The steady-state Greenʹs function method in unimolecular reactions. Generalization of the MFPT concept. I. Irreversible reactions Original Research Article

We investigate two forms of macroscopic kinetic equations for evaluation of different reaction rate constants for irreversible unimolecular reactions in liquids. The steady-state differential and integral equations for calculation of the rate constants were formulated. New forms of the Greenʹs function, the steady-state Greenʹs functions, convenient for calculation of the rate constant, were introduced and their physical meaning was established. The concept of the mean first passage time (MFPT) was generalized from the “MFPT to a point” to the definition of the “effective MFPT”. The effective MFPT was defined as the average time for particles to reach a region on the surface, rather than a point. Applications of the steady-state Greenʹs function method as well as the effective MFPT concept are shown for one- and two-dimensional potential surface reactions. The rate constant for the one- and two-dimensional harmonic oscillator and bistable potentials are presented for all barrier heights.