Proper treatment of K-point sampling for bulk-amorphous

[qew394]

Hello,

I am trying to generate amorphous structures to train machine learning potential. I know there are several limit to amorphous structure due to the inherent DFT condition, 'periodic boundary condition(PBC)'. But many applications and approaches are attempted such as vacuum slab with single k-point along the vacuum direction(NxNx1) and other people build the amorphous structure with large cell under PBC(crystal in macro but amorphous in local). Based on these facts, I thought that 1x1x1 k-point might be proper for large amorphous structure like did for vacuum slab. On the other hand, some people say that energy convergence must be tested by increasing k-points.

As it is assumed that statements above are all correct, then I expected that fast convergence will be achieved as cell size gets larger. But it was not true. The moderate convergence always reaches for the higher k-point density in regardless of cell size.

It seems all my question arises because of unreasonable approach: amorphous structure with periodic DFT simulation.
But I just want to find which one is better approach about k-point sampling for large amorphous cell.



Here's my question.
1. Like single k-point is applied along the vacuum direction due to the broken PBC condition, then will it be ok if I put 1x1x1 kpoint for amorphous bulk structure as long as the cell is large enough, even though convergence is not achieved at 1x1x1? which means 1x1x1 is 'more correct' than 3x3x3 for large amorphous cell. 
2. In many DFT papers, it is said that "we set the K-point density by 0.02(2pi/A)" or "DFT is calculated using 1x1x1 k-point sampling since the cell is large", saying like 'lower number of k-points is ok because our cell is large'. But I believe the concept of 'less number of kpoint is ok for larger cell' is only valid only if the large cell is formed with 'exactly the same' and smaller unit cells. Am I correct ?


Thank you for reading my long questions !

[Anders Blom]

Interesting question. I think the truth both practically and principally, lies somewhere between your points 1 and 2.

No matter the size of the cell, if we use PBC we enforce a quasi-periodicity on the system, which numerically may be hard to converge (the self-consistent loop) with too few k-points. So in practice you might want something like 3x3x3 because of that, even if yes, if the cell was large enough, 1x1x1 should be enough. The problem might however be that "large enough" may be too large for DFT...

On the other hand, if by converge you mean "minimize the total energy as function of k-point sampling", I would actually stick to 1x1x1 since there are other approximations in DFT that may be larger. Energy convergence in k-point sampling is notoriously slow and typically even oscillates, and for special systems even depends whether or not you include "magical numbers" like multiples of 3 in the case of graphene (ok, this is not so relevant for amorphous systems with no symmetries).

So, in summary, I would use the largest possible cell from a practical perspective, and stick to 1x1x1, unless there is convergence issues in the SCF loop.