# From
C_{60} to Infinity: Large-Scale Quantum
Chemistry Calculations of the Heats of Formation of Higher Fullerenes

dataset

posted on 10.02.2016, 17:51 by Bun Chan, Yukio Kawashima, Michio Katouda, Takahito Nakajima, Kimihiko HiraoWe have carried out large-scale computational
quantum chemistry
calculations on the K computer to obtain heats of formation for C

_{60}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 (C_{60}), 2683.4 ± 17.7 (C_{70}), 2862.0 ± 18.5 (C_{76}), 2878.8 ± 13.3 (C_{78}), 2946.4 ± 14.5 (C_{84}), 3067.3 ± 15.4 (C_{90}), 3156.6 ± 16.2 (C_{96}), 3967.7 ± 33.4 (C_{180}), 4364 (C_{240}) and 5415 (C_{320}) 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 Δ_{f}*H*per carbon = 722*n*^{–0.72}+ 5.2 kJ mol^{–1}(*n*= the number of carbon atoms), which enables an estimation of Δ_{f}*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.