Statistics and kinetics of single-molecule electron transfer dynamics in complex environments: A simulation model study

Dynamics of the environments of complex systems such as biomolecules, polar solvents, and glass plays an important role in controlling electron transfer reactions. The kinetics is determined by the nature of a complex multidimensional landscape. By quantifying the mean and high-order statistics of the first-passage time and the associated ratios, the dynamics in electron transfer reactions controlled by the environments can be revealed. We consider real experimental conditions with finite observation time windows. At high temperatures, exponential kinetics is observed and there are multiple kinetic paths leading to the product state. At and below an intermediate temperature, nonexponential kinetics starts to appear, revealing the nature of the distribution of local traps on the landscape. Discrete kinetic paths emerge. At very low temperatures, nonexponential kinetics continues to be observed. We point out that the size of the observational time window is crucial in revealing the intrinsic nature of the real kinetics. The mean first-passage time is defined as a characteristic time. Only when the observational time window is significantly larger than this characteristic time does one have the opportunity to collect enough statistics to capture rare statistical fluctuations and characterize the kinetics accurately.