Normal mode analysis of the velocity correlation function in supercooled liquids

Madan, B.; Keyes, T.; Seeley, G.
May 1991
Journal of Chemical Physics;5/15/1991, Vol. 94 Issue 10, p6762
Academic Journal
Further results are given on the application of harmonic normal mode analysis to liquid state dynamics. A new configuration space-normal mode theory is presented for the velocity correlation function. Here, the hopping rate, ωv, of the phase point among the local minima of the potential in configuration space plays a key role. A new relation is given connecting the unstable mode lobe, 〈ρ(ω)>u, of the averaged density of states to the topology of the potential in configuration space. This relation is used to express the hopping rate in terms of 〈ρ(ω)>u. With the hopping rate in hand, the velocity correlation function is calculated from the theory in supercooled Lennard-Jones argon at unit density and over the temperature range T=150 K down to T=80 K, where the theory predicts a glass transition. Agreement between theory and computer simulation is excellent. The predicted hopping rates are also in good agreement with the simulation results of Stillinger and Weber.


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