Multipole approach to orientational interactions in solidC60

We calculate electrostatic multipole moments of ${\mathrm{C}}_{60}$ up to l=18 using the quantum-mechanical charge distribution with icosahedral symmetry obtained from ab initio calculations. It is found that the second nonzero moment (l=10) is comparable to the first nonzero moment (l=6). The values of several low-order multipole moments are almost 10 times smaller than those found from the charge distribution of recently proposed potential models and thus the actual Coulomb interaction between ${\mathrm{C}}_{60}$ molecules is much smaller than previously predicted. Much better agreement with calculated multipoles is obtained from a model which introduces point charges at the center of hexagonal and pentagonal plaquettes, following the physical arguments of David et al. [Nature 353, 147 (1991)]. We show that a multipole expansion including only l=6 and 10 moments can predict the potential due to a ${\mathit{C}}_{60}$ molecule at distances R≥2${\mathit{R}}_0$ within an error of about 5%, where ${\mathit{R}}_0$ is the radius of the ${\mathrm{C}}_{60}$ molecule. At distances less than R<3/2${\mathit{R}}_0$ the multipole expansion is qualitatively incorrect even if one includes the terms up to l=18, indicating the importance of short-range quantum effects at these distances. The Coulomb interaction we obtain predicts two nearly degenerate, locally stable configurations for solid ${\mathrm{C}}_{60}$ (1) a metastable structure with Pa3 symmetry and setting angle φ=23.3°, close to experimentally observed value, and (2) a global minimum with the Pa3 structure but a setting angle φ=93.6°. We give physical arguments for expecting two such configurations and give a qualitative explanation for their near degeneracy. We conclude that a satisfactory intermolecular potential requires a first-principles calculation of the quantum-mechanical short-range repulsive interactions.