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Unified theory of reversible target reactions

We discuss two fundamental reversible diffusion influenced reactions: (i) A+B⇌C and (ii) A+B⇌C+D. In the pseudo-unimolecular case, we prove that reaction (i) is a special case of (ii), which thus constitutes a unified reversible problem of multiparticle kinetics. For static A and C (the “target” limit), we suggest to treat this problem as follows. First we generalize the Smoluchowski theory to reaction (ii). In Laplace space, we combine this with a power-law theory, determining the combination coefficient so that the unified theory reduces correctly in all known limits. We also show how to rewrite it in the time domain, with the generalized Smoluchowski theory as the leading term. Comparison with Brownian simulations shows near perfect agreement for both versions of our theory under all conditions.