We discuss the lattice relaxation upon doping of fullerens C60 and C70
, using a Longuet-Higgins-Salem model and we calculate the A(g)-type v
ibrational modes. We then exploit the VEH (valence effective Hamiltoni
an) method to study the electronic structures of the fullerenes. The v
alence electronic DOS (densities of states) are calculated to be in ex
cellent agreement with synchrotron photoemission experiments. We apply
the VEH/SOS (Sum-Over-States) approach to study the nonlinear optical
response of C60 and C70.