Non-additivity of polarizabilities and van der Waals C6 coefficients of fullerenes

We present frequency-dependent polarizabilities and C6 dipole-dipole dispersion coefficients for a wide range of fullerene molecules including C60, C70, C78, C80, C82, and C84. The static and dynamic polarizabilities at imaginary frequencies are computed using time-dependent Hartree-Fock, B3LYP, and CAM-B3LYP ab initio methods by employing the complex linear polarization propagator and are subsequently utilized to determine the C6 coefficients using the Casimir-Polder relation. Overall, the C60 and C70 average static polarizabilities α(0) agree to better than 2% with linear-response coupled-cluster single double and experimental benchmark results, and the C6 coefficient of C60 agrees to better than 1% with the best accepted value. B3LYP provides the best agreement with benchmark results with deviations less than 0.1% in α(0) and C6. We find that the static polarizabilities and the C6 coefficients are non-additive, and scale, respectively, as N(1.2) and N(2.2) with the number of carbon atoms in the fullerene molecule. The exponent for C6 power-dependence on N is much smaller than the value predicted recently based on a classical-metallic spherical-shell approximation of the fullerenes.