Why are harmonic baths models useful

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  

We can also take another route. Obviously, we can repeat the development that lead to Eq. (4.12) for any harmonic system. We can define such a system by 

these concepts are found to be useful and their usefulness stems from timescale considerations. We will repeatedly see that for many chemical processes the relevant timescales for environmental interactions are short. This does not mean that the system sees its environment for just a short time, but that the dynamics is determined by a succession of short time interactions. If subsequent interactions are uncorrelated with each other, each can be treated separately and for this treatment a harmonic bath picture might suffice. Two conditions need to be satisfied for this to be a good approximation  

In the instantaneous normal mode picture, the density should be high enough and the temperature low enough so that the solvent stays not too far from its equilibrium configuration and therefore the contribution of modes of imaginary frequencies can be disregarded. 

The timescale of environmental (solvent) motions that determine the solvent dynamical effect on the process of interest should be shorter than the timescale on which the solvent can be described as a harmonic medium. 

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