Computing the relative gas-phase populations of C60 and C70: Beyond the traditional ΔHf,298o scale

Zdeněk Slanina, Xiang Zhao, Noriyuki Kurita, Hitoshi Gotoh, Filip Uhlík, Jerzy M. Rudziński, Kee Hag Lee, Ludwik Adamowicz

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Computations and experiments have shown that the relative heat of formation (i.e., the heat of formation per carbon atom) of C70 is lower than of C60. Moreover, various computations suggest that this is actually a general trend among fullerene cages. The relationship is particularly important for gas-phase fullerenes. Experiments have shown that C60 is typically more populated than C70 when produced in high-temperature gas-phase synthesis. It is not immediately obvious how to reconcile those two terms, or whether the relative heats of formation and the relative populations are in conflict or in agreement. This article deals with this problem, treating it as a general task of relative stabilities of gas-phase clusters of different dimensions (i.e., nonisomeric clusters) under different types of thermodynamic equilibria. The results are then applied to C60 and C70 and point out that the conventional standard pressure of 1 atm is considerably different from actual fullerene-synthesis conditions. Apparently, we should expect considerably lower cluster pressures in carbon-arc synthesis. At 1 atm, C70 is more populated than C60, but at the conditions of a saturated carbon vapor the stability order is reversed in favor of C60 so that an agreement with experiment is obtained already within the thermodynamic treatment. The pressure effects are modeled using the MNDO, AM1, PM3, and SAM1 quantum-chemical semi-empirical methods as well as the available experimental data. The computations consistently show that, if the pressure effects are considered, C60 becomes more populated than C70. Relationships of the thermodynamic treatment to more sophisticated but impractical kinetic analysis are also discussed.

Original languageEnglish (US)
Pages (from-to)216-221
Number of pages6
JournalJournal of Molecular Graphics and Modelling
Issue number2
StatePublished - Apr 2001


  • Gibbs function
  • Relative heats of formation
  • Relative populations of fullerenes
  • Semiempirical methods
  • Stability measures

ASJC Scopus subject areas

  • Spectroscopy
  • Physical and Theoretical Chemistry
  • Computer Graphics and Computer-Aided Design
  • Materials Chemistry


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