# Photoemission Spectra of Solids

I know that in non-periodic codes such as Gaussian the fluorescence spectra of molecule can be calculated in the following manner.

1. Relax geometry
2. TD-DFT to find excited state
3. Relax excited state geometry
4. TD-DFT again to find new excited state level
5. Vertical emission is step 4 excited state to step 4 ground state

Is this possible to do for bulk / nanoparticle materials in some analogous manner for photoemission spectra? If so, what do we learn in the process?

• For the calculation of photoemission spectra you would typically use DFT together with a code implementing the GW approximation to many-body perturbation theory. Such spectra and many optical properties are natural outputs of such codes. Commented Oct 31, 2020 at 9:02
• Does GW give emission spectra? I have yet to see that Commented Oct 31, 2020 at 13:05
• Well, there is an overview article: frontiersin.org/articles/10.3389/fchem.2019.00377/full But of course, the question is which features of such a spectrum can be calculated in this way. There are contributions from physical processes that are not covered by the GW approximation. Maybe the person who actually answers your question can discuss this. Commented Oct 31, 2020 at 16:19
• Why not run steps 1-5 in a plane-wave basis set with a periodic code? Commented Jan 22, 2021 at 20:54
• I don't actually know of any periodic codes allowing for excited states to be optimized geometrically. That wouls be a good answer if you know otherwise. Commented Jan 23, 2021 at 3:23

## 1 Answer

This is a complicated question for which I do not have a full answer. However, here are some thoughts:

1. Excited state relaxation. In solids, the calculation of excited states typically requires the many-body GW approximation for quasi-particle energies and the solution of the Bethe-Salpeter equation for excitonic properties. The calculation of forces, a prerequisite to perform geometry optimizations, is not standard in these approaches. This paper by Ismail-Beigi and Louie discusses an approach to calculate forces in the excited state, but despite being almost 20 years old, there is not much in terms of follow-up. My best guess as to why there is not much work in this direction is because excitations are typically screened rather effectively in solids, so geometry changes in the excited state tend to be smaller than in molecules.

2. Out-of-equilibrium BSE. If one ignores geometry changes in the excited state, then it is possible to study recombination using the out-of-equilibrium Bethe-Salpeter equation. In this paper [disclaimer: I am a co-author] this is used to calculate phonon-assisted luminescence in an indirect band gap semiconductor.