Non-Rigid Treatment of Interactions Between C₆₀ Molecules

Abstract

Atom-atom van der Waals interaction energies are compared between bimolecular clusters of C₆₀ and circumcoronene, a model of graphite, with the aid of molecular mechanics. The minimum in the potential energy curve of the former is shallower and higher than the latter. Average equilibrium distance (3.08 Å) in the bimolecular cluster C₆₀–C₆₀ agrees well with the experimental value (2.96 Å). Equilibrium configurations of the C₆₀–C₆₀ cluster contain quite a few inter-cage atom-pairs in the repulsive region. Analysis of molecular as well as electronic structure in the closest possible approach under stringent conditions indicate that C₆₀ molecule is highly resilient ball.

Notes

This value is larger than graphite (2.7 × 10¹² cm²/dyne) and diamond (0.18): Fischer, J. E.; Heiney, P. A.; McGhie, A. R.; Romanow, W. J.; Denenstein, A. M.; McCauley, J. P. Jr.; Smith, A. B. III, Science 1991, 252, 1288.

MOPAC version 6.01 by J. J. P. Stewart was obtained from the Japan Chemistry Program Exchange, c/o Japan Association for International Chemical Information, Nakai Bldg., 6–25–4 Honkomagome, Bunkyo-ku, Tokyo 113, program No. P049.

In these two-step calculations, the total energy did not change significantly, but the atomic energy gradients leveled off.

Small overestimation of the equilibrium distances in both clusters from those in C₆₀ crystal and graphite, respectively, is caused by the inadequacy of our models.

Each C₆₀ molecule is surrounded by twelve molecules in the fee crystals. Experimental ΔH°(s) of C₆₀ crystals=54.6±1.7 kcal/mol (Diogo, H. P.; da Piedade, M. E. M.; Dennis, T. J. S.; Hare, J. P.; Kroto, H. W.; Taylor, R.; Walton, D. R. M. J. Chem. Soc., Faraday Trans. 1993, 89, 3541), 56±5 kcal/mol (Steele, W. V.; Chirico, R. D.; Smith, N. K.; Billups, W. E.; Elmore, P. R.; Wheeler, A. E. J. Phys. Chem. 1992, 96, 4731).

The reported elongation of C-C bonds in C₆₀ crystals at 5K^{6, 7} was not reproduced in our model, but MM3 responded to the opposite direction. In fact, one cannot expect MM3 to respond to such a change, because the variable electronegativity self-consistent field informations obtained during the π-SCF calculations are not fed back to the intermolecular van der Waals interaction potential. AMI responded positively to the elongation effect, but only insignificantly.

The experimental R value is computed from the cell constant (14.0408 Å) of the P_a3 space group reported in a communication.⁶ This cell constant is misquoted in its full account.⁷