# Is there an energy gap correction factor that needs to be used in DFT calculations?

I am a beginner and have performed the DFT calculation in Quantum ESPRESSO for calculation of the direct and indirect bandgap of Silicon. I found the indirect bandgap to be 0.6551 eV. Now, I have several doubts:
1)Is this calculated indirect bandgap at room temp. or at 0K?
2)If it is at room temperature the indirect bandgap should be around 1.1 eV as from the literature. So is there any energy correction factor that has to be performed to calculate the actual band gap values?
Please, clarify my doubts.
Thanks!

I would like to add a few clarifications to Jack's answer:

1. Standard DFT calculations with fixed ionic positions are actually not even 0 K. A better way to describe them is that they are static lattice calculations. The difference between static lattice and 0 K is the contribution from quantum zero-point fluctuations. This contribution is generally small, particularly for heavy ions, but can also be sizeable. In the case of silicon, it changes the band gap by about 50 meV.
2. It is actually possible to include the role of temperature in the band gap of a semiconductor using DFT. There are two main contributions to this temperature dependence: thermal expansion and electron-phonon coupling. Both can be calculated using DFT (or beyond-DFT methods), and in the case of silicon you can find details in this paper [disclaimer: I am the author].

Is this calculated indirect bandgap at room temp. or at 0K?

• QE is based on the density functional theory (DFT). DFT is a ground-state (0K) theory and hence the calculated bandstructure is 0K.

If it is at room temperature the indirect bandgap should be around 1.1 eV as from the literature. So is there any energy correction factor that has to be performed to calculate the actual band gap values?

• First of all, the DFT with PBE functional will underestimate the bandgap of semiconducting materials, you can correct this by HSE06 calculation or GW calculation. Both HSE06 and GW can give you the bandgap values comparable to the experiment. The temperature effect can not be considered in the framework of DFT.
• Just want to add to this answer that there is no universal "correction factor" as I interpreted from the question. Different functionals have different band gap errors for different materials. HSE06 when used with the 'default' 0.25 mixing parameter of exact exchange can significantly overestimate band gap. Mixing factors can be optimized empirically or calculated self-consistently for a given material. Commented Sep 27, 2020 at 22:23