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

Theoretical expressions are presented, at various levels of approximation, for the density of states <ρu(ω)≳ of harmonic modes with imaginary frequencies in liquids; these are also referred to as unstable modes. The relation between the frequency integral of <ρu(ω)≳, which is the fraction of unstable modes fu and the barrier crossing Boltzmann factor for self-diffusion is clarified. A new relation between the potential energy of the supercooled liquid and fu 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.