How can I find the binding energy for exciton (optical gap) with VASP?

What is the best way to find the binding energy for exciton using VASP? I have heard about the method of calculating it through the dielectric tensor with local field effects and effective masses, but I'm not sure. The computational resources do not allow me to perform the GW-BSE calculations. Thank you in advance for your help.

• To my knowledge, this is not accessible through Kohn-Sham DFT, unfortunately. GW-BSE is what is generally used. And also, the exciton binding energy is equal to the difference between the electronic and optical band gap. Feb 5, 2021 at 18:03

1 Answer

The model you are describing corresponds to a Wannier-Mott exciton and the binding energy is approximated by:

$$\tag{1} E_{\mathrm{B}}=\frac{\mu}{\epsilon^2_{\infty}}R,$$

where $$\mu$$ is the reduced mass of the electron and hole, $$\epsilon_{\infty}$$ is the high frequency dielectric constant, and $$R$$ is the Rydberg constant. You can in principle construct all necessary parameters from a VASP calculation.

This model is appropriate for materials with a large dielectric response that leads to weak electron-hole interactions and large excitons spanning multiple primitive cells. If you have a system with poor dielectric screening (e.g. an organic semiconductor), then excitons are strongly bound and highly localized, and this model will not provide a good description.

• Circling back to the main question, how can you access the dielectric function without a BSE calculation, as OP posted? Asking because I am not aware of such a method. Feb 5, 2021 at 18:59
• @Xivi76 I am not sure I understood that this was the question, but in any case, one can calculate the dielectric properties of a material at the single-particle level. Another question is whether the results will be useful. Here is the VASP wiki link: vasp.at/wiki/index.php/Dielectric_properties_of_SiC Feb 5, 2021 at 19:20
• Interesting, thank you. @ProfM Feb 5, 2021 at 21:29
• Add answer to ProfM. To read the supplementary of following paper: doi.org/10.1021/jacs.6b09645 Apr 11, 2021 at 0:41