The quantal translation-rotation (TR) states of the (p-H-2)(4)@5(12)6(4) and (o-D-2)(4)@5(12)6(4) hydrate clathrate sII inclusion compounds have been computed by nuclear-orbital/configuration-interaction methods. The model of these compounds in a rigid, high-symmetry 5(12)6(4) cage is treated in detail. The low-energy TR level structures of both isotopomers within this model are found to consist of states that can be readily described in terms of a small number of single-H-2 and double-H-2 excitation modes. The use of the high-symmetry results to facilitate the calculation and interpretation of (p-H-2)(4) and (o-D-2)(4) TR states in low-symmetry physically realizable 5(12)6(4) cages is also reported. (C) 2013 AIP Publishing LLC.