As with many things, finding the "best" value is a matter of experience. It will depend on your material, the dimensionality and size, and - ultimately - a crucial balancing of computational time vs. accuracy, since in theory you should have infinitely many k-points (except if the dimensionality is reduced in any direction) and an infinite mesh cut-off.
All one can do on a general level is to provide some guidelines for how to obtain this experience in the most efficient way.
- For any direction in which the system is finite, you only need 1 k-point. Thus, for a nanotube (or any other effectively 1D system) you only need more than k-points in the tube axis direction.
- There is a general rule of reciprocal vs. real space which tells you that the shorter the period, the more k-points you need.
- The task of computing the electron density on the one hand, and the transmission spectrum on the other, may have completely different requirements in terms of k-points, in order to obtain an acceptable level of accuracy. A good example if the Fe/MgO/Fe magnetic-tunnel junction, where you do need quite many XY k-points (perhaps 9x9) for the electron density (i.e. the self-consistent loop), you will need upwards of 200x200 for the transmission spectrum, at least in the configuration where the electrodes have parallel spin polarization, due to the presence of very sharp resonant tunneling peaks.
- The more localized the atomic orbitals are, the larger the mesh cut-off needs to be. Thus, systems with a lot of d-electrons tightly bound to the core need a higher value (perhaps 150 H or more) than a simple sp2 bonded graphene nanotube, where 40-50 H might be enough (at least for energies).
- An accurate evaluation of forces requires a larger mesh cut-off (smaller grid point distance) than required for the electron structure.
Ultimately, you need to test your system, and get to know it, from the perspective of k-points, mesh cut-off, and other parameters. Only then can you have confidence in the results.
If other users have further general (or specific) insights, I hope you will share them with the community in this thread.
