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8. At the time of submission, the author was made aware of parallel work conducted by Z. Bačić and coworkers [“General selection rule in the inelastic neutron scattering spectroscopy of a diatomic molecule confined inside a near-spherical nanocavity,” J. Phys. Chem. Lett. (in press)] in which the general selection rule of Sec. III is also derived—albeit via a different, non-group-theory avenue.
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21. Technically, as per Sec. II, this group is rather than Ih; however, permutation symmetry plays no direct role in the INS selection rule, and will therefore be ignored in this section.
22. This is just the ml = 0 state, Yl0.

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Recently [M. Xu , J. Chem. Phys. , 064309 (2013)], an unexpected selection rule was discovered for the title system, contradicting the previously held belief that inelastic neutron scattering (INS) is not subject to any selection rules. Moreover, the newly predicted forbidden transitions, which emerge only in the context of coupled H translation-rotation (TR) dynamics, have been confirmed experimentally. However, a simple physical understanding, e.g., based on group theory, has been heretofore lacking. This is provided in the present paper, in which we (1) derive the correct symmetry group for the H@C TR Hamiltonian and eigenstates; (2) complete the INS selection rule, and show that the set of forbidden transitions is actually much larger than previously believed; and (3) evaluate previous theoretical and experimental results, in light of the new findings.


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