Fullerene Stability by Geometrical Thermodynamics

This work proves that stability of C-60 is a geometrical property of the thermodynamics of the system: a significant methodological advance since a detailed treatment of the energetics may be avoidable. This approach may be fruitful, not only for fullerenes but also for general problems of molecular stability and in other applications of conformational chemistry. For the non-chiral C-60, C-384, and the weakly-chiral C-28, C-76 and C-380 (of these, C-380 and C-384 are classed as unspirallable), Schlegel projections are used to show that these fullerenes can all be represented by pairs of spirals counter-propagating in anti-parallel (C2) symmetry. For C-60, the high symmetry is used to construct an analytical approximation for the spherical double-spirals, shown mathematically to be Maximum Entropy (MaxEnt) using the formalism of Quantitative Geometrical Thermodynamics (QGT). Therefore C-60 is necessarily stable. This MaxEnt stability criterion is general, depending only on the geometry and not the kinematics of the system. The sense and degree of chirality for C-76 and C-380 is also quantified using a Shannon entropy-based fragmentation metric.