthieu

I'm not sure this would work in abinit - there are a few places where the weights might not be used explicitly, and then you would get spurious kpt contributions. Interesting test though! Try it for a ground state run and tell us if it works.

cheers

Matthieu

Matthieu Verstraete

University of Liege, Belgium

University of Liege, Belgium