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Aim:
I want to obtain a reasonably accurate ionization energy (or work function in other terms) for a 2-dimensional periodic material using the GW theory. I'm using Quantum Espresso and Yambo.

Doubt:
If I'd want to obtain $I_p$ (or $W$) from a Quantum Espresso DFT calculation, I would have to calculate the vacuum energy (from the average potential), and subtract this from the HOMO value. In the documentation of another software I'm using (AMS SCM), which only implements GW for molecular systems (G0W0 tutorial of SCM), it is stated that the resulting HOMO energy from a G0W0 calculation, $E_{GW}^{HOMO}$, is the negative of the ionization potential,$I_p$: $$ I_p = - E_{G_0W_0}^{HOMO} $$ However, they give no reference to this statement, and I couldn't find anything useful regarding Yambo or a general case.

The various tutorials of Yambo (e.g. this) 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 if the absolute values are WRT vacuum.

Is it a fundamental property of G0W0 that $E_{GW}^{HOMO} = -I_p$? If not, is it at least true for Yambo as well?

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  • $\begingroup$ @NikeDattani I'm not sure I agree with your edit. The main point of my question is indeed what you wrote, but the part where I asked about the Yambo code was also an important part, since that is the specific problem I'm facing. I agree with some of my questions being too specific to Yambo and slightly off-topic though. $\endgroup$
    – Neinstein
    Commented May 27, 2022 at 8:34
  • $\begingroup$ Please ask questions one at a time. The first question is whether or not "E = I" is a fundamental property of G0W0. If the answer is no, then you can ask another question such as "Is Yambo similar to SCM in that E=-I for G0W0?". The rest of the questions are totally on topic, but they need to be asked one at a time on this site. We have a one question per post policy here :) $\endgroup$ Commented May 28, 2022 at 3:33

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In the meantime, Daniele Varsano answered me on the Yambo forum. I quote him below:

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.

The zero-point of the GW energy in Yambo is thus not always the vacuum energy, that was an SCM-specific feature.

Link to the thread: http://www.yambo-code.eu/forum/viewtopic.php?p=11888#p11888

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    $\begingroup$ Indeed, the underlying reason is that in periodic systems (as those calculated by Quantum ESPRESSO) there is no exact formula for the "vacuum level", and the manual procedure you're following to determine it is difficult to automate (depends on the system, etc.). $\endgroup$ Commented May 27, 2022 at 16:01

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