Efficient quantum-chemical geometry optimization and the structure of large icosahedral fullerenes

Geometry optimization is efficient using generalized Gaunt coefficients, which significantly limit the amount of cross differentiation for multi-center integrals of high-angular-momentum solid-harmonic basis sets. The geometries of the most stable C240, C540, C960, C1500, and C2160 icosahedral fullerenes are optimized using analytic density-functional theory, which is parameterized to give the experimental geometry of C60. The calculations are all electron, the orbital basis set includes d functions and the exchange-correlation-potential basis set includes f functions. The largest calculation on C2160 employed about 39000 basis functions.