  Electron transfer is at the heart of many fundamental physical, chemical, and
biochemical processes essential for life. Exact simulation of reactions in
these systems is often hindered by the large number of degrees of freedom and
by the essential role of quantum effects. In this work, we experimentally
simulate a paradigmatic model of molecular electron transfer using a
multi-species trapped-ion crystal, where the donor-acceptor gap, the electronic
and vibronic couplings, and the bath relaxation dynamics can all be controlled
independently. We employ the ground-state qubit of one ion to simulate the
electronic degree of freedom and the optical qubit of another ion to perform
reservoir engineering on a collective mode encoding a reaction coordinate. We
observe the real-time dynamics of the spin excitation, measuring the transfer
rate in several regimes of adiabaticity and relaxation dynamics. The setup
allows access to the electron transfer dynamics in the non-perturbative regime,
where there is no clear hierarchy among the energy scales in the model, as has
been suggested to be optimal for many rate phenomena, including photosynthesis.
Our results provide a testing ground for increasingly rich models of molecular
excitation transfer processes that are relevant for molecular electronics and
light-harvesting systems.
