Integral encounter theories of multistage reactions. I. Kinetic equations

Abstract

The matrix kinetic equations for multi-stage reactions in liquid solutions are derived using a newly developed original method based on a many-particle master equation. The method leads to an infinite hierarchy for vector correlation patterns that can be truncated two different ways. The simplest one reproduces the conventional Integral Encounter Theory (IET), while the other allows a general modification of the kernel, resulting in the matrix formulation of so called Modified Encounter Theory (MET). Unlike IET, MET accounts for all binary contributions and correctly restores the long-time asymptotics of bimolecular reactions. The matrix MET, applied in Part II to reversible reactions of inter-molecular energy transfer, significantly improves the results obtained with other methods.

Effect of an external field on the reversible reaction of a neutral particle and a charged particle in three dimensions. II. Excited-state reaction

“…However, the present results can be used to devise efficient Brownian dynamics for accurate numerical results. [42][43][44][45][46] When quantum mechanical effects are non-negligible, we can apply the quantum correction methods [47][48][49][50] to classical data from efficient Brownian dynamics simulations.…”

Contact and Distant Luminescence Quenching in Solutions

“…Such an obtained MET was shown to correct IET even better than the first multiparticle kernel (MPK1) theory [27], which at first corrected the false IET asymptote of quenching. However, Advances in Physical Chemistry 7 the authors of the MPK1 intuitively neglected some threeparticle correlations in comparison with others, while MET accounts explicitly for all of them [24,25]. An excellent analysis of the drawback in MPK1 and its consequences was recently presented by Ivanov [44].…”

“…To account for the higher ones by MET, one only has to modify the kernels of the integral equations. In [24,25] this was recommended to be done by the substitution of the generalized decay rates…”

“…Creation of MET extended IET to higher concentrations keeping its advantages in accounting for the reaction reversibility but eliminating some of the weaknesses demerits in the asymptotic description of the long time kinetics. The contemporary matrix versions of IET [14,15] and MET [24][25][26] allow considering reactions of any complexity and arbitrary number of internal electronic states of the reactants and products including their spin states.…”

Accumulation and Decay of Macroscopic Correlations in Elementary Reactions Kinetics

“…This method was successfully used in the derivation of kinetic equations of a wide class of chemical reactions [52][53][54][55][56][57][58][59][60] and in examining the applicability of the concepts of the Encounter Theory. 61,62 Now we briefly discuss the main steps of the method to show how the subsequent steps increase the accuracy of kinetic equations derived.…”