Translational-rotational coupling in strongly anharmonic molecular crystals with orientational disorder

TLDR: In this article, a lattice dynamics sheme is developed for handling large amplitude librational motions or hindered rotations, anharmonic translational vibrations and translation-rotation coupling in molecular crystals.

Abstract: We have developed a new lattice dynamics sheme for handling large amplitude librational motions or hindered rotations, anharmonic translational vibrations and translation-rotation coupling in molecular crystals. This formalism is based on expanding the intermolecular potential in the molecular displacements and including the cubic and higher terms, while retaining its exact anisotropy. This potential is first used to construct mean field states for the molecular translations and hindered rotations, and next to solve the equations of motion for the crystal in the random phase approximation (RPA), which takes into account the correlations between the molecular motions as well as translation-rotation coupling. It is illustrated that this scheme gives very accurate results for the ordered a and 7 phases of solid nitrogen, while It also yields, for the first time, a quantum dynamical description of the molecular motions in the plastic s phase and a fairly accurate α—s transition temperature.

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Figure 1 shows the structures of these modifications,

Fig. 2 . — Orientational probability distributions of the molecular axes in a. (Fig. 2a) and 7 (Fig. 2b) nitrogen. Contours of cons tant probability for the molecule in the origin, calculated in the mean field model, are plotted as functions of the polar angles

Fig. 3. — Orientational probability distribution of the molecular axes for the delocalized (Fig. 3a) and localized (Fig. 3b) mean field states in /3-nitrogen. Figure 3a applies to both molecules in the unit cell. Figure 3b Is drawn for one molecule in the unit cell; the other molecule in the celi is rotated over 0 = 180°. The distribution does not change qualitatively up to (at least) T = 70 K ; it just becomes slightly wider with increasing tempe rature. Reading of the contour plot as in Figure 2,

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