# Energy per unit cell in NWChem differs for different supercells despite the same k-points density

I try to compute the unit cell energy of the $$\ce{Ti2CO2}$$ MXene with NWchem.

Computing the 1x1 supercell with 4x4x1 K-points grid I got -1875 Ha.

Computing the 2x2 supercell with 2x2x1 K-points grid I got -7502 Ha, that means -1875.5 Ha per unit cell.

I understand, that for useful results convergence should be reached with K-points and the basis set. But here I just want to understand the source of the 0.5 Ha discrepancy. Previously I thought, that NxM supercell is equivalent to NxM K-points grid. Apparently it is not true. What is the source of such a significant difference?

Here are the NWchem inputs:

1x1 supercell with 4x4x1 K-points

title "nwtest"

permanent_dir /home/pvst/prg/regr/nwtest

scratch_dir /home/pvst/prg/regr/nwtest

start nwtest

geometry units angstrom nocenter noautosym noautoz
system crystal units angstrom
lattice_vectors
3.0136139399999999e+00 0.0000000000000000e+00 0.0000000000000000e+00
-1.5068069700000000e+00 2.6098661399999998e+00 0.0000000000000000e+00
0.0000000000000000e+00 0.0000000000000000e+00 3.0000000000000000e+01
end
Ti 3.4287223190009325e-01 6.5239607890387818e-01 2.1337608300333333e-01
Ti 6.7638044023217136e-01 3.1914803561534388e-01 1.2846060203666668e-01
C  9.5644354566451414e-03 9.8572931602538050e-01 1.7248868730000000e-01
O  6.7625413136791823e-01 3.1911195292184602e-01 2.4912464496666664e-01
O  3.4304300093474527e-01 6.5247955598213170e-01 9.7693002513333335e-02
end

basis noprint
* library 3-21g
end

dft
maxiter 2000
xc revpbe
mult 1
end
nwpw
monkhorst-pack 4 4 1
mult 1
end



2x2 supercell with 2x2x1 K-points

title "nwtest"

permanent_dir /home/pvst/prg/regr/nwtest

scratch_dir /home/pvst/prg/regr/nwtest

start nwtest

geometry units angstrom nocenter noautosym noautoz
system crystal units angstrom
lattice_vectors
6.0272278799999999e+00 0.0000000000000000e+00 0.0000000000000000e+00
-3.0136139399999999e+00 5.2197322799999997e+00 0.0000000000000000e+00
0.0000000000000000e+00 0.0000000000000000e+00 3.0000000000000000e+01
end
Ti 1.7143611595004662e-01 3.2619803945193909e-01 2.1337608300333333e-01
Ti 3.3819022011608568e-01 1.5957401780767194e-01 1.2846060203666668e-01
C  4.7822177283225707e-03 9.9286465801269030e-01 1.7248868730000000e-01
O  3.3812706568395912e-01 1.5955597646092301e-01 2.4912464496666664e-01
O  1.7152150046737263e-01 3.2623977799106585e-01 9.7693002513333335e-02
Ti 1.7143611595004657e-01 8.2619803945193904e-01 2.1337608300333333e-01
Ti 3.3819022011608568e-01 6.5957401780767189e-01 1.2846060203666668e-01
C  4.7822177283225655e-03 4.9286465801269025e-01 1.7248868730000000e-01
O  3.3812706568395912e-01 6.5955597646092301e-01 2.4912464496666664e-01
O  1.7152150046737266e-01 8.2623977799106596e-01 9.7693002513333335e-02
Ti 6.7143611595004660e-01 3.2619803945193909e-01 2.1337608300333333e-01
Ti 8.3819022011608557e-01 1.5957401780767194e-01 1.2846060203666668e-01
C  5.0478221772832266e-01 9.9286465801269030e-01 1.7248868730000000e-01
O  8.3812706568395923e-01 1.5955597646092301e-01 2.4912464496666664e-01
O  6.7152150046737269e-01 3.2623977799106585e-01 9.7693002513333335e-02
Ti 6.7143611595004660e-01 8.2619803945193904e-01 2.1337608300333333e-01
Ti 8.3819022011608579e-01 6.5957401780767189e-01 1.2846060203666668e-01
C  5.0478221772832255e-01 4.9286465801269025e-01 1.7248868730000000e-01
O  8.3812706568395923e-01 6.5955597646092301e-01 2.4912464496666664e-01
O  6.7152150046737269e-01 8.2623977799106596e-01 9.7693002513333335e-02
end

basis noprint
* library 3-21g
end

dft
maxiter 2000
xc revpbe
mult 1
end
nwpw
monkhorst-pack 2 2 1
mult 1
end


• Are those atomic coordinates correct? I'm not very familiar with NWCHEM but I thought these should be Cartesian coordinates in Angstroms, but your data look like fractional coordinates. – Phil Hasnip Feb 8 at 17:27
• @PhilHasnip Thank you for noting this. Indeed, it looks counter-intuitive, but it is correct. NWchem expects fractional coordinates along periodic coordinates. Anyway, even if geometry is out of equilibrium, supercell energy should be exact multiple of the unit cell, is not it? – user36313 Feb 9 at 6:04
• Yes, it should be a multiple; however, if the coordinates had been absolute coordinates then some atoms would be extremely close together, and that could have caused issues. FWIW I just ran this in CASTEP to check there was nothing weird, and E(supercell) - 4*E(cell) = 7.5 meV (about 0.3 mHa) which looks about right for default tolerances. Does NWCHEM include the gamma-point in its k-point grid? – Phil Hasnip Feb 9 at 17:19
• Couldn't it be that the basis set got much larger when you quadrupled the cell? Looks like the basis set is fairly small to start with and now you have 4 times as many basis functions. If this is the reason, you should be seeing a much smaller difference if starting from a larger basis set. – albapa Feb 10 at 22:45
• +1. I've also added an edit to make the chemical formula more readable. Here you can take a look so that you know how to do it next time! mattermodeling.stackexchange.com/posts/4314/revisions – Nike Dattani Feb 12 at 7:05

It turns out, that NWchem do not support K-points with Gaussian basis. The nwpw section in my input files, that contains the K-point grid specification, actually configures another calculation (with plane-wave basis) that is never launched by the task directive.