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Does electron transfer (ET) kinetics within a single-electron trajectorydescription always coincide with the ensemble description? This fundamentalquestion of ergodic behavior is scrutinized within a very basic semi-classicalcurve-crossing problem of quantum Landau-Zener tunneling between two electronicstates with overdamped classical reaction coordinate. It is shown that in thelimit of non-adiabatic electron transfer (weak tunneling) well-described by theMarcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit ofthe so-called solvent-controlled adiabatic electron transfer a profoundbreaking of ergodicity occurs. The ensemble survival probability remains nearlyexponential with the inverse rate given by the sum of the adiabatic curvecrossing (Kramers) time and inverse MLD rate. However, near to adiabaticregime, the single-electron survival probability is clearly non-exponential butpossesses an exponential tail which agrees well with the ensemble description.Paradoxically, the mean transfer time in this classical on the ensemble levelregime is well described by the inverse of nonadiabatic quantum tunneling rateon a single particle level.

Quantum breaking of ergodicity in semi-classical charge transfer dynamics