Cross Convergence Effects With CNTs

[Mamikon Gulian]

Hello,

I am working on converging unit cell sizes for a CNT (i.e., converging the vacuum volume to approach a "single" CNT system). If anyone has an experience with this, what kind of cross-convergence effects should I expect between the vacuum padding, ecut, and the k-point sampling?

Many thanks,

Mamikon

[mverstra]

Hello,

I am working on converging unit cell sizes for a CNT (i.e., converging the vacuum volume to approach a "single" CNT system). If anyone has an experience with this, what kind of cross-convergence effects should I expect between the vacuum padding, ecut, and the k-point sampling?

Many thanks,

Mamikon

Dear Mamikon,

1) ecut is basically independent of all the rest. It is essentially influenced only by the pseudopotentials used

2) In general the k-point grid is only correlated to the smearing used for metallic systems, which may be your case, but:

3) if you have vacuum, strange things can happen:
a) sometimes the dielectric response is described better if you have k-points in the perpendicular direction to the tube (for a perfectly isolated system the bands should be flat). See e.g. http://dx.doi.org/10.1016/j.cpc.2006.07.018 (preprint http://arxiv.org/abs/cond-mat/0608215). In this case there can be a link between vacuum and the number of k-points needed.
b) There can be free-electron-like states in the box. As the box gets bigger, their energy decreases to some asymptotic limit, and their DOS increases. These are unoccupied, but can be quite close to the Fermi level in some cases (graphene for instance). You will never converge these entirely, but they are usually not too important.

In practice you can converge the vacuum independently from the rest in most cases.

What you have not mentioned is the number of bands: normally higher bands are more delocalized, so nband does not correlate with ecut, but it will correlate with the vacuum. If you need accurate high-lying bands (e.g. for GW or optics) you need a lot of vacuum.

Final word of warning: you must always consider the physical quantity you are studying, to check for convergence. The total energy converges quite quickly, but that doesn't mean that phonon frequencies or optical properties are converged: usually they need (many) more bands plane waves and k-points.

Cheers

Matthieu