Spherical-shell model for the van der Waals coefficients between fullerenes and/or nearly spherical nanoclusters

Abstract

Fullerene molecules such as C60 are large nearly spherical shells of carbon atoms. Pairs of such molecules have a strong long-range van der Waals attraction that can produce scattering or binding into molecular crystals. A simplified classical-electrodynamics model for a fullerene is a spherical metal shell, with uniform electron density confined between outer and inner radii (just as a simplified model for a nearly spherical metallic nanocluster is a solid metal sphere or filled shell). For the spherical-shell model, the exact dynamic multipole polarizabilities are all known analytically. From them, we can derive exact analytic expressions for the van der Waals coefficients of all orders between two spherical metal shells. The shells can be identical or different, and hollow or filled. To connect the model to a real fullerene, we input the static dipole polarizability, valence electron number and estimated shell thickness t of the real molecule. Our prediction for the leading van der Waals coefficient C6 between two C60 molecules ((1.30 ± 0.22) × 105 hartree bohr6) agrees well with a prediction for the real molecule from time-dependent density functional theory. Our prediction is remarkably insensitive to t. Future work might include the prediction of higher-order (e.g. C8 and C10) coefficients for C60, applications to other fullerenes or nearly spherical metal clusters, etc. We also make general observations about the van der Waals coefficients.