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Lattice Dynamics of Solid Cubane within the Quasi-Harmonic Approximation

Solid cubane, which is composed of weakly interacting cubic molecules, exhibits many unusual and interesting properties, such as a very large thermal expansion and a first-order phase transition at T$_{p}$=394 K from an orientationally-ordered phase of R$\bar{3}$ symmetry to a {\it non-cubic} disordered phase of the same symmetry with a volume expansion of 5.4%, among the largest ever observed. We study the lattice dynamics of solid cubane within the quasi-harmonic and rigid-molecule approximation to explain some of these unusual dynamical properties. The calculated phonon density of states, dispersion curves and thermal expansion agree surprisingly well with available experimental data. We find that the amplitude of thermally excited orientational excitations (i.e. librons) increases rapidly with increasing temperature and reaches about 35$^{\rm o}$ just before the orientational phase transition. Hence, the transition is driven by large-amplitude collective motions of the cubane molecules. Similarly the amplitude of the translational excitations shows a strong temperature dependence and reaches one tenth of the lattice constant at T=440 K. This temperature is in fair agreement with the experimental melting temperature of 405 K, indicating that the Lindemann criterion works well even for this unusual molecular solid.