Unstable modes in liquids density of states, potential energy, and heat capacity

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Abstract
Theoretical expressions are presented, at various levels of approximation, for the density of states <ρ u (ω)≳ of harmonic modes with imaginary frequencies in liquids; these are also referred to as unstable modes. The relation between the frequency integral of <ρ u (ω)≳, which is the fraction of unstable modes f u and the barrier crossing Boltzmann factor for self‐diffusion is clarified. A new relation between the potential energy of the supercooled liquid and f u is derived. The averaged barrier energy/particle for diffusion enters this relation as a parameter and our consequent estimates of the barrier are in good agreement with existing estimates.