Confirming a Predicted Selection Rule in Inelastic Neutron Scattering Spectroscopy: The Quantum Translator-Rotator H 2 Entrapped Inside C 60 Minzhong Xu, 1 Mónica Jiménez-Ruiz, 2 Mark R. Johnson, 2 Stéphane Rols, 2 Shufeng Ye, 1 Marina Carravetta, 3 Mark S. Denning, 3 Xuegong Lei, 4 Zlatko Bačić, 1,5,* and Anthony J. Horsewill 6,† 1 Department of Chemistry, New York University, New York, New York 10003, USA 2 Institut Laue-Langevin, BP 156, 38042 Grenoble, France 3 School of Chemistry, University of Southampton, Southampton SO17 1BJ, United Kingdom 4 Department of Chemistry, Columbia University, New York, New York 10027, USA 5 NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China 6 School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom (Received 15 August 2014; published 17 September 2014) We report an inelastic neutron scattering (INS) study of a H 2 molecule encapsulated inside the fullerene C 60 which confirms the recently predicted selection rule, the first to be established for the INS spectroscopy of aperiodic, discrete molecular compounds. Several transitions from the ground state of para-H 2 to certain excited translation-rotation states, forbidden according to the selection rule, are systematically absent from the INS spectra, thus validating the selection rule with a high degree of confidence. Its confirmation sets a precedent, as it runs counter to the widely held view that the INS spectroscopy of molecular compounds is not subject to any selection rules. DOI: 10.1103/PhysRevLett.113.123001 PACS numbers: 33.20.Sn, 61.05.fg, 61.48.-c, 67.80.ff The confinement of a light molecule such as H 2 inside a nanosize cavity results in the quantization of the transla- tional motions of the center of mass (c.m.) of H 2 , which couple to the quantized rotational degrees of freedom of the molecule. Inelastic neutron scattering (INS) spectroscopy is a powerful probe for investigating the highly quantum coupled translation-rotation (TR) dynamics of hydrogen molecules entrapped in the nanocavities of diverse host materials [1,2]. In particular, in recent years it has been used to probe in detail the TR dynamics of a hydrogen molecule encapsulated in the fullerene C 60 [3–5] and the azacyclic-thiacyclic open-cage fullerene [6], as well as in the cages of clathrate hydrates [7,8]. INS was also used to investigate the quantum rotation of H 2 O inside C 60 [9]. The remarkable power of INS stems from two distinctive features. One of them is the unusually large cross section for the incoherent neutron scattering from the hydrogen ( 1 H) nucleus [10], ∼15 times greater than for any other nucleus, including deuterium ( 2 H) [2], which makes INS a highly selective probe of the quantum dynamics of the entrapped hydrogen molecules. The other unique feature of INS is that neutrons, unlike photons, can induce nuclear spin transitions. This allows the observation of rotational Δj ¼ 1 transitions involving the interconversion between the nuclear spin isomers para-H 2 (total nuclear spin I ¼ 0, even rotational quantum numbers j ¼ 0; 2; …) and ortho- H 2 (total nuclear spin I ¼ 1, odd j ¼ 1; 3; …), which are forbidden in the optical, infrared, and Raman spectroscopy. The measured INS spectra contain a wealth of information about the quantum TR dynamics of the guest molecule and its anisotropic interactions with the host cage. However, complete and quantitative extraction of this encoded information is possible only with the help of theory capable of rigorously simulating the INS spectra in their full complexity. This essential prerequisite was met with the recent development of the sophisticated quantum method- ology for accurate calculations of the INS spectra, i.e., the energies and the intensities of the TR transitions, of a hydrogen molecule confined inside a nanoscale cavity of an arbitrary shape [11,12]. The treatment rigorously incorpo- rates the TR dynamics of the nanoconfined H 2 , yielding INS spectra with a uniquely high degree of realism. This has allowed reliable interpretation and assignment of the INS spectra measured for H 2 entrapped in C 60 [13] and in the cages of clathrate hydrates [14]. Selection rules play a central role in spectroscopy in general, determining whether transitions between certain pairs of states of a system are allowed or forbidden [15]. Knowing them is crucial for the correct interpretation and assignment of the experimental spectra. It has been taken for granted that the INS spectroscopy of discrete (aperiodic) molecular systems, including supramolecular complexes such as H 2 @C 60 , is not subject to any selection rules [1,2,16,17], in contrast to the optical, infrared (IR), and Raman, spectroscopies. The only known selection rules are the phonon symmetry selection rules established for the coherent INS of crystals [18], based on their space-group symmetry. We have challenged this widely held view recently [13], by deriving a new and entirely unexpected selection rule for the incoherent INS spectra of a H 2 molecule confined in a near-spherical nanocavity, such as that of C 60 (powdered sample), where the orbital angular PRL 113, 123001 (2014) PHYSICAL REVIEW LETTERS week ending 19 SEPTEMBER 2014 0031-9007=14=113(12)=123001(5) 123001-1 © 2014 American Physical Society