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I have been looking at the scaling of supercell calculations. I am looking at perfect bcc Fe with a two-atom basis (simple cubic lattice vectors). Then I scale the supercell and adjust the k-points accordingly, for 2x2x2 and 3x3x3 times the original lattice vectors. The total energy does not scale exactly but differs by around 0.2 - 0.4 meV per atom, which is quite significant for a 3x3x3, or 54-atom system. I am doing these calculations with very small energy tolerance EDIFF = 0.000001 , PREC=accurate or high and even the k-point sampling adjusted but there is always an error: with or without magnetism. Is there something I'm missing? What else might cause the total energies to differ?
<span class='smallblacktext'>[ Edited ]</span>

please check
1) if the k-meshes you use are converged
2) if the k-mehses are the same qualitatively (eg all including the Gamma point or not,...) and make sure that
3) the calculations have stopped because they have reached the afforded convergence (1e-6eV energy differences), not because they have reached the limit of electronic scf steps (NELM). NELM=60 by default, if more than 60 stepsa re necessary to reach electronic convergence, please increase this parameter in INCAR explicitely.
4) the charge and magnetization densities (last columns of OSZICAR) should be converged. If they are not, please decrease
the mixing parameters (AMIX,BMIX, AMIX_MAG,BMIX_MAG)

Thanks for the reply. However, I don't see why the k-meshes need to be converged as long as they constitute the same sampling density in the two systems. I understand that they should be the same qualitatively and this is the case for my systems.

Here is my k-mesh
------------------------
Automatic mesh (cubic sys)
0
Gamma
6 6 6
0 0 0
-------------------
for the large system, and 12x12x12 for the small system.
-----------------------
POSCAR file
bcc-fe
2.834
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
2
direct
0.0 0.0 0.0
0.5 0.5 0.5
-------
for the small system, extended to 2x2x2 for the large system.

The INCAR file:
-------------------------------------------------
SYSTEM = bcc-Fe
ENCUT = 400 energy cutoff [eV]
EDIFF = 0.000001 convergence of electronic relaxation[eV]
ISMEAR = -5 smearing (-5=tetrahedron with Bloechl)
ISIF = 2 stress tensor calc (0=no)
IBRION = -1 ion movement (-1=fixed)
EDIFFG = -0.01 convergence of ionic relaxation [eV]
NSW = 0 max number of ionic steps
ISPIN = 1
NBANDS = 20
ISTART=0
IALGO=38
NELM=200
PREC=High
ISYM=0
AMIX=0.01
BMIX=0.1
-----------------------------
for the small system with 2 Fe atoms, and same for the large system with 16 atoms except more (160) bands.

I tried reducing the mixing but it always gives the same total energy to a high degree of precision. The energy always converges eventually: it doesn't reach the max iterations.

In the non-magnetic system (case shown here) the energy difference between the 2-atom and 16-atom systems is about 0.2 meV per atom.