Polarizabilities and van der Waals C₆ coefficients of fullerenes from an atomistic electrodynamics model: Anomalous scaling with number of carbon atoms

The van der Waals C₆ coefficients of fullerenes are shown to exhibit an anomalous dependence on the number of carbon atoms N such that C₆ ∝ N^2.2 as predicted using state-of-the-art quantum mechanical calculations based on fullerenes with small sizes, and N^2.75 as predicted using a classical-metallic spherical-shell approximation of the fullerenes. We use an atomistic electrodynamics model where each carbon atom is described by a polarizable object to extend the quantum mechanical calculations to larger fullerenes. The parameters of this model are optimized to describe accurately the static and complex polarizabilities of the fullerenes by fitting against accurate ab initio calculations. This model shows that C₆ ∝ N^2.8, which is supportive of the classical-metallic spherical-shell approximation. Additionally, we show that the anomalous dependence of the polarizability on N is attributed to the electric charge term, while the dipole–dipole term scales almost linearly with the number of carbon atoms.