  The molecular photo cell, i.e., a single molecule donor-acceptor complex,
beside being technologically important, is a paradigmatic example of a
many-body system operating in strong non-equilibrium. The quantum transport and
the photo-voltaic energy conversion efficiency of the photocell, attached to
two external leads, are investigated within the open quantum system approach by
solving the Lindblad master equation. The interplay of the vibrational degrees
of freedom corresponding to the molecules (via the electron-phonon interaction)
and the environment (via dephasing) shows its signature in the efficiency at
maximum power. We find vibration assisted electron transport in the medium to
strong electron-phonon coupling regime when the system does not suffer
dephasing. Exposure to dephasing hampers such a vibration assisted electron
transport in a specific range of dephasing rate.
