Kinetic theory of bimolecular reactions in liquid. III. Reversible association–dissociation: A+B⇄C

A theoretical formalism based on the fully renormalized kinetic theory is applied to a diffusion-influenced pseudo-first order reaction kinetics of reversible association–dissociation $\mathrm{A+B\rightleftarrows C}$ including unimolecular decay processes. Linear response of the system, initially at equilibrium, to a thermal perturbation is examined and a rate kernel equation for the reactant concentrations is derived. The rate kernel has a hierarchical structure and the propagator appeared in the kernel expression is truncated by a disconnected approximation. When the unimolecular reactions are turned off, the response of the system not only shows the long-time power law of $t^{\text{−3/2}}$ but also displays the proper behavior over the whole time region in accordance with previous computer simulation results. Moreover, it is shown that the amplitude of the long-time behavior predicted by previous workers is modified by a certain correction factor $P$ which contains dynamical correlation effects. In this way, many-body complication inherent to the history of reactive pair creation is properly implemented in the description of the reversible kinetics. We compare the present theory with the other existing theories such as the rate equation, the superposition approximation, and the convolution approaches. In some limiting cases, results obtained from the present theory can be reduced to those from the existing theories.