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Translation-rotation states of H2
: New insights from a perturbation-theory treatment
S. Mamone, J. Y.-C. Chen, R. Bhattacharyya, M. H. Levitt, R. G. Lawler, A. J. Horsewill, T. Rõõm, Z. Bačić, and N. J. Turro, Coord. Chem. Rev. 255, 938 (2011).
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S. Mamone, “Theory and spectroscopy of dihydrogen endofullerenes,” Ph.D. thesis, University of Southampton, School of Chemistry, 2011.
M. Ge, U. Nagel, D. Hüvonen, T. Rõõm, S. Mamone, M. H. Levitt, M. Carravetta, Y. Murata, K. Komatsu, J. Y.-C. Chen, and N. J. Turro, J. Chem. Phys. 134, 054507 (2011).
M. Ge, U. Nagel, D. Hüvonen, T. Rõõm, S. Mamone, M. H. Levitt, M. Carravetta, Y. Murata, K. Komatsu, X. Lei, and N. J. Turro, J. Chem. Phys. 135, 114511 (2011).
A. J. Horsewill, S. Rols, M. R. Johnson, Y. Murata, M. Murata, K. Komatsu, M. Carravetta, S. Mamone, M. H. Levitt, J. Y.-C. Chen, J. A. Johnson, X. Lei, and N. J. Turro, Phys. Rev. B 82, 081410(R) (2010).
A. J. Horsewill, K. S. Panesar, S. Rols, J. Ollivier, M. R. Johnson, M. Carravetta, S. Mamone, M. H. Levitt, Y. Murata, K. Komatsu, J. Y.-C. Chen, J. A. Johnson, X. Lei, and N. J. Turro, Phys. Rev. B 85, 205440 (2012).
A. J. Horsewill, K. Goh, S. Rols, J. Ollivier, M. R. Johnson, M. H. Levitt, M. Carravetta, S. Mamone, Y. Murata, J. Y.-C. Chen, J. A. Johnson, X. Lei, and N. J. Turro, Phil. Trans. R. Soc. A 371, 20110627 (2013).
M. Xu, M. Jiménez-Ruiz, M. R. Johnson, S. Rols, S. Ye, M. Carravetta, M. S. Denning, X. Lei, Z. Bačić, and A. J. Horsewill, Phys. Rev. Lett. 113, 123001 (2014).
Throughout this paper we use “isotropic” to refer to any tensor invariant to rotation about any axis fixed to the C60 cage and passing through the center of that cage including all spherical tensors of rank 0.
R. N. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley-Interscience, New York, 1988).
This matches the λ-splitting behavior characterized for (n, l, j) = (1, 1, 1) of H2 in a spherically symmetric cavity. See Appendix B of Ref. 24.
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We report an investigation of the translation-rotation (TR) level structure of H2 entrapped in C60, 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 H2@C60 is decomposed into a sum over bipolar spherical tensors. A zeroth-order Hamiltonian, , 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 H2 center of mass (c.m.) from the cage center. The remaining terms in the potential are treated as perturbations. The eigenstates of , constructed to also account for the coupling of the angular momentum of the H2 c.m. about the cage center with the rotational angular momentum of the H2 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.
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