We present a novel methodology which allows rigorous quantum calculation of the inelastic neutron scattering (INS) spectra of a heteronuclear diatomic molecule confined inside a nanoscale cavity of an arbitrary shape. This generalizes the approach recently developed by us for the quantum simulation of the INS spectra of nanoconfined homonuclear diatomics. The key distinguishing feature of our approach is the use of the fully coupled 5D translation-rotation (TR) energy levels and wave functions as the initial and final states of the INS transitions. The computed INS spectra embody the full complexity of the quantum TR dynamics of the guest heteronuclear molecule in the anisotropic confinement and are therefore highly realistic. Utilizing this methodology, we compute at several temperatures the INS spectra of HD molecule in the small cage of the structure II clathrate hydrate, which are in very good overall agreement with the experimental INS spectra. (C) 2013 Elsevier B. V. All rights reserved.