Microscopic and macroscopic polarization in C₆₀ fullerene clusters as calculated by an electrostatic interaction model

The dipole-dipole polarizability, α, and the second hyperpolarizability, γ, as well as the corresponding linear and third-order susceptibilities, χ⁽¹⁾ and χ⁽³⁾, have been calculated for C₆₀ fullerene clusters by a point-dipole interaction (PDI) model. The size dependences of a linear chain, a monolayer film, and a face-centered cubic crystal cluster have been investigated. It is found that the effects of the surrounding molecules on the molecular α and γ are large, in particular for the chain and the film because of the anisotropic surroundings, and that large clusters are required to obtain converged results. A localized PDI model gives the opportunity to divide α and γ into fragment contributions, and it is found that α and γ of molecules in the middle of the chain converge slower than the properties for the end molecules with respect to the length of the chain. Similar results are found for the monolayer film. Finally, χ^(a) and χ⁽³⁾ have been calculated by using a modified local-field theory including the induced dipole moments of the surrounding molecules explicitly. The corresponding refractive index and dielectric constant compare well with experiments. On the other hand, the comparison of χ⁽³⁾ with experiments is complicated by dispersion and vibrational contributions. Nonetheless, our value of χ⁽³⁾ is in good agreement with a recent quantum chemical calculation adopting a self-consistent reaction-field model.