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We investigate the effect of inertia on barrierless electronic reactions insolution by suggesting and examining different probability distributionfunctions (PDF) of relevant Brownian functionals associated with the lifetimeand reactivity of the process. Activationless electronic reaction in solutioncan be modeled as a free Brownian motion with inertial term in the underdampedregime. In this context we suggest several important distribution functionsthat can characterize the reaction kinetics. Most of the studies on Brownianfunctional which has vast potential application in diverse fields, are confinedin the overdamped regime. To the best of our knowledge, we are attempting firsttime to incorporate the much important inertial effects on the study ofdifferent PDFs related with Brownian functionals of an underdamped Brownianmotion with time dependent drift and diffusion coefficients using celebratedbackward Fokker-Planck and path decomposition methods. We have explorednontrivial scaling behaviour of different PDFs and calculated explicitly thecritical exponents related with the asymptotic limits in time.

Barrierless reaction kinetics : Inertial effect on different distribution functions of relevant Brownian functionals