Accuracy Limits of the Generalized Gradient Approximation¶
Electronic Band Gap¶
When computations of the Electronic Band Gap are executed through Density Functional Theory, operated in conjunction with the Generalized Gradient Approximation (GGA), a systematic under-estimation of the band gap is to be expected. This is a well-known shortcoming of the GGA technique, and should be taken into account when following the procedure for calculating the band-gap of semiconducting materials.
Further modifications to the input files and settings to correctly predict the band gap are possible, but lie beyond the scope of the present discussion.
Hybrid functionals 1 are a class of approximations to the exchange–correlation energy functional in DFT that incorporate a portion of exact exchange energy from Hartree–Fock theory 2, with the rest of the exchange-correlation energy from other sources (ab-initio or empirical).
The GW Approximation¶
For the sake of this short introduction, it suffices to know that the GWapproximation is obtained using a systematic algebraic approach on the basis of Green function techniques, the most suitable approach for studying excited-state properties of extended systems. It constitutes an approximate expansion of the self-energy up to linear order in the screened Coulomb potential, which describes the interaction between the crystalline atoms. The implementation of theapproximation relies on a perturbative treatment starting from Density Functional Theory.