Band gap corrections for molecules and solids using Koopmans theorem and Wannier functions

We have proposed a method for correcting the Kohn-Sham eigen energies in the density functional theory (DFT) based on the Koopmans theorem using Wannier functions. The method provides a general approach applicable for molecules and solids for electronic structure calculations. It does not have any adjustable parameters and the computational cost is at the DFT level. For solids, the calculated eigen energies agree well with the experiments for not only the band gaps, but also the energies of other valence and conduction bands. For molecules, the calculated eigen energies agree well with the experimental ionization potentials and electron affinities, and show better trends than the traditional Delta-self-consistent-field (?SCF) results.