From small fullerenes to the graphene limit: A harmonic force-field method for fullerenes and a comparison to density functional calculations for Goldberg-Coxeter fullerenes up to C980

We introduce a simple but computationally very efficient harmonic force field, which works for all fullerene structures and includes bond stretching, bending, and torsional motions as implemented into our open-source code Fullerene. This gives accurate geometries and reasonably accurate vibrational frequencies with root mean square deviations of up to 0.05 Å for bond distances and 45.5 cm(-1) for vibrational frequencies compared with more elaborate density functional calculations. The structures obtained were used for density functional calculations of Goldberg-Coxeter fullerenes up to C980. This gives a rather large range of fullerenes making it possible to extrapolate to the graphene limit. Periodic boundary condition calculations using density functional theory (DFT) within the projector augmented wave method gave an energy difference between -8.6 and -8.8 kcal/mol at various levels of DFT for the reaction C60 →graphene (per carbon atom) in excellent agreement with the linear extrapolation to the graphene limit (-8.6 kcal/mol at the Perdew-Burke-Ernzerhof level of theory).