  We present a symmetry-based calculation of the electronic structure of a
compound semiconductor quantum dot (QD) in the sp^3s* tight-binding model
including the spin-orbit interaction. The Hamiltonian matrix is diagonalized
exactly for CdTe QD sizes up to 60 {\AA}. The surface dangling bonds are
passivated by hydrogen through a careful analysis of the density of states and
wave functions. The calculated size dependence of the energy gap shows a
reasonable agreement with the available experimental data. Our symmetry
analysis indicates that, in contrast with a reported prediction of the
three-band effective-mass model, the fundamental interband transition remains
dipole-allowed in CdTe nanocrystals.
