default k-points integration methods?

[jinylee]

Dear ATK team,

Based on my knowledge, there will be k-point integration (as gaussian smearing or tetrahedron methods) in every SCF steps in periodic system calculation.

When we calculate DOS by different k-point integration schemes (gaussian smearing or tetrahedron method), we can use .nc file  of the previous SCF results.
I think if DOS by certain k-point integration scheme should be meaningful, the SCF calculations also performed by the same integration scheme.

However, I don't know what integration scheme operate during SCF calculations which occur far before the DOS calculations.

Thus, I'd like to know what is the default k-point integration method during SCF calculations in ATK.

Thank you in advance for your answers.

[Nordland]

Dear ATK team,

Hey!

Based on my knowledge, there will be k-point integration (as gaussian smearing or tetrahedron methods) in every SCF steps in periodic system calculation.

In each step in SCF, the Hamiltonian is calculated for a set of different fourier components given by your k-points in your Monkhorst-Pack grid. In ATK the Hamiltonian is
represented  in a real space representation, so you will only need enough fourier components to make this Hamiltonian converged.
This is usually a few number of k-points needed to obtain this.

When we calculate DOS by different k-point integration schemes (gaussian smearing or tetrahedron method), we can use .nc file  of the previous SCF results.
I think if DOS by certain k-point integration scheme should be meaningful, the SCF calculations also performed by the same integration scheme.

This comes down to what you mean with meaningful. Since ATK uses a real space Hamiltonian, it is possible to calculate any fourier component from this,
as a post-process. If the real space Hamiltonian is converged in terms of k-points, this is an exact operation - and the DOS can then be calculated as correct for
any new k-points that might not have been in the SCF part.

[jinylee]

Dear ATK team,

Thank your for your reply.

Because I'm not used to the real space based computational codes,
I've tried to understand the concepts introduced in [ J. Phys.: Condens. Matter, 2002, 14, 2745, M. Soler et al.].

Followed by the first question, I have another one.

Does your answer mean Brillouin-zone integration not occurs until the end of the SCF process?

If you have problem to explain explicitly, please let me know appropriate references. It would really help me to understand.

Thank you in advance for your answers.

[Anders Blom]

No the k-point integration takes place in each step, using the k-point mesh specified for the calculator.

The point is that after this, for post-processing, you can specify any other k-point sampling for e.g. the band stucture, DOS, etc.

[jinylee]

Thank you for your answer Dr. Anders Blom.

I have one more question.

No the k-point integration takes place in each step, using the k-point mesh specified for the calculator.

Then, what scheme of k-point integration take place during each step of integrations?

for example,  as follows

1st SCF steps (gaussian smearing ) -> (post process) -> 2nd DOS (tetrahedron scheme)

In this case, is the final DOS  meaningful though two different integration schemes are applied?

Thank you in advance for your answers.

[Anders Blom]

When doing the k-point integration to obtain the real-space Hamiltonian, we perform a Fourier transform, so there is no smearing needed. Things are very different in a plane-wave basis where you solve for the k-space Hamiltonian.

Yes, the DOS is meaningful in this scheme.

[jinylee]

Thank you for your reply. Now I understand clearly.

By the way, what if the post process is transmission (or current)?

It also needs k-point sampling.

for example, as follows

1st SCF steps -> post process (read .nc file) -> transmission (or current)

I think k-point sampling in transmission means there is k-point integration to result in transmission.

Then, is the Brillouin-zone integration method related with the integration during transmission calculation?

Thank you in advance your reply.

[Anders Blom]

Yes and no. The total transmission is a sum over contributions from individual k-points, and it's a straight sum (no smearing).

However, the sampling density needed to get accurate transmission (and hence current) may be very different than for the electron density (which is what you Fourier transform in the scf, essentially), so the convergence in k-points for the transmission needs to separately and carefully checked.