I am confused about the calculation of the charge defect formation energy equation with these two terms (from figure below):

  1. $\Delta V$: alignment term, and
  2. $E_{corr}$: correlation term.

How can I calculate these two terms by using VASP package?

enter image description here


1 Answer 1


First, the energy correction term, $E_{corr}$. It arises due to presence of periodic boundary conditions (defects are spuriously repeated) and of background charge compensation (hidden from the user). There are several correction schemes, but all of them requires the knowledge of the dielectric constant of the system:

Second, potential alignment term (PA, $\Delta V$). Never seen such, looks like a compensation of imperfectness of DFT band energies (in particular, VBM).

UPD: formula from Lany and Zunger suitable for calculation

$E_{corr} \approx \frac{2}{3} \frac{\alpha_M q^2} {\varepsilon L}$,

where $L$ is the size of the cell (in Angstrom), $q$ - charge (in e), $\varepsilon$ - dielectric constant. Resulted energy is in eV.

  • 1
    $\begingroup$ +1 but if I understood correctly, the OP asked about some implementations (how to calculate the defect formation energy, not the theoretical description of the calculation method). In that case, PyCDT and doped are just two of the codes that automate this process of finding each term of the defect formation energy and works with VASP. There are others code too such as Spinney. $\endgroup$ Nov 12, 2023 at 12:09
  • $\begingroup$ @AbdulMuhaymin if you could provide your comment as an answer along with the theoretical background raised by Leon, then that would be great, thank you! $\endgroup$ Nov 13, 2023 at 3:34
  • $\begingroup$ thanks for the point, @AbdulMuhaymin. Added equation for calculations which we used in our study (differs in length units from Lany and Zunger). I have not used the mentioned software, agree that answer mentioned them would be nice! $\endgroup$
    – Leon A
    Nov 25, 2023 at 10:04

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