What parameters should be checked on both unit cell and super cell to make sure the calculations are going fine?

Question

Question is based on further learning about the previously asked question - Do NSCF calculations on Supercell gives different band gap than the Unit Cell?

How should I compare SCF and NSCF calculations on both? How are Band structures compared? The nbnd (that is number of electrons) increases when we increase number of atoms, that i have observed. What else can be checked here? How do I make sure the super cell created is correct or not?

Answer 1

Here are some thoughts about calculations involving primitive cells and supercells:

1. The energy cutoff used should be the same between a primitive cell and a supercell.
2. The density of $\mathbf{k}$-points should be the same between a primitive cell and a supercell. This may not be possible in practice if the grid sizes are not commensurate with the supercell sizes, and if this is the case, you want to build the corresponding grid that gives the closest possible density between the two sizes. In general, if the primitive cell calculations are well-converged with respect to $\mathbf{k}$-point grid size, this should be fine.
3. There are several programs that allow you to automate the construction of a supercell from a given primitive cell, and one I like is c2x. If the forces and stresses for the primitive cell vanish, then they should also vanish for the supercell. There may be slight differences due to the possible $\mathbf{k}$-point grid inconsistency described above. If you perform a geometry relaxation and the supercell changes, then this means that your primitive cell was not a true primitive cell of the system. In what follows, I will assume that the primitive cell of the system was a true primitive cell.
4. The density of states of the primitive and supercell should be the same, so this is a good quantity to check that you are calculating electronic quantities correctly.
5. The band structures will look different superficially due to band folding (when you increase the cell size the Brillouin zone becomes correspondingly smaller). However, there should still be a one-to-one correspondence between the band structures of the primitive cell and the supercell. A good overview of band folding can be found in this other question/answer.
6. If the supercell is $n$ times larger than the primitive cell, then the number of electrons in the supercell should be $n$ times larger. However, due to band folding, the number of bands at a given $\mathbf{k}$-point will also be $n$ times larger, so the Fermi energy and density of states will not change.
7. For a band structure calculation for the same reciprocal space path, you need to convert the $\mathbf{k}$-points used in the primitive cell to those corresponding to the supercell, taking into account that the supercell Brillouin zone is smaller. This will still exhibit band folding, but you should be able to identify the primitive cell bands within the band folded supercell bands as the paths are now identical.
8. You can use band unfolding to have a more direct comparison between the primitive and supercell band structures.