### Abstract

We report an investigation of the translation-rotation (TR) level structure of H_{2} entrapped in C_{60}, in the rigid-monomer approximation, by means of a low-order perturbation theory (PT). We focus in particular on the degree to which PT can accurately account for that level structure, by comparison with the variational quantum five-dimensional calculations. To apply PT to the system, the interaction potential of H_{2}@C_{60} is decomposed into a sum over bipolar spherical tensors. A zeroth-order Hamiltonian, Ĥ0, is then constructed as the sum of the TR kinetic-energy operator and the one term in the tensor decomposition of the potential that depends solely on the radial displacement of the H_{2} center of mass (c.m.) from the cage center. The remaining terms in the potential are treated as perturbations. The eigenstates of Ĥ0, constructed to also account for the coupling of the angular momentum of the H_{2} c.m. about the cage center with the rotational angular momentum of the H_{2} about the c.m., are taken as the PT zeroth-order states. This zeroth-order level structure is shown to be an excellent approximation to the true one except for two types of TR-level splittings present in the latter. We then show that first-order PT accounts very well for these splittings, with respect to both their patterns and magnitudes. This allows one to connect specific features of the level structure with specific features of the potential-energy surface, and provides important new physical insight into the characteristics of the TR level structure.

Original language | English (US) |
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Article number | 084310 |

Journal | Journal of Chemical Physics |

Volume | 145 |

Issue number | 8 |

DOIs | |

State | Published - Aug 28 2016 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

_{2}in C

_{60}: New insights from a perturbation-theory treatment.

*Journal of Chemical Physics*,

*145*(8), [084310]. https://doi.org/10.1063/1.4961650