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We present a detailed study of the electronic properties of CdSe nanocrystals in the absence and presence of a dielectric medium. The electronic structure of the nanocrystal is modeled within the framework of the empirical pseudopotential method. We use a real-space grid representation of the wave function, and obtain the eigenvalues and eigenstates of the one-electron Hamiltonian using a slightly modified version of the filter-diagonalization method. The band gap, density of states, chargedoi:10.1063/1.478431 fatcat:zgwtlneh3bh6vmnzuc6xpgprci