Normal-mode analysis of liquid-state dynamics

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Abstract
Harmonic normal-mode analysis is applied to Lennard-Jones (LJ) liquids. The configuration-averaged density of (vibrational) states is obtained via numerical eigenanalysis of the force-constant matrices appropriate to an ensemble of liquid configurations; the configurations are generated by computer simulation. The contribution of unstable modes is included and plays a crucial role in the analysis. It is argued that the density of states contains information which may be used to construct theories of liquid-state dynamics. The argument is pursued at two levels. First, it is demonstrated that a glance at the density of states conveys a powerful, intuitive understanding of several aspects of the dynamics. Second, a theory of the self-diffusion constant is constructed which may be regarded as a preliminary attempt to base systematic transport theory upon normal-mode quantities.