Non-Markovian and non-Condon vibrationally assisted electron transfer in an effective ligand--receptor complex

We investigate vibrationally assisted electron transfer in an effective ligand--receptor complex using finite-temperature non-Markovian quantum-state diffusion with explicitly colored environmental noise. The model comprises donor and acceptor electronic states, an explicit bound-ligand vibrational mode, and a Gaussian protein--solvent bath. Linearization of a coordinate-dependent diabatic Hamiltonian yields two distinct system--environment interactions: diagonal coupling, which modulates the donor--acceptor energy gap, and off-diagonal non-Condon coupling, which modulates the electronic tunneling matrix element. In the rapidly equilibrating diagonal-bath limit, the model recovers the expected Marcus--Levich--Jortner vibronic-transfer behavior. Persistent environmental correlations instead generate non-exponential dynamics characterized by transient oscillations, back-transfer, and memory-dependent damping. Under matched weak-tunneling conditions, off-diagonal coupling opens a direct transition pathway and produces a larger finite-time acceptor population throughout the investigated parameter space. Because these dynamics do not generally support a unique kinetic rate, the enhancement is quantified using a time-averaged transfer yield. Comparisons with exact closed-system and commuting pure-dephasing limits validate the deterministic propagator and colored-noise construction, respectively, while the noncommuting dynamics are evaluated within a declared first-order finite-memory closure. These results identify ligand vibration, environmental memory, and non-Condon tunneling modulation as cooperating mechanisms that can dynamically regulate electron transfer in receptor-like environments, while maintaining a clear distinction between a mechanistic coarse-grained model and an atomistically parameterized biological complex.