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.
Haseeb et al. (Wed,) studied this question.