Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction

The non-Markovianity of the electron transfer in an oligothiophene-fullerene heterojunction described by a spin-boson model is analyzed using the time dependent decoherence canonical rates and the volume of accessible states in the Bloch sphere. The dynamical map of the reduced electronic system is computed by the hierarchical equations of motion methodology (HEOM) providing an exact dynamics. Transitory witness of non-Markovianity is linked to the bath dynamics analyzed from the HEOM auxiliary matrices. The signature of the collective bath mode detected from HEOM in each electronic state is compared with predictions of the effective mode extracted from the spectral density. We show that including this main reaction coordinate in a one-dimensional vibronic system coupled to a residual bath satisfactorily describes the electron transfer by a simple Markovian Redfield equation. Non-Markovianity is computed for three inter fragment distances and compared with a priori criterion based on the system and bath characteristic timescales.