Formation energy including size effect correction

[asiyeh_shokri2]

Hello,

I need to calculate formation energy for my structure, but I dont know how to do the size correction part and charge correction part.
I appreciate any help.

Best regards,
Asiyeh

[jonathan_lahnsteiner2]

Dear asiyeh_shokri2,

I am not sure if I can answer your question properly because I am lacking enough information
about what system your are studying or what kind of formation energy you want to calculate.

In general, to do size and charge corrections in finite periodic systems the standard way is to compute
the quantity of interest for several different box sizes and then extrapolate this results to an
infinity large box size.
I hope this helps. If you need more advice please send your input files or supply me
with more information what you want to do exactly.

All the best

Jonathan

[asiyeh_shokri2]

Thank you for your reply.
I am looking for the formula below:
ΔEf(d;q)=G(d;q) −G(bulk)− ∑iniμi+q(ϵVBM+EF)+Ecorr

where ΔEf(d;q) represents the defect formation energy, G(d;q) and G(bulk) are the free energies of the defective and pristine supercells, respectively, ni are the amount of atoms added or removed from the host material in order to create the defect, μi are the chemical potentials of these atoms, ϵVBM is the valence band maximum eigenvalue, EF is the Fermi level, which can range within the material band gap, and Ecorr is an energy term that corrects for finite-size effects originating from the use of the supercell approach.

I know the theory, but this correction I dont know how to calculate. there are also some packages like Sppiney but I have no experience using them and I am looking for help. About the incar tags and the way to calculate this part.

Best,
Asiyeh

[jonathan_lahnsteiner2]

Dear asiyeh_shokri2,

In principle you have to compute the finite size corrections once for your defect structure
and once for your pristine structure. The term you call Ecorr contains two terms. The finite size corrections arising in your defect structure and the finite size correction in your bulk structure.
To compute finite size corrections, you compute the quantity which is in your case the total energy for different system sizes. Then you plot the so obtained energies versus the inverse system size. This curve can be extrapolated to an infinite system size. Then you compute your formation energy for some chosen system size. The finite size correction for the bulk system (E(bulk)) would then be the difference of the energy of the infinitely large system minus the total energy of the system you are using for the formation energy computation. Then you compute the finite size correction for your defect structure E(d;q) completely analogously. From these two values you can compute the finite size correction of your formation energy as Ecorr = E(d;q) - E(bulk).
Maybe it is also a good approximation to say that the finite size effects of the bulk and defect structure cancel each other out. But you should try this first.
I hope this helps!


All the best Jonathan