  The optical excitations in C$_{60}$ and higher fullerenes, including isomers
of C$_{76}$, C$_{78}$, and C$_{84}$, are theoretically investigated. We use a
tight binding model with long-range Coulomb interactions, treated by the
Hartree-Fock and configuration-interaction methods. We find that the optical
excitations in the energy region smaller than about 4 eV have most of their
amplitudes at the pentagons. The oscillator strengths of projected absorption
almost accord with those of the total absorption. Next, off-resonant third
order susceptibilities are investigated. We find that third order
susceptibilities of higher fullerenes are a few times larger than those of
C$_{60}$. The magnitude of nonlinearity increases as the optical gap decreases
in higher fullerenes. The nonlinearity is nearly proportional to the fourth
power of the carbon number when the onsite Coulomb repulsion is $2t$ or $4t$,
$t$ being the nearest neighbor hopping integral. This result, indicating
important roles of Coulomb interactions, agrees with quantum chemical
calculations of higher fullerenes.
