Barrierless reaction kinetics : Different distribution functions of relevant Brownian functionals

Abstract

We investigate different first passage properties of a barrierless electronic reactions in solution by suggesting and examining different probability distribution functions (PDFs) of relevant Brownian functionals associated with the lifetime and reactivity of the process. Activationless electronic reaction in solution can be modelled as a free Brownian motion with inertial term in the underdamped regime. In this context we suggest several important distribution functions that can characterize the reaction kinetics. Our study is based on the investigation of different PDFs related with Brownian functionals of an effectively reduced Brownian motion with time dependent drift and diffusion coefficients. Our analytical results are compared with the numerically simulated corresponding Langevin equation and we obtain a very good agreement. We have explored various nontrivial scaling behaviour of different PDFs and calculated explicitly the power law related with the asymptotic limits and they can be further verified experimentally.