Solid hydrogen lattice dynamics

A scheme as described here is indispensable for a quantum dynamical treatment of strongly delocalized systems, such as solid hydrogen (van Kranendonk, 1983) or the plastic phases of other molecular crystals. We have shown, however (Jansen et al., 1984), that it is also very suitable to treat the anharmonic librations in ordered phases. Moreover, the RPA method yields the exact result in the limit of a harmonic crystal Hamiltonian, which makes it appropriate to describe the weakly anharmonic translational vibrations, too. We have extended the theory (Briels et al., 1984) in order to include these translational motions, as well as the coupled rotational-translational lattice vibrations. In this section, we outline the general theory and present the relevant formulas for the coupled... 

More recently, interest in the lattice vibrations of molecular solids has centered around the elucidation of intermolecular potential functions. If a pair potential is assumed, it can be tested by calculating the observables by application of the appropriate lattice dynamics. Dows (1962) was the first to attempt a calculation of lattice vibrational frequencies from an assumed potential. He treated solid ethylene and used a model which represented the pair interaction by repulsions between hydrogen atoms on neighboring molecules. 

In Section II of this review we discuss the different forms of classical lattice dynamical treatments which have been applied to molecular solids. The applications to specific systems and comparison of results with experiment will then be taken up. In Section III we give a short treatment of quantum lattice dynamics, which has been developed to deal with quantum solids as helium and hydrogen. Classical approaches in the harmonic approximation fail for these systems. In Section IV, intensities of infrared and Raman spectra in the lattice vibration region are discussed. A group theoretical appendix has been added for the reader who is not familiar with this aspect. 

Acetanilide, and some of its isotopomers, have been studied by INS spectroscopy [56-58]. The dispersion curves of the fully deuterated material have been measured by coherent INS [59]. A comprehensive analysis of acetanilide in the solid state was carried out with molecular dynamics simulations [57]. This includes all the lattice modes, as shown in Fig. 10.27 The simulations suggested that the barrier to the methyl torsion was enhanced when the peptide group is hydrogen-bonded and that this was a through-bond polarization effect. The methyl torsion was... 

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