Equilibrium radial distribution

In this equation g(r) is the equilibrium radial distribution function for a pair of reactants (14), g(r)4irr2dr is the probability that the centers of the pair of reactants are separated by a distance between r and r + dr, and (r) is the (first-order) rate constant for electron transfer at the separation distance r. Intramolecular electron transfer reactions involving "floppy" bridging groups can, of course, also occur over a range of separation distances in this case a different normalizing factor is used. 

In the conventional Debye-Huckel treatment the equilibrium radial distribution function for a pair of reactants g(r) is simply equal to exp(-w/RT) with w given by (15)... 

Strength). At dilute concentrations, the probability of a three-body interaction is small. Therefore, the equilibrium radial distribution fiinc-tiong(r) is independent of concentration to a first approximation. Under these circumstances, the hard sphere potential is given by... 

As discussed in Chap. 4, under equilibrium conditions the function fi becomes a gaussian or maxwellian distribution function for the molecular velocities, and g becomes an equilibrium radial distribution function, i.e.. 

For moderately dense systems, say v<0.49, at which a first-order phase transition from a random to order collisional gas is first possible (Adler and Wainwright 1957), the complete pair distribution function for a colliding pair is assumed to be the product of the single particle distribution function of each sphere, evaluated at its center, and a factor gQ that incorporates the influence of the volume occupied by the spheres on their collision frequency. This factor is the equilibrium radial distribution function, evaluated at the point of contact. It is given as a function of v by Carnahan and Starling (1970) as... 

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