Dear all,
I am currently performing total energy calculations for periodic structures using ABINIT, varying both the k-point meshes and the choice of supercell (effectively sampling different periodicities).
My objective is to verify that, for a given structure, the total energy per primitive cell remains consistent across simulations, irrespective of the supercell size employed. However, I have observed a persistent gap of approximately 5 × 10⁻⁴ Hartree between the energy per cell calculated from the primitive unit cell and that obtained from a 2×2 supercell or 2x2x2 supercell.
To investigate the source of this gap, I have also varied the energy cutoff (ecut) and symmetry options (nsym=0 or nsym=1). After these adjustments, I confirmed that the numerical accuracy for these parameters is already on the order of 10⁻⁷ Hartree.
Thus, despite these adjustments, the energy gap remains. I would appreciate any insights or suggestions regarding possible sources of this inconsistency. I believe that it might be related to Brillouin zone sampling, pseudopotential behavior, or some numerical issues that can come from the supercell construction.
For clarity, I have also attached the input files and a graph that illustrate the results. (These can be downloaded from the link below as a .zip or .targz or normal file)
Link: ABINIT_Forum_Q - Google Drive
Thank you in advance for your guidance.
Dear adadenizkoc,
Do you have a similar plot where you have the same k-point density?
In my opinion, the behaviour that you are observing is normal.
What I mean by this that in your in your input files from unit to supercell, you are effectively changing the k-point density sampling. So for the unit cell when you are using 12x12x12 k-points, a fair comparison to 2x2x1 would be to scale with the cell and employ a 6x6x12 k-points to be on the same footing of sampling, instead of the 12x12x12 that you are currently using, the same goes for the 2x2x2 with an equivalent of 6x6x6 k-points sampling. So for future reference, the k-point sampling must be scaled commensurately across calculations when going for supercells (or at least close to commensurate if you are building, for example, \sqrt2 x \sqrt3 x \sqrt5 supercells).
In your sets, between the unit cell, 2x2x1 and 2x2x2 cells you are effectively using 4 times more k-points, respectively 8 times more k-points.
What you are effectively observing in your plot is that you are converged within 0.5 mHa (equivalent of 1579 K) in total energy across different k-point samplings within the 3157 K smearing (which is in fact twice the energy “gap” that you are observing, a.k.a the spread of the Gaussian smearing that you are currently using). For your own edification, you can perform a convergence k-points test by decreasing the smearing (for example how would your plot look at 1000 K, 100 K or 10 K smearing? will the “gap” that you observe fall within the spread of the Gaussian smearing?).
Cheers,
Bogdan