Unstable instantaneous normal modes and diffusion in supercooled liquids

At supercooled temperatures, liquid fluidity requires barrier crossing on the multidimensional potential energy surface or landscape. However, most equilibrium quantities are then dominated by configurations close to the local minima and do not contain information about the barriers. Thus, they are not indicated as the basis of a theory for long-time dynamics, specifically, for the self-diffusion constant, D(T). By contrast, the unstable instantaneous normal modes (INMs) are well-defined equilibrium properties with contributions only from configurations with some downward curvature of the potential, primarily, regions above the inflection points and the barriers. They are uniquely well suited to describe long-time dynamics, and the results of pursuing that idea are described herein: (1) The well developed and successful INM theory of self-diffusion. (2) The theory and functional form of the unstable density of states, which contains information about the topography of the landscape, a significant factor in the nature of supercooled dynamics. (3) A random energy model and the soft potential model provide simplification and add additional insight. (4) Despite the focus on dynamics, the configurational entropy is expressed in terms of the unstable INM, and the heat capacity has unstable INM contributions.