The reversible reaction A+B = C in solution. A system-size expansion approach on the base of reactive many-particle diffusion equations

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Abstract
The diffusion‐influenced reaction A+B■C is reconsidered by using an approach which starts directly from the reactive many‐particle diffusion equations which govern the change in time of system states with a defined number of reactive particles. The classical problem is transformed into a more compact ‘‘quantum’’ one by using a second quantization procedure. In this way, by straightforward operator manipulations, exact state‐specific evolution equations can be derived. To prove the conditions for an approximate deterministic description of macroscopic systems, a system‐size expansion in the sense of van Kampen is applied to these equations. By approximating the triplet and quadruplet terms in the evolution equations, a rate equation, a Fokker–Planck equation for the particle number fluctuations, and an evolution equation for the AB‐pair distribution function can be derived which are consistent with one another. The results of this approach are compared with those of other recent studies including the stochastic approach I used in [Chem. Phys. 150, 187 (1991)].