Transition from stochastic events to deterministic ensemble average in electron transfer reactions revealed by single-molecule conductance measurement.

Electron transfer reactions can now be followed at the single-molecule level, but the connection between the microscopic and macroscopic data remains to be understood. By monitoring the conductance of a single molecule, we show that the individual electron transfer reaction events are stochastic and manifested as large conductance fluctuations. The fluctuation probability follows first-order kinetics with potential dependent rate constants described by the Butler-Volmer relation. Ensemble averaging of many individual reaction events leads to a deterministic dependence of the conductance on the external electrochemical potential that follows the Nernst equation. This study discloses a systematic transition from stochastic kinetics of individual reaction events to deterministic thermodynamics of ensemble averages and provides insights into electron transfer processes of small systems, consisting of a single molecule or a small number of molecules.