The influence of the “cage” effect on the mechanism of reversible bimolecular multistage chemical reactions proceeding from different sites in solutions

Doktorov, A.B.

doi:10.1063/1.4961543

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…Our understanding of how the diffusive motion of the reactants influences kinetics started with the seminal work of Smoluchowski on irreversible reactions more than 100 years ago. The generalization to reversible diffusion-influenced reactions is a challenging many-body problem that has been attacked by many people from different directions using a variety of approaches. − For simple reactions like A + B ⇌ C and A + B ⇌ C + D, a consensus has been reached as to what is the simplest theory that (1) reduces to the rate equations of chemical kinetics when diffusion is fast, (2) is exact at short times and asymptotically (i.e., gives the correct amplitude of the power-law relaxation to equilibrium), and (3) is exact in the geminate limit (i.e., for the reversible reaction of an isolated pair of particles).…”

Section: Introductionmentioning

confidence: 99%

Theory of Diffusion-Influenced Reaction Networks

Gopich

Szabó

2018

J. Phys. Chem. B

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A formalism is developed to describe how diffusion alters the kinetics of coupled reversible association-dissociation reactions in the presence of conformational changes that can modify the reactivity. The major difficulty in constructing a general theory is that, even to the lowest order, diffusion can change the structure of the rate equations of chemical kinetics by introducing new reaction channels (i.e., modifies the kinetic scheme). Therefore, the right formalism must be found that allows the influence of diffusion to be described in a concise and elegant way for networks of arbitrary complexity. Our key result is a set of non-Markovian rate equations involving stoichiometric matrices and net reaction rates (fluxes), in which these rates are coupled by a time-dependent pair association flux matrix, whose elements have a simple physical interpretation. Specifically, each element is the probability density that an isolated pair of reactants irreversibly associates at time t via one reaction channel on the condition that it started out with the dissociation products of another (or the same) channel. In the Markovian limit, the coupling of the chemical rates is described by committors (or splitting/capture probabilities). The committor is the probability that an isolated pair of reactants formed by dissociation at one site will irreversibly associate at another site rather than diffuse apart. We illustrate the use of our formalism by considering three reversible reaction schemes: (1) binding to a single site, (2) binding to two inequivalent sites, and (3) binding to a site whose reactivity fluctuates. In the first example, we recover the results published earlier, while in the second one we show that a new reaction channel appears, which directly connects the two bound states. The third example is particularly interesting because all species become coupled and an exchange-type bimolecular reaction appears. In the Markovian limit, some of the diffusion-modified rate constants that describe new transitions become negative, indicating that memory effects cannot be ignored.

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