Pentagon adjacency as a determinant of fullerene stability

Abstract

Optimisation of geometries of all 40 fullerene isomers of C₄₀, using methods from molecular mechanics and tight-binding to full abinitio SCF and DFT approaches, confirms minimisation of pentagon adjacency as a major factor in relative stability. The consensus predictions of 11 out of 12 methods are that the isomer of lowest total energy is the D₂ cage with the smallest possible adjacency count, and that energies rise linearly with the number of adjacencies. Quantum mechanical methods predict a slope of 80–100 kJ mol^-1 per adjacency. Molecular mechanics methods are outliers, with the Tersoff potential giving a different minimum and its Brenner modification a poor correlation and much smaller penalty.