Low bath densities

For a large particle in a fluid at liquid densities, there are collective hydro-dynamic contributions to the solvent viscosity r, such that the Stokes-Einstein friction at zero frequency is In Section III.E the model is extended to yield the frequency-dependent friction. At high bath densities the model gives the results in terms of the force power spectrum of two and three center interactions and the frequency-dependent flux across the transition state, and at low bath densities the binary collisional friction discussed in Section III C and D is recovered. However, at sufficiently high frequencies, the binary collisional friction term is recovered. In Section III G the mass dependence of diffusion is studied, and the encounter theory at high density exhibits the weak mass dependence. 

Collision-induced vibrational excitation and relaxation by the bath molecules are the fundamental processes that characterize dissociation and recombination at low bath densities. The close relationship between the frequency-dep>endent friction and vibrational relaxation is discussed in Section V A. The frequency-dependent collisional friction of Section III C is used to estimate the average energy transfer jjer collision, and this is compared with the results from one-dimensional simulations for the Morse potential in Section V B. A comparison with molecular dynamics simulations of iodine in thermal equilibrium with a bath of argon atoms is carried out in Section V C. The nonequilibrium situation of a diatomic poised near the dissociation limit is studied in Section VD where comparisons of the stochastic model with molecular dynamics simulations of bromine in argon are made. The role of solvent packing and hydrodynamic contributions to vibrational relaxation are also studied in this section. 

This has the low friction (low bath density) limit of k(- -j g j , and at high friction gives, upon rearrangement, the exact result for diffusion in a field of force [23] ... 

At very low bath densities the dissociation rate of a pair of particles can be cast in terms of the rate of accumulation of energy up to a dissociation energy This is well-studied for unimolecular reactions in which the transition state is fixed, but for bimolecular reactions the complexity associated with angular momentum leads to complications Nevertheless, an assumption will be made that a threshold energy Q can be defined such that when E > Q dissociation may take place at a rate k (E), which depends only on the relative density of states of the reactSt and the transition state [3] The steady state dissociation rate is then given by... 

The treatment of diatomic recombination and dissociation using the theory of section IV has been previously applied, at least for impulsive collisions [21]. In the low bath density regime, an adiabatic correction factor C has been used [9] based on the form for B for an exponentially repulsive potential [26]. The important result was that the iodine recombination rate could be accounted for over the entire range of bath densities using as input the diatomic potentials and the atomic diffusion... 

The use of the effective potential V(R) - 2kX nR to describe encounter Hnd reaction dynamics has been developed, and applications to a variety of physical processes have been discussed. Further work especially in the low bath density regime, is required to clarify the use of the J-averaging procedure and to extend its use to polyatomic systems. The theory is simple to use and in many cases where reasonable models of the potential V(R ) can be made, a direct comparison of reaction rates can he made in both gas and liquid phases. 

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