Quantum effects of translational motions in solid para-hydrogen and ortho-deuterium: anharmonic extension of the Einstein model

An anharmonic extension of the Einstein model is developed in order to describe the effect of translational zero point motion on structural and thermodynamic properties of para-H-2 and ortho-D-2 crystals in the zero temperature limit. Accordingly, the molecules carry out large amplitude translational motions in their matrix cage, which are formed by the frozen environment of all other molecules. These translations lead from the molecular equilibrium positions via the harmonic to the anharmonic domain of the potential energy surface. The resulting translational distributions are roughly isotropic, and they have approximately Gaussian shapes, with rather broad full widths at half-maximum, FWHM(para-H-2/ortho-D-2) = 1.36/1.02 angstrom. The translational zero point energies induce expansions of the crystals, in nearly quantitative agreement with experimental results. Furthermore, they make significant contributions to the sublimation energies and zero pressure bulk moduli. These quantum effects decrease with heavier molecular masses. The corresponding isotope effects for ortho-D-2 compared to para-H-2 are confirmed by application of the model to Ar crystals. The results imply consequences for laser induced reaction dynamics of dopants with their host crystals.