Hyperpolarizability of the C60 fullerene cluster

Motivated by a discrepancy of five orders of magnitude between three different hyperpolarizability measurements on the CGO fullerene, we calculated the optical response of this cluster using a tight-binding Hamiltonian and compared the results to those for a benzene molecule. Our Hamiltonian reproduces the linear polarizability and hyperpolarizability of benzene reasonably well. For C60, our calculations of the bare polarizability agree only with two of the optical response measurements and indicate that the corresponding linear and nonlinear response of CGO is much larger than that of C6H6. We find that screening effects decrease this difference strongly, and also reduce the calculated hyperpolarizability of CGO to a value which is two orders of magnitude below the favored measurements. PACS: 42.65.An; 36.40. +d; 71A5.Gm in [8J. In an attempt to clarify the situation for these interesting systems [9], we have calculated the optical response of an isolated C60 cluster. Since this is not easy even for simple molecules, we first verified the validity of our approach by applying the same computational techniques to the benzene molecule which is well understood. Let us consider an isolated C60 molecule in the electric field ifj'. The induced dipole moment p is given (to the lowest three orders) by