## Abstract

This chapter deals with computational and theoretical support to fullerene/nanocarbon research needed for interpretations, rationalizations, and generalizations of experimental results. In particular, predictions of various nanocarbon stabilities, or even populations, based on quantum-chemical and statistical-mechanical methods, are surveyed. The calculations are, with respect to high temperatures in fullerene electric-arc syntheses, frequently based on the Gibbs energy. Considerable thermal effects on the relative isomeric and nonisomeric populations thus revealed in the theoretical treatments originate, on molecular level, in a complex interplay between rotational, vibrational, electronic, relative potential-energy, symmetry, and chirality factors. The considered treatments are built upon a presumption of the (inter-isomeric) thermodynamic equilibrium; however, some kinetic and catalytic aspects are also included. The survey is focused on empty fullerenes, metallofullerenes, clusterfullerenes, and nonmetal endohedrals. The covered quantum-chemical treatments are the semiempirical, ab initio Hartree-Fock, density-functional theory, and perturbation approaches. The calculations have already yielded a reasonable computation-observation agreement for the isomeric systems with empty C_{76} till C_{96} cages, and mostly also when applied to metallofullerenes. This relatively large tested set supports the belief in still wider applicability of the Gibbs-energy calculations to basically all classes of nanocarbons. This chapter is complementary to this volume chapter Theoretical Prediction of Fullerene Reactivity.

Original language | English (US) |
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Title of host publication | Handbook of Fullerene Science and Technology |

Publisher | Springer Nature |

Pages | 111-179 |

Number of pages | 69 |

ISBN (Electronic) | 9789811689949 |

ISBN (Print) | 9789811689932 |

DOIs | |

State | Published - Jan 1 2022 |

Externally published | Yes |

## Keywords

- Clusterfullerenes
- DFT and ab initio calculations
- Fullerenes
- Gibbs-energy evaluations
- Isomeric and nonisomeric relative stabilities
- Kinetic control and catalysis
- Metallofullerenes

## ASJC Scopus subject areas

- General Biochemistry, Genetics and Molecular Biology
- General Engineering