  We theoretically investigate an exciton-coupled electron transfer (XCET)
process that is conversion of an exciton into a charge transfer state. This
conversion happens in an exciton transfer (XT) process, and the electron moves
away in an electron transfer(ET) process in multiple environments (baths). This
XCET process plays an essential role in the harvesting of solar energy in
biological and photovoltaic materials. We develop a practical theoretical model
to study the efficiency of XCET process that occurs either in consecutive or
concerted processes under the influence of non-Markovian baths. The role of
quantum coherence in the XT-ET system and the baths is investigated using
reduced hierarchal equations of motion (HEOM). This model includes independent
baths for each XT and ET state, in addition to a XCET bath for the conversion
process. We found that, while quantum system-bath coherence is important in the
XT and ET processes, coherence between the XT and ET processes must be
suppressed in order to realize efficient irreversible XCET process through the
weak off-diagonal interaction between the XT and ET bridge sites arises from a
XCET bath.
