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 [rho(u)(omega)] of harmonic modes with imaginary frequencies in liquids; these are also referred to as unstable modes. The relation between the frequency integral of [rho(u)(omega)], 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.