I'm running some SCF calculations in VASP, and when looking at the OUTCAR, I see that for each KPOINT there is a slightly different value for the HOMO/LUMO (looking at Band No. and Occupation values, where HOMO has an occupation of 2 and LUMO has an occupation of 0). Do I average the different HOMO/LUMO values of each KPOINT to get the HOMO/LUMO for the single point calculation or would that be inaccurate?


1 Answer 1


No, the HOMO is the highest energy eigenvalue for the corresponding band, across the Brillouin zone. It isn't technically a HOMO because it isn't a molecular orbital ("MO") it's a band, so what you're really looking for is the valence band maximum ("VBM"). If we could somehow use the exact exchange-correlation functional, DFT would give the correct VBM.

In the same way, the LUMO is the lowest energy eigenvalue for the corresponding band, across the Brillouin zone, and is more correctly called the conduction band minimum ("CBM"). Even the exact exchange-correlation functional doesn't get the correct CBM simply by reading off the Kohn-Sham eigenvalues, you need to use a more sophisticated method to get this (e.g. TD-DFT).

As a final note, even these DFT values are likely to be rather approximate because the SCF k-point set probably doesn't sample all of the symmetry points and paths in the system. You may be fortunate and have the VBM and CBM at the $\Gamma$-point, and used an odd k-point grid, but in general it's better to perform a band-structure calculation and sample all of the high-symmetry paths and points.

  • $\begingroup$ Thank you for the information. How would I be able to find the VBM/CBM for the system from a single point calculation? $\endgroup$
    – lzzard
    Jan 3 at 4:20
  • $\begingroup$ @Izzard you can't get it very precisely, in general, but the process is just to get the highest value of the top occupied band across the Brillouin Zone (VBM), and the lowest value of the bottom conduction band (CBM). $\endgroup$ Jan 5 at 14:57
  • $\begingroup$ @lzzard sorry, wrong tag in the previous comment! $\endgroup$ Jan 6 at 0:16

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