Inelastic neutron scattering spectrum of H₂@C₆₀ and its temperature dependence decoded using rigorous quantum calculations and a new selection rule

In the supramolecular complex H₂@C₆₀, the lightest of molecules, H₂, is encapsulated inside the most highly symmetric molecule C₆₀. The elegance and apparent simplicity of H ₂@C₆₀ conceal highly intricate quantum dynamics of the coupled translational and rotational motions of the guest molecule in a nearly spherical nanoscale cavity, which embodies some of the most fundamental concepts of quantum mechanics. Here we present the first rigorous and highly accurate quantum calculations of the inelastic neutron scattering (INS) spectra of this prototypical endohedral fullerene complex and their temperature dependence. The calculations enable complete assignment of the recently reported experimental INS spectra of H₂@C₆₀ measured at several temperatures. We also derive a new and unexpected selection rule for the INS spectroscopy of H₂ in a near-spherical confinement, which explains why the INS transitions between certain translation-rotation eigenstates of H₂ in C₆₀ have zero intensity and do not appear in the spectra.