Is the HOMO energy obtained from GW calculation always a value relative to the vacuum energy (-Ip)?

Aim:
I want to obtain a 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 SCM code (in the AMS package) works, I've tested it for isolated h-passivated hBN nanoparticles. However, the code does not implement GW for periodic systems, and I couldn't reach a convergent territories by increasing the nanoparticle size before running out of computer resources. Therefore, I turned to 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. On the other hand, the SCM documentation (specifically, the G0W0 tutorial) states 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.

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 $$E_{GW}^{HOMO} = -I_p$$, or is this specific to the SCM code?

If no, is it at least true for Yambo as well?

• @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. May 27 at 8:34
• 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 :) May 28 at 3:33

1 Answer

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 property.

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

• 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.). May 27 at 16:01