How to obtain the total energy from GW calculations for defect formation energies?

Running Abinit Many-body theory
1

Dear Abinit community,

I am currently studying a Copper (Cu) impurity in a Silicon supercell using Abinit and Abipy. I have performed standard DFT calculations for different charge states (neutral, +1, -1). I have also run G0W0 calculations for these systems to correct the electronic structure.

Even though the wavefunctions remain identical to the Kohn-Sham ones, the fact that the eigenvalues are significantly shifted implies that the total energy should also change.

My goal now is to calculate the defect formation energy as a function of the Fermi level using these GW results. To do this using the standard thermodynamic formula, I need the total energy of the supercell for each charge state after the GW correction.

Could you please explain how I can extract or calculate this GW total energy etotal in Abinit/Abipy?

Getting the accurate formation energies at the GW level is a step for my workflow, as I need to know the most stable charge state to perform BSE (Bethe-Salpeter Equation) calculations on top of these GW results to simulate the Photoluminescence (PL) spectra of the Cu defect in Silicon.

Any guidance on how to get the etotal from my GW outputs would be highly appreciated.

Thank you in advance for your time and help!

Best regards,

gw.abi (5.0 KB)

2

Hi Jules,

In fact you don’t need GW total energies.
GW state energies are by definition quasiparticle energies which means that they are to be interpreted directly as total energy differences:

\epsilon^{GW}_\mathrm{HOMO} = E(q=0) - E(q=+1)

and

\epsilon^{GW}_\mathrm{LUMO} = E(q=-1) - E(q=0)

And this is precisely what you need when plotting the charge state stability as a function of the Fermi level.

Be careful that the GW quasiparticle energies are vertical energies, which means no relaxation.

If you want thermodynamic values, you need to account for the atomic relaxation as well.
Check out this review paper for instance:
https://doi.org/10.1002/pssb.201046094

Best,
Fabien

3

Hi Fabien,

Thank you very much for the quick answer and the reference.

Best regards, Jules