Does electron transfer (ET) kinetics within a single-electron trajectory
description always coincide with the ensemble description? This fundamental
question of ergodic behavior is scrutinized within a very basic semi-classical
curve-crossing problem of quantum Landau-Zener tunneling between two electronic
states with overdamped classical reaction coordinate. It is shown that in the
limit of non-adiabatic electron transfer (weak tunneling) well-described by the
Marcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit of
the so-called solvent-controlled adiabatic electron transfer a profound
breaking of ergodicity occurs. The ensemble survival probability remains nearly
exponential with the inverse rate given by the sum of the adiabatic curve
crossing (Kramers) time and inverse MLD rate. However, near to adiabatic
regime, the single-electron survival probability is clearly non-exponential but
possesses an exponential tail which agrees well with the ensemble description.
Paradoxically, the mean transfer time in this classical on the ensemble level
regime is well described by the inverse of nonadiabatic quantum tunneling rate
on a single particle level
