To predict the thermal conductivity of a dielectric or insulating material requires the phonon frequencies and lifetimes. Techniques for predicting these quantities have been proposed based in molecular dynamics simulation and lattice dynamics calculations. Here, two expressions for the phonon spectral energy density are described and applied to two test systems: Lennard-Jones argon and Stillinger-Weber silicon. One spectral energy density expression is derived from lattice dynamics theory, while the other uses only the atomic velocities from molecular dynamics simulation. We find that while the spectral energy density using only atomic velocities can predict the phonon frequencies, it is not generally able to predict the lifetimes due to terms omitted in the derivation.

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