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I am new to DFT calculation and I want to compute DFT total energy and atomic forces of an atomic configuration, given the atomic positions and lattice vectors.

I have an extended xyz with DFT energy and forces from a paper. XYZ file is pasted at the end of the question.

My goal is to do my own DFT calculation using the atomic position information and reproduce the energy and forces data. However, I haven't been able to do so.

In the paper, the authors used VASP with PBE exchange-correlation function, 500 eV energy cutoff, and 4x4x4 grid points. I don't have access to VASP, and I was trying to do the calculation using quantum espresso. With my initial attempt, the atomic forces that I got differed by about 1e-2 eV/angstrom, but the energy that I got was about -16,000 eV vs -500 in the paper/xyz file.

I don't know why my energy is off by a lot, while the forces are pretty close. Is this an expected behavior from comparing calculations using 2 different DFT software? Is there another way to compute DFT total energy and forces given xyz file?

Note: I used quantum espresso calculator in ASE to do the calculation.

Code

from ase.io import read
from ase.calculators.espresso import Espresso


# Read the xyz file
atoms = read("inst_cubic_diamond_temp300_strain0.0_step1001.xyz", format="extxyz")

# Calcualtor
calc = Espresso(
    pseudopotentials={"C": "C.pbe-n-kjpaw_psl.1.0.0.UPF"},
    tstress=True,
    tprnfor=True,
    outdir=<outdir>,
    pseudo_dir=<pseudo_dir>,
    kpts=(4, 4, 4),
    koffset=True,
)
atoms.calc = calc

# Compute energy and forces
energy = atoms.get_potential_energy()
print("Energy:", energy)
forces = atoms.get_forces()

XYZ file

64
Lattice="7.10842262195238 0 0 0 7.10842262195238 0 0 0 7.10842262195238 " PBC="1 1 1" Properties=species:S:1:pos:R:3:force:R:3 Energy="-512.86187833"
C     2.515720524176340e-02   3.867550579089600e-03   7.089434672581682e+00 -5.37951000e-01  -9.43653100e-01   8.96908860e-01
C     1.776933986593727e+00   1.732049273644261e+00   2.572083207130320e-02  4.26181090e-01   1.51736004e+00   3.81343080e-01
C     7.082577532701300e+00   1.802144789342045e+00   1.769809143517475e+00  1.13683654e+00  -6.10598840e-01   7.06415680e-01
C     1.730755114222064e+00   7.103866760858615e+00   1.834766904598202e+00  5.28662040e-01   3.17688010e-01  -1.12025143e+00
C     8.721281061942280e-01   8.735364979679285e-01   8.966439895472150e-01  1.05603720e-01   2.62228850e-01   5.75211080e-01
C     2.696528798085684e+00   2.679314544279508e+00   9.295221501861438e-01 -7.81283670e-01  -5.78397410e-01  -1.85532276e+00
C     9.346490289165925e-01   2.672186644581529e+00   2.654060735574339e+00 -2.03034942e+00   1.70433750e-01  -3.59527500e-02
C     2.678101420875179e+00   9.199713446381380e-01   2.689016972481999e+00 -6.26726520e-01  -1.33007226e+00   1.56036970e-01
C     3.511187368839771e+00   7.101188022878494e+00   7.107915220793385e+00  9.31579400e-02  -4.02755650e-01   8.05187710e-01
C     5.312681026669824e+00   1.769173081861437e+00   7.067010726921535e+00  6.70675890e-01  -1.36012410e-01   1.35187542e+00
C     3.546168769563506e+00   1.802083870160192e+00   1.830411431890475e+00  8.04017590e-01  -7.92153530e-01  -1.76726650e+00
C     5.379223112984097e+00   3.912248340524160e-02   1.782229477108722e+00 -2.47505791e+00  -2.16700570e-01  -5.76459000e-03
C     4.425585354722698e+00   8.827204378245163e-01   8.970133431865501e-01  2.16665110e-01   8.11297010e-01  -2.73793900e-01
C     6.213865521165564e+00   2.672265050483028e+00   8.666035823024164e-01  2.11940450e-01  -9.71874700e-02  -3.56909090e-01
C     4.454692212824812e+00   2.667208331883838e+00   2.664322099047440e+00  1.78292390e-01   3.44728770e-01   2.32568650e-01
C     6.202805881832237e+00   9.258737522764287e-01   2.730940032231068e+00  4.33003680e-01   5.79964000e-02  -1.57874570e+00
C     3.423771754923000e-03   3.576000047014824e+00   7.096407537582318e+00  7.40474130e-01  -4.69554600e-01   5.82278100e-02
C     1.773121668458395e+00   5.291121536284495e+00   7.096664293807353e+00  5.47373550e-01   2.29641219e+00  -6.93962180e-01
C     7.061366710445481e+00   5.370766791266893e+00   1.766795669916178e+00  1.08575565e+00  -1.16270741e+00  -3.20823180e-01
C     1.783560955749675e+00   3.595632230775192e+00   1.744914310154615e+00 -1.61832200e-02  -1.34411611e+00   6.86037350e-01
C     9.147487865392240e-01   4.470236769241776e+00   8.314481673929444e-01 -1.97196630e+00  -7.49626810e-01   2.35244402e+00
C     2.602983378091007e+00   6.204381819127091e+00   9.149161188076987e-01  1.82101717e+00  -1.18240660e-01  -3.90261780e-01
C     7.917225343283958e-01   6.245417605564732e+00   2.701292578588703e+00  2.03609908e+00  -3.15842450e-01  -7.80305460e-01
C     2.658791177575270e+00   4.409512997926200e+00   2.662736565382049e+00  6.59346630e-01   2.03379123e+00  -1.16759940e+00
C     3.571911211239574e+00   3.541409467366737e+00   7.066099498225877e+00  1.32691510e-01   8.00661400e-02   1.22032686e+00
C     5.332296008047452e+00   5.301607810249293e+00   7.096567761428173e+00 -7.19261300e-01   1.61148671e+00   5.60174190e-01
C     3.599161989111380e+00   5.298915424097742e+00   1.755959945895381e+00 -1.45534256e+00   1.23807627e+00   5.26815840e-01
C     5.343400430443285e+00   3.555400122598969e+00   1.724019670536935e+00 -7.94688100e-02  -1.22034087e+00   1.68260656e+00
C     4.495938763993136e+00   4.410190288433433e+00   8.644839217613586e-01 -1.90959096e+00   6.98633670e-01  -3.14938090e-01
C     6.177803853456268e+00   6.250621184175251e+00   8.693900128852301e-01  1.68162569e+00  -6.84345710e-01   1.99048910e-01
C     4.467966552309626e+00   6.254770441542771e+00   2.656286880286244e+00 -7.57695100e-02  -1.03345062e+00  -3.54654490e-01
C     6.207880087151072e+00   4.401281444532239e+00   2.639561757040551e+00  7.66324170e-01   1.46387162e+00  -1.26064490e-01
C     7.092034222733816e+00   6.469645546521559e-02   3.611905542679158e+00 -3.69020620e-01  -1.32917779e+00  -7.38472440e-01
C     1.813401260897720e+00   1.798810015038325e+00   3.567437312210998e+00 -6.60443250e-01   1.25397500e-01  -5.29906640e-01
C     9.131195360747199e-03   1.777007203346713e+00   5.386779579481836e+00  1.49964985e+00   4.50847890e-01  -1.38667509e+00
C     1.762572342784958e+00   7.084367575685467e+00   5.258194825119071e+00 -1.44468190e-01   4.70378990e-01   2.27251762e+00
C     8.933156128238523e-01   9.138509927623180e-01   4.435922067475571e+00  2.19887730e-01   2.63211500e-01   6.47886620e-01
C     2.734726120286932e+00   2.672868982068823e+00   4.419541631642722e+00 -1.61252743e+00  -8.08281400e-02   1.02152425e+00
C     9.668444966470966e-01   2.659522421010190e+00   6.248003507545436e+00 -2.34920086e+00  -7.79319900e-02  -1.55410930e-01
C     2.621514609355990e+00   8.887661512628261e-01   6.206886542921475e+00  1.00247324e+00  -9.82742760e-01   2.23900990e-01
C     3.560229798179676e+00   1.192011389147800e-02   3.571414759003793e+00 -1.08340810e-01  -6.94958780e-01  -6.32829660e-01
C     5.303243173957251e+00   1.783785084314883e+00   3.608673698334975e+00  6.65906520e-01   1.93424360e-01  -2.00882610e-01
C     3.528356910667667e+00   1.767911834435971e+00   5.347927358304606e+00  7.39111180e-01  -2.47114860e-01  -1.04495492e+00
C     5.329030825201182e+00   7.096177437942109e+00   5.369101643268158e+00 -3.08175260e-01  -1.14381900e-02   1.84117730e-01
C     4.422761249499998e+00   8.668823746375728e-01   4.494489925294728e+00  3.83796370e-01   4.22127430e-01  -5.75045160e-01
C     6.241506267102304e+00   2.679197823980088e+00   4.509426711577681e+00 -9.90742090e-01  -1.47647882e+00  -1.25004513e+00
C     4.432864237317125e+00   2.645875244758956e+00   6.162178971863699e+00  2.14951310e-01   1.37021740e-01   2.03719183e+00
C     6.276550008692416e+00   8.743755050897671e-01   6.235059780796678e+00 -2.36728919e+00   4.92518030e-01  -1.75193300e-01
C     7.065680456712427e+00   3.515117189201012e+00   3.569630900347304e+00  2.01679955e+00   6.47574810e-01  -7.38426790e-01
C     1.744524484258135e+00   5.323755096101070e+00   3.489180474334740e+00 -2.31814270e-01  -5.78952010e-01   2.30748316e+00
C     7.087238738665912e+00   5.312598853304337e+00   5.367801939276317e+00  8.84590350e-01   6.63457880e-01  -2.04867967e+00
C     1.836661512479110e+00   3.526170004448624e+00   5.351513557516396e+00 -1.23618594e+00   5.61918680e-01  -1.49124744e+00
C     8.644019616485500e-01   4.381350493769153e+00   4.431205771235654e+00  6.54489790e-01   1.65426557e+00   5.88371370e-01
C     2.638706329462460e+00   6.199561100158887e+00   4.412298788750978e+00  5.65976410e-01   3.85331420e-01  -6.55854390e-01
C     8.855542105019791e-01   6.193752239362274e+00   6.199043180486793e+00  4.21980700e-01   3.69641240e-01   2.30177540e-01
C     2.676275196019875e+00   4.452567718556373e+00   6.202611111052449e+00  5.14470800e-01  -6.82406950e-01  -3.64222200e-02
C     3.579314420145626e+00   3.572309993748555e+00   3.522390171804665e+00  1.20915900e-02  -5.19302820e-01   8.08118950e-01
C     5.377902368061301e+00   5.343446208684958e+00   3.488438141760533e+00 -1.17684527e+00   1.56643050e-01   2.46875405e+00
C     3.545122765174973e+00   5.343271341488506e+00   5.291750347349461e+00  3.51595720e-01  -8.43737200e-01   5.14030800e-01
C     5.342069378307690e+00   3.526753748114178e+00   5.351913690625676e+00 -3.28223650e-01   2.01570343e+00  -1.31587457e+00
C     4.480059756291901e+00   4.450995690893960e+00   4.393124174154658e+00 -6.06505570e-01   2.54363480e-01   8.42964100e-01
C     6.221970331384210e+00   6.256644790419212e+00   4.501010623532506e+00  3.77290300e-02  -1.34160519e+00  -1.84268948e+00
C     4.403452996558423e+00   6.178451075335819e+00   6.250501549422556e+00  6.40125260e-01   1.35140560e+00  -1.06078985e+00
C     6.211810831607253e+00   4.482924592776214e+00   6.216467417097163e+00  8.36191500e-02  -2.43405957e+00   4.62511060e-01
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  • $\begingroup$ +1 but please put your script in a code block. Most people will not click on your link, since we don't know whether or not it leads to a dangerous website. $\endgroup$
    – Nike Dattani
    Apr 28 at 1:16
  • $\begingroup$ It is possible that you can get different values for absolute energies depending on the software that you use. That's why relative energies are important. $\endgroup$
    – Hemanth Haridas
    Apr 28 at 2:33
  • $\begingroup$ @HemanthHaridas Thanks. How is relative energy different conceptually? Sorry, I'm new to this. And can we extract that value from QE output file? $\endgroup$
    – Yonatan Kurniawan
    Apr 28 at 4:14
  • $\begingroup$ Lets say that you are comparing two structures: say graphene and hexagonal boron nitride. What you can do is optimize the geometries for both these at same level of theory, and then extract the energies. Now you can find the energy of one material relative to the other by taking the difference in their energies. $\endgroup$
    – Hemanth Haridas
    Apr 28 at 4:45
  • 1
    $\begingroup$ @YonatanKurniawan Please do not add google drive links. Reasons for this are listed here: mattermodeling.meta.stackexchange.com/questions/393/…. Instead paste the content of your file inline, inside a code block using a ''' ''' .You can also find instructions on how to handle files with more than 30000 characters in the link. $\endgroup$
    – Vandan Revanur
    Apr 28 at 7:29

1 Answer 1

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If there is no special care taken to parametrize different DFT codes in the same way, it is expected that the total energies from these codes differ.

Most DFT codes distinguish between energetically low lying core electrons confined to a small region around the atomic nucleus and valence electrons that are more involved in the interactions between atoms. In pseudopotential codes like Quantum Espresso or VASP the core electrons are replaced by a potential that leads to smooth wave functions of the valence electrons. This implies that for comparable total energies identical pseudopotentials have to be used. In all-electron codes, such as LAPW codes, besides the valence electrons also the core electrons are treated within the DFT scheme. But here it is also important for comparable total energies to have identical core-valence separations between the codes, because the degree of relativistic description between core electrons and valence electrons typically differs. Of course, the energy also depends on the choice of the approximation to the exchange-correlation functional.

While the total energy is sensitive to all these different aspects, energy differences are not, at least not in a significant way.

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  • $\begingroup$ Does this mean that the implementation of PBE in VASP might be different than the implementation of PBE in QE? $\endgroup$
    – Yonatan Kurniawan
    Apr 28 at 16:41
  • $\begingroup$ No, PBE in QE and VASP should be the same, though there may be differences in numerical details which should not be of relevance here. The PBE functional is well defined in the paper J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865. Please note that there are several other functionals with very similar names, e.g., revPBE, RevPBE, PBEsol. For parametrizations of the LDA functional there may be additional relativistic corrections beyond the paper in which they were suggested. $\endgroup$
    – Gregor Michalicek
    Apr 28 at 17:15
  • $\begingroup$ I wanted to make clear that the total energies from different xc functionals are not comparable. When you talk about an xc functional, it is typically an approximation to the real xc functional of Kohn-Sham DFT. PBE is a so-called Generalized Gradient Approximation to this functional. $\endgroup$
    – Gregor Michalicek
    Apr 28 at 17:21
  • $\begingroup$ I see. Thanks for the explanation. So, if the goal is to generate data for training an interatomic potential, I assume the quantity used would be the absolute energy. In this case, how do we know if the DFT-generated energy value is accurate enough? $\endgroup$
    – Yonatan Kurniawan
    Apr 28 at 18:41
  • 1
    $\begingroup$ The answer is very complete, the total energy is strongly dependent on the pseudopotential used. Reason why an interatomic potential should be made with Cohesive energy (by subtracting the atomic energy) not the total or absolute energy. If you use the cohesive energy for your potential, the same level of theory should match approximately no matter the code used. $\endgroup$
    – M06-2x
    Apr 28 at 18:50

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