### Abstract

Recent synthesis of the endohedral complexes of C_{70} and its open-cage derivative with one and two H_{2} molecules has opened the path for experimental and theoretical investigations of the unique dynamic, spectroscopic, and other properties of systems with multiple hydrogen molecules confined inside a nanoscale cavity. Here we report a rigorous theoretical study of the dynamics of the coupled translational and rotational motions of H _{2} molecules in C_{70} and C_{60}, which are highly quantum mechanical. Diffusion Monte Carlo (DMC) calculations were performed for up to three para-H_{2} (p-H_{2}) molecules encapsulated in C_{70} and for one and two p-H_{2} molecules inside C _{60}. These calculations provide a quantitative description of the ground-state properties, energetics, and the translation-rotation (T-R) zero-point energies (ZPEs) of the nanoconfined p-H_{2} molecules and of the spatial distribution of two p-H_{2} molecules in the cavity of C_{70}. The energy of the global minimum on the intermolecular potential energy surface (PES) is negative for one and two H_{2} molecules in C_{70} but has a high positive value when the third H_{2} is added, implying that at most two H_{2} molecules can be stabilized inside C_{70}. By the same criterion, in the case of C_{60}, only the endohedral complex with one H_{2} molecule is energetically stable. Our results are consistent with the fact that recently both (H _{2})_{n}@C_{70} (n = 1, 2) and H_{2}@C _{60} were prepared, but not (H_{2})_{3}@C_{70} or (H_{2})_{2}@C_{60}. The ZPE of the coupled T-R motions, from the DMC calculations, grows rapidly with the number of caged p-H_{2} molecules and is a significant fraction of the well depth of the intermolecular PES, 11% in the case of p-H_{2}@C_{70} and 52% for (p-H_{2})_{2}@C_{70}. Consequently, the T-R ZPE represents a major component of the energetics of the encapsulated H_{2} molecules. The inclusion of the ZPE nearly doubles the energy by which (p-H_{2})_{3}@C_{70} is destabilized and increases by 66% the energetic destabilization of (p-H_{2})_{2}@C _{60}. For these reasons, the T-R ZPE has to be calculated accurately and taken into account for reliable theoretical predictions regarding the stability of the endohedral fullerene complexes with hydrogen molecules and their maximum H_{2} content.

Original language | English (US) |
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Pages (from-to) | 9826-9832 |

Number of pages | 7 |

Journal | Journal of the American Chemical Society |

Volume | 132 |

Issue number | 28 |

DOIs | |

State | Published - Jul 21 2010 |

### ASJC Scopus subject areas

- Catalysis
- Chemistry(all)
- Biochemistry
- Colloid and Surface Chemistry

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## Cite this

_{70}: Quantum dynamics, energetics, maximum occupancy, and comparison with C

_{60}.

*Journal of the American Chemical Society*,

*132*(28), 9826-9832. https://doi.org/10.1021/ja103062g