Dear Himani,

Both methods are ok to sample the Brillouin zone and you can choose the one that you think its better.

The calculations of the electron self-energy due to electron-phonon interaction require a good sampling of the Brillouin zone and careful convergence checks.

Using random q-grids has the advantage that you can increase the number of q-points included in your calculation by just calculating more q-points and giving them a new weight in the integral as 1/Nq (Nq is the number of q-points).

Also in random grids, you can give more importance to regions on the Brillouin zone that have a larger contribution to the integrals (this requires some kind of adaptative sampling).

With regular meshes normally you increase the number of k and q points until you are converged. This has a drawback that if you are not converged with for example 12x12x12 you will have to do for example a 16x16x16 which means you will be calculating repeated points.

The general consensus in the literature is to use random q-grids for the self-energy:

https://journals.aps.org/prl/abstract/1 ... 107.255501https://journals.aps.org/prl/abstract/1 ... 105.265501https://journals.aps.org/prb/abstract/1 ... .93.155435https://www.sciencedirect.com/science/a ... via%3DihubNow for the convergence of the two cases, you can find some useful discussions here:

In the case of a random Q-grid the error should go as 1/sqrt(Nq)

(see

https://en.wikipedia.org/wiki/Monte_Carlo_integration)

In the case of regular grids, the error should decrease as 1/[Nq^(2/d)] where d is the number of dimensions

(see

https://math.stackexchange.com/question ... -integrals)

This would seem to indicate that regular grids are better for integrals in less than 4 dimensions.

But don't take my word for it.

If you reach some conclusion about this topic please share.

Cheers,

Henrique