  The optical spectra of CdSe nanocrystals up to 55 A in diameter are analyzed
in a wide range of energies from the fine structure of the low-energy
excitations to the so-called high-energy transitions. We apply a symmetry-based
method in two steps. First we take the tight-binding (TB) parameters from the
bulk sp^{3}s^{*} TB model, extended to include the spin-orbit interaction. The
full single-particle spectra are obtained from an exact diagonalization by
using a group-theoretical treatment. The electron-hole interaction is next
introduced: Both the Coulomb (direct) and exchange terms are considered. The
high-energy excitonic transitions are studied by computing the electric dipole
transition probabilities between single-particle states, while the transition
energies are obtained by taking into account the Coulomb interaction. The fine
structure of the lowest excitonic states is analyzed by including the
electron-hole exchange interaction and the wurtzite crystal-field terms in the
exciton Hamiltonian. The latter is diagonalized in the single electron-hole
pair excitation subspace of progressively increasing size until convergence.
The peaks in the theoretical transition spectra are then used to deduce the
resonant and nonresonant Stokes shifts, which are compared with their measured
values in photoluminescence experiments. We find that the final results depend
on the crystal-field term, the relative size of the surface and the degree of
saturation of the dangling bonds. The results show a satisfactory agreement
with the available experimental data.

Mesoscale and Nanoscale Physics