Unstable modes in supercooled and normal liquids: Density of states, energy barriers, and self-diffusion

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Abstract
The unstable mode density of states 〈ρu(ω;T)〉 is obtained from computer simulation and is analyzed, theoretically and empirically, over a broad range of supercooled and normal liquid temperatures in the unit density Lennard‐Jones liquid. The functional form of 〈ρu(ω;T)〉 is determined and the ω, T dependence is seen to be consistent with a theory given by us previously. The parameters in the theory are determined and are related to the topological features of the potential energy surface in the configuration space; it appears that diffusion involves a low degree of cooperativity at all but the lowest temperatures. It is shown that analysis of 〈ρu(ω;T)〉 yields considerable information about the energy barriers to diffusion, namely, a characteristic ω‐dependent energy and the distribution of barrier heights, gν(E). The improved description of 〈ρu(ω;T)〉 obtained in the paper is used to implement normal mode theory of the self‐diffusion constant D(T) with no undetermined constants; agreement with simulation in the supercooled liquid is excellent. Use of a lower frequency cutoff on the contribution of unstable modes to diffusion, in an attempt to remove spurious contributions from anharmonicities unrelated to barrier crossing, yields the Zwanzig–Bassler temperature dependence for D(T). It is argued that the distribution of barriers plays a crucial role in determining the T dependence of the self‐diffusion constant.