Is the G0W0 HOMO energy calculated by Yambo a value relative to the vacuum energy (-Ip)?

Concerns issues with computing quasiparticle corrections to the DFT eigenvalues - i.e., the self-energy within the GW approximation (-g n), or considering the Hartree-Fock exchange only (-x)

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Godot11
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Is the G0W0 HOMO energy calculated by Yambo a value relative to the vacuum energy (-Ip)?

Post by Godot11 » Wed May 25, 2022 10:36 am

Aim:
I want to obtain reasonably accurate ionization energy (or work function in other terms) for a 2-dimensional hBN monolayer. The exact material does not matter much respective to the question, the point is it being a 2D periodic material.

Method:
The GW model, in general, gives a pretty accurate ionization potential. For an isolated molecule, the ADF code (in the SCM - AMS package, link) works well (I've tested it for isolated h-passivated hBN nanoparticles); However, the code does not implement GW for periodic systems, so I am trying to use Yambo.

Doubt:
If I were to obtain the ionization potential (or work function) from a Quantum Espresso DFT calculation, I would have to calculate the vacuum energy from the average potential far away from the slab/monolayer, and subtract this from the HOMO energy (or the Fermi level). On the other hand, the SCM documentation (specifically, their G0W0 tutorial) states that the resulting HOMO energy from a G0W0 calculation is already the negative of the ionization potential:

Ip = - HOMO_G0W0

However, they give no reference to this statement, and I couldn't find anything useful from an online research.

The various GW tutorials of Yambo (e.g. this one on bulk hBN) on G0W0 only use the GW energies to obtain the band gap value. This is a relative energy between two bands, so tells me nothing about if the absolute values are WRT vacuum.

Question(s):
  1. Is it a fundamental property of G0W0 that $E_{GW}^{HOMO} = -I_p$?
  2. If no, is it at least true for Yambo?
  3. If no, how should I get the corresponding vacuum energy for the Yambo result? Is the vacuum energy obtained from the DFT result unchanged for the GW result, or should I use some other method to calculate it?
Last edited by Godot11 on Wed May 25, 2022 11:11 am, edited 1 time in total.
Gergely Nagy
ELI-ALPS - Ultrafast Science Division - Computational and Molecular Science group (CAMS)
3 Wolfgang Sandner St., 6728 Szeged, Hungary
www.eli-alps.hu

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Daniele Varsano
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Re: Is the G0W0 HOMO energy calculated by Yambo a value relative to the vacuum energy (-Ip)?

Post by Daniele Varsano » Wed May 25, 2022 10:59 am

Dear Godot11,
please sign your post with your name and affiliation, this is a rule of the forum. You can do it once and for all by filling the signature in our user profile.

In Yambo, the zero of the energy is set at the valence band maximum (VBM). The GW will give you the correction to the corresponding KS eigenvalue.
If you want this value relative to the vacuum you will need to align it wrt the vacuum energy calculated by QE in the way you described, ie apply the QP correction to the work function you calculated with QE.

Best,
Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

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Godot11
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Re: Is the G0W0 HOMO energy calculated by Yambo a value relative to the vacuum energy (-Ip)?

Post by Godot11 » Wed May 25, 2022 11:17 am

Thanks for the useful information. In this case, I will proceed with the vacuum energy calculation from the DFT result, and subtract the value from Yambo's G0W0 energy.

Also thanks for the heads-up, I added my signature. :D
Gergely Nagy
ELI-ALPS - Ultrafast Science Division - Computational and Molecular Science group (CAMS)
3 Wolfgang Sandner St., 6728 Szeged, Hungary
www.eli-alps.hu

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