Wannier Koopmans method for band gap calculations of extended systems

We have developed a method to correct the density functional theory band gap problem, especially for extended systems. In this method, the Wannier functions are generated and the Hamiltonian is required to satisfy the Koopman theory (the total energy is linearly dependent on the occuption number) when a Wannier function is partially occupied. The resulting Hamiltonian gives a correction term for the Kohn-Sham eigen equation. This method can be considered as an extention of the delta DFT method to bulk systems. We have used this method to study common semiconductors, alkali halides, 2D materials, organic crystals, as well as oxides. We found in general, the accuracy of this Wannier Koopman method (WKM) is on a par with the GW results.
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