Velocity autocorrelation function , mode results

The barrier crossing dynamics is determined by the memory kernel K(c), and Russell and Sceats suggested that it be modeled such that it gave the same velocity autocorrelation function in the vicinity of the outer minimum Rq of K(R) as exjjected from a superposition of the damp>ed conformational normal modes of the polymer, j,J = 1, N — 1. The potential P(R) is expanded about Rq with a force constant ficoi, where coq is defined by an integral such as Eq. (7.20), but with the range of integration extended to infinity. The result is that... 

Consider Eq. (6.84). This result was obtained for a harmonic system of identical and equivalent atoms. We could however reverse our reasoning and define a vibrational spectrum for a dense atomic system from the velocity autocorrelation function according to Eq. (6.84). Since this function can be computed for all systems, including liquids and disordered solids, we may use (6.84) as a definition of a spectrum that may be interpreted as density of modes fimction for such media. We can then use it in expressions such as (4.33), and (6.92). Is this approach to dynamics in condensed phases any good ... 

The dynamics of different modes of molecular librations (hindered rotations) and intramolecular vibrations in supercritical water can now be analyzed in terms of velocity autocorrelation functions for the corresponding projections (Eqns. 22-27) (Kalinichev and Heinzinger 1992, 1995 Kalinichev 1993). The velocity autocorrelation functions calculated for the quantities Qi (Eqns. 25-27) are shown in Figure 19 for two extreme cases of high-density and low-density supercritical water. The Fourier transforms of these functions result in the spectral densities of the corresponding vibrational modes. They are shown in Figure 20 for the supercritical thermodynamic states listed in Table 5. 

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