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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



task dft gradient

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



task dft gradient
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7
  • $\begingroup$ 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. $\endgroup$
    – Phil Hasnip
    Feb 8, 2021 at 17:27
  • $\begingroup$ @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? $\endgroup$
    – user36313
    Feb 9, 2021 at 6:04
  • 1
    $\begingroup$ 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? $\endgroup$
    – Phil Hasnip
    Feb 9, 2021 at 17:19
  • $\begingroup$ 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. $\endgroup$
    – albapa
    Feb 10, 2021 at 22:45
  • 1
    $\begingroup$ +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 $\endgroup$
    – Nike Dattani
    Feb 12, 2021 at 7:05

2 Answers 2

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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.

Summing up, with NWchem you can use either K-points with plane-waves, or a supercell with Gaussian basis. But even with a supercell you can't get periodic boundaries with Gaussian basis.

Thanks to Eric Bylaska and Edoardo Aprà for bold hints here.

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1
  • $\begingroup$ Just mentioning that CP2K is a code that does periodic calculations with Gaussian basis sets. It also has an implementation of k-points but not all features are supported, see cp2k.org/faq:kpoints $\endgroup$
    – leopold.talirz
    Jun 26, 2021 at 23:47
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No, the Gaussian basis module of NWChem does not support periodic boundary conditions. The calculation described here did not stop because of a bug in the code. The bug and the fix are described in this Github issue.

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1
  • $\begingroup$ +1. Nice first answer! Welcome to our new community, and thank you for your contribution! We hope to see much more of you in the future !!! I've edited your answer only since you forgot the punctuation at the end ;) $\endgroup$
    – Nike Dattani
    Feb 12, 2021 at 23:44

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