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I am trying to do a DFT calculation of Oxygen atoms with the VASP code. My settings follow the official tutorial on the Oxygen atom of VASP. But it turns out the energy levels of the two spin components are very different, which is obviously wrong. My question is:

Why can't DFT describe the electronic configuration and energy level of a single atom? Is this issue related to the concept of "unrestricted-spin DFT"?

Here is the result:

 Fermi energy:        -7.3248173814

 spin component 1

 k-point     1 :       0.0000    0.0000    0.0000
  band No.  band energies     occupation
      1     -25.0682      1.00000
      2     -10.7441      1.00000
      3     -10.7433      1.00000
      4      -8.6436      1.00000
      5      -0.5792      0.00000
      6       1.8046      0.00000
      7       1.9955      0.00000
      8       2.0142      0.00000
 Fermi energy:        -7.3248173814

 spin component 2

 k-point     1 :       0.0000    0.0000    0.0000
  band No.  band energies     occupation
      1     -21.4031      1.00000
      2      -7.3891      1.00000
      3      -6.2821      0.00000
      4      -6.2806      0.00000
      5      -0.3297      0.00000
      6       1.9176      0.00000
      7       2.1797      0.00000
      8       2.4480      0.00000
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1 Answer 1

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I am unfamiliar with this exact tutorial but this looks fine to me, you have 4 electrons in one spin and 2 in the other, giving a net 2 unpaired electrons. This is correct when you look at the ground state of oxygen and is consistent with that tutorial page. I do not think there is any reason DFT cannot describe a single atom correctly, although molecular oxygen will be problematic (maybe you are thinking of this).

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  • $\begingroup$ but the band energies should be the same between two spin channels, the result aren’t as it should be. $\endgroup$
    – Jack
    May 8, 2022 at 5:42
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    $\begingroup$ Why do you think the energies should be the same given this is an unrestricted calculation? $\endgroup$
    – Ian Bush
    May 8, 2022 at 7:54
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    $\begingroup$ @Jack The band energies of the two spin channels are only equal when the net spin is zero, i.e. when the system respects time-reversal symmetry. Note that some textbooks may draw orbital diagrams in a way that alpha and beta orbital energy levels are the same even though the net spin is not zero, but strictly speaking this is an approximation. $\endgroup$
    – wzkchem5
    May 8, 2022 at 8:58
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    $\begingroup$ Why are you talking about bands where do you have a single atom? Bands are only meaningful for periodical structures. $\endgroup$
    – Camps ♦
    May 9, 2022 at 20:06
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    $\begingroup$ @Camps I agree with you conceptually and if we are being fully correct in terminology, however I think most people reading should understand these are orbital energies not bands. Maybe an edit to the original post clarifying terminology could be useful though. To be clear, VASP calls these band energies in the output so its up to the user to be aware band energies == orbital energies when the structure is not periodic $\endgroup$
    – Tristan Maxson
    May 9, 2022 at 23:02

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