Usually the GW Density Functional Theory (DFT) gives larger band gaps in semiconductors compared to the LDA and GGA methods. This seems to be related to the screened potential in GW, but it is not clear to me how.
The standard DFT (LDA & GGA) could not properly capture the exchange-correlation of a quantum system being investigated, it sort of lacks interaction/quantum property resulting to smaller gaps (inaccurate result in other words).
A better method that will give bigger gaps (closely accurate results/closer to experiments) should be performed. This is why we perform GW approximation.
GW approximation give a more accurate picture of band gaps (larger than LDA & GGA) largely from the nature of its solution. Typically, band gap materials requires solving the non-inhomogeneous differential equation (Time Dependent Schrodinger equation). GW properly handles this by employing a Green's function method. Further solving this we can obtain the:
- Dyson's Equation
- vertex corrections
- polarization function, and the
- dynamically screened potential.
None of this is implemented by the standard DFT (LDA & GGA). We could not attribute the accuracy of GW to a certain variable or term but rather to the METHOD.
You may consult the references below regarding the relevant equations.
Interaction/quantum property within exchange-correlation may involve electron-electron interaction, electron screening/shielding, electron-electron repulsion, electron-spin interaction, decoupling, etc.
Indeed the screening potential plays an important role in this calculation. Relative to experimental studies GGA and LDA tend to produce significant underestimations of band gap energies. This underestimation can be attributed to the inherent lack of charge derivative discontinuity in these approximations, as discussed in "The effects of copper doping on photocatalytic activity at (101) planes of anatase TiO2: A theoretical study".