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.

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Reversible diffusion-influenced pseudo first order reaction A+B ⇌C with static particles in excess is rigorously studied. Under most general assumptions, the problem of the reversible reaction kinetics is reduced to the consideration of the effective irreversible reaction studied by conventional methods. In the framework of the average t-matrix approximation (ATA) we reproduce some results derived earlier and establish their applicability limits. Rigorous investigation of the kinetics behavior at long times shows that the t−3/2 law predicted earlier and reproduced by ATA has a different concentration-dependent amplitude. On the basis of diagrammatic summation, providing correct long-time asymptotics, a modified theory has been developed. The range of validity of the modified theory is much wider than that of ATA and similar theories.