On the application of instantaneous normal mode analysis to long time dynamics of liquids

Abstract

While the applicability of instantaneous normal mode (INM) analysis of liquids to short time dynamics is in principle obvious, its relevance to long time dynamics is not clear. Recent attempts by Keyes and co-workers to apply information obtained from this analysis to self-diffusion in supercooled liquid argon is critically analyzed. By extending the range of frequencies studied we show that both imaginary and real branches of the density of modes are represented better, for large ω, by ln[ρ(ω)]∼ω2/T than by ln[ρ(ω)]∼ω4/T2 as advocated by Keyes [J. Chem. Phys. 101, 5081 (1994)]. However, since in the relevant frequency range the two fits almost overlap, the numerical results obtained by Keyes, showing good agreement with the simulation results for self-diffusion in supercooled liquid argon, remain valid even though implications for the frequency dependence of the barrier height distribution change. We also explore other possibilities for extracting information from the INM analysis: (1) The density of ‘‘zero force modes,’’ defined as the distribution of normal modes found at the bottom or top of their parabolic potential surfaces, can be computed with no appreciable additional numerical effort. This distribution provides a better representation than the total density of modes for the normal mode distribution at well bottoms and at saddles, however, we find that it makes little difference in quantitative analysis. (2) We suggest that the ratio ρu(ω)/ρs(ω) between the density of modes in the unstable and stable branches provide an estimate for the averaged barrier height distribution for large ω. Using this estimate in a transition state theory calculation of the average hopping time between locally stable liquid configurations and using the resulting time in a calculation of the self-diffusion coefficient yields a very good agreement with results of numerical simulation.