  Bridge-mediated electron transfer (ET) between a donor and an acceptor is
prototypical for the description of numerous most important ET scenarios. While
multi-step ET and the interplay of sequential and direct superexchange transfer
pathways in the donor-bridge-acceptor (D-B-A) model is increasingly understood,
the influence off-diagonal system-bath interactions on the transfer dynamics is
less explored. Off-diagonal interactions account for the dependence of the ET
coupling elements on nuclear coordinates (non-Condon effects) and are typically
neglected. Here we numerically investigate with quasi-adiabatic propagator path
integral (QUAPI) simulations the impact of off-diagonal system-environment
interactions on the transfer dynamics for a wide range of scenarios in the
D-B-A model. We demonstrate that off-diagonal system-environment interactions
can have profound impact on the bridge-mediated ET dynamics. In the considered
scenarios the dynamics itself does not allow for a rigorous assignment of the
underlying transfer mechanism. Further, we demonstrate how off-diagonal
system-environment interaction mediates anomalous localization by preventing
long-time depopulation of the bridge B and how coherent transfer dynamics
between donor D and acceptor A can be facilitated. The arising non-exponential
short-time dynamics and coherent oscillations are interpreted within an
equivalent Hamiltonian representation of a primary reaction coordinate model
that reveals how the complex vibronic interplay of vibrational and electronic
degrees of freedom underlying the non-Condon effects can impose
donor-to-acceptor coherence transfer on short timescales.
