Non-Markovian Electron Transfer in Ligand–Receptor Complexes: Insights from Non-Gaussian Anharmonic Baths

Electron transfer (ET) in protein receptor–ligand
complexes
is governed by environmental structure, memory, and fluctuation statistics.
We investigate ET dynamics within a non-Markovian open-quantum-systems
framework using a non-Markovian stochastic Schrödinger equation
(NMSSE), contrasting the conventional harmonic (Gaussian)
bath approximation with an anharmonic, non-Gaussian
environment modeled by discrete Poisson (shot-noise) events. The model
consists of a two-state donor–acceptor dimer coupled to a discrete
vibrational mode and embedded in a structured protein–membrane
environment. To represent anharmonicity beyond harmonic-bath theory,
we introduce a finite-memory shot-noise description at the level of
the second cumulant that implements instantaneous kicks on the coupled
electronic–vibrational manifold. Ensemble-averaged trajectory
simulations yield populations and coherences across broad parameter
ranges. Three robust regimes emerge: (i) a weakly anharmonic regime, where many small events per correlation time render the
compound-Poisson bath effectively Gaussian and harmonic, and non-Gaussian
predictions are quantitatively close; (ii) an intermediate
anharmonic regime, where intermittency and higher-order statistics
become dynamically relevant, enhancing ET and qualitatively reshaping
population and coherence dynamics, particularly at weak electronic
coupling; and (iii) a strongly anharmonic sparse-event
regime, where impulsive events drive pronounced, irregular energy
exchange and the largest deviations from harmonic-bath behavior. These
results delineate when harmonic approximations are sufficient and
when explicit anharmonic, non-Gaussian bath models are required for
faithful ET dynamics in biomolecular environments.