Accurate density-functional calculations on large systems

Efforts to compute accurate all-electron density-functional energies for large molecules and clusters using Gaussian basis sets are reviewed and their use in fullerene science described. The foundation of this effort, variational fitting, is described first. When discovered experimentally, C-60 was naturally assumed to be particularly stable, but local-density-functional calculations showed that C-60 is quite unstable relative to the higher fullerenes and graphene (a single sheet of graphite). In addition to raising questions about the relative abundance of the various fullerenes, this work conflicted with the then state-of-the-art density-functional calculations on crystalline graphene. Now high accuracy molecular and band structure calculations are in fairly good agreement with each other and experiment. These calculations clearly demonstrate that each of the 12 pentagons, which are necessary to close a fullerene, is best viewed as a rather high-energy, more than 2 eV, defect in a graphene sheet. The effect of the heptagon, the second most common defect in fullerene materials, is described. Most recently, we have developed accurate, variational gradient-corrected forces for use in geometry optimization of clusters and in molecular-dynamics simulations of friction. The gradient-corrected optimized geometry of C-60 is given. (C) 1997 John Wiley & Sons, Inc.