  A model study of the singlet excitons in the C60 molecule with emphasis on
the Coulomb interaction between excited electron and hole leads to a physical
understanding of the interaction effects on the absorption spectra and to a new
identification of the forbidden excitons in the third-harmonic generation
spectra. These conclusions may be tested experimentally on the model
predictions related to the optical Kerr effect. The model shows that, with
sufficiently strong interatomic than onsite interaction, a T_{2G} exciton could
have very low energy or become unstable against the closed-shell ground state.
Properties of these interesting cases beyond the C60 are briefly examined.
