Electronic energy levels in semiconductor nanocrystals: A Wannier function approach

We present a flexible and computationally efficient scheme for calculating electronic eigenstates of semiconductor nanocrystals using Wannier functions. With this method, we compute the band gap of CdS nanocrystals and compare our calculations with experiment. This approach also enables us to study the dependence of the gap on nanocrystal shape. By investigating spherical, cubical, and tetrahedral nanocrystals, we show that the gap is sensitive to the total number of atoms in a nanocrystal but not to their arrangement. Our theoretical analysis gives justification and clarification to the band-structure discretization method.