From C60 to Infinity: Large-Scale Quantum Chemistry Calculations of the Heats of Formation of Higher Fullerenes

We have carried out large-scale computational quantum chemistry calculations on the K computer to obtain heats of formation for C60 and some higher fullerenes with the DSD-PBE-PBE/cc-pVQZ double-hybrid density functional theory method. Our best estimated values are 2520.0 ± 20.7 (C60), 2683.4 ± 17.7 (C70), 2862.0 ± 18.5 (C76), 2878.8 ± 13.3 (C78), 2946.4 ± 14.5 (C84), 3067.3 ± 15.4 (C90), 3156.6 ± 16.2 (C96), 3967.7 ± 33.4 (C180), 4364 (C240) and 5415 (C320) kJ mol–1. In our assessment, we also find that the B3-PW91-D3BJ and BMK-D3­(BJ) functionals perform reasonably well. Using the convergence behavior for the calculated per-atom heats of formation, we obtained the formula Δf H per carbon = 722n –0.72 + 5.2 kJ mol–1 (n = the number of carbon atoms), which enables an estimation of Δf H for higher fullerenes more generally. A slow convergence to the graphene limit is observed, which we attribute to the relatively small proportion of fullerene carbons that are in “low-strain” regions. We further propose that it would take tens, if not hundreds, of thousands of carbons for a fullerene to roughly approach the limit. Such a distinction may be a contributing factor to the discrete properties between the two types of nanomaterials. During the course of our study, we also observe a fairly reliable means for the theoretical calculation of heats of formation for medium-sized fullerenes. This involves the use of isodesmic-type reactions with fullerenes of similar sizes to provide a good balance of the chemistry and to minimize the use of accompanying species.