title: From C60 to Infinity: Large-Scale Quantum Chemistry Calculations of the Heats of Formation of Higher Fullerenes.
abstract: 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 ΔfH per carbon = 722n(-0.72) + 5.2 kJ mol(-1) (n = the number of carbon atoms), which enables an estimation of ΔfH 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.
authors.affiliation: School of Chemistry, University of Sydney , Sydney, New South Wales 2006, Australia.|RIKEN Advanced Institute for Computational Science , 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan.
authors.forename: Bun
authors.initials: B
authors.lastname: Chan
authors.affiliation: RIKEN Advanced Institute for Computational Science , 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan.
authors.forename: Yukio
authors.initials: Y
authors.lastname: Kawashima
authors.affiliation: RIKEN Advanced Institute for Computational Science , 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan.
authors.forename: Michio
authors.initials: M
authors.lastname: Katouda
authors.affiliation: RIKEN Advanced Institute for Computational Science , 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan.
authors.forename: Takahito
authors.initials: T
authors.lastname: Nakajima
authors.affiliation: RIKEN Advanced Institute for Computational Science , 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan.
authors.forename: Kimihiko
authors.initials: K
authors.lastname: Hirao