The Grimme-D2 is a semi-empirical dispersion correction scheme that introduces longer range van der Waal's forces to the system, which can be an important correction for any structure where you have further atoms along the line normal to your sheet.

I am not a Q.E. user, but I would guess that has something to do with "ignoring" the periodic boundary conditions along Z. Either by fixing it during relaxation or by imposing an open boundary condition (my hunch is the former). Something like this is necessary for a nanosheet, as if you don't have significant spacings between your layers, you get the bulk properties instead of the nanolayer ones.

Hope that provides some insight!

Dear Mahtab Goodarzi,

cell_dofree select the variable(s) that are allowed to vary in a cell-relaxation calculation. Therefore in your calculations, the z component of the lattice vector is the only one that would change. Is this what you want?

vdw_corr includes a van der Waals correction to the calculation. In 2D materials, where the van der Waals correction is dominant only along the z-direction (since in the x-y plane one has covalent bonding), this is normally not necessary.

I hope this helps,

Roberto