Polarization waves and van der Waals cohesion ofC60fullerite

An approach based on the concept of polarization waves is developed for the computation of the van der Waals cohesive energy of ${\mathrm{C}}_{60}$ fullerite. The dynamical polarizability properties of the ${\mathrm{C}}_{60}$ molecule are simulated by an empirical model consisting of a spherical dielectric shell of finite thickness. The shell material is an isotropic continuum with a dielectric function designed to exhibit the large σ-plasmon resonance observed in all forms of solid carbon in the vacuum ultraviolet around 20–30 eV. The eigenmodes of the polarization fluctuations on the hollow-molecular model consist of multipolar surface plasmons of angular momentum l. In the solid, the quasistatic interaction between the surface plasmons on different molecules creates multipolar polarization waves. Their dispersion relations are calculated throughout the first Brillouin zones of the fcc and hcp lattices, incorporating high values of the angular momentum. Strong mixing of the successive angular momenta occurs, particularly for low l values. The attractive part of the cohesive energy of the crystal is obtained from the zero-point energy of the polarizaton waves. With values of the shell parameters adjusted to reproduce ultraviolet-spectroscopic data, the van der Waals binding energy is found to be of order 2 eV per molecule and depends rather sensitively on the assumed static polarizability of the shell. No significant difference is found between the cohesion of the two fcc and hcp compact lattices at any multipolar order. The exact polarization-wave cohesive energy is compared to the approximate result obtained by summing the pairwise-additive attractions between two identical molecular shells. The comparison indicates that the multipolar terms of higher l’s are crucial in both computations and, as a consequence, that the many-body, nonadditive terms make a relatively weak contribution to the cohesion. The repulsive part of the interactions in the close-contact areas between molecules, which is to be added to the present van der Waals energy, is responsible for the lattice stability and for the orientational ordering of the molecules at low temperature.