Multilayer Multistate Reaction Coordinate Model for Nonadiabatic Dynamics in Open Quantum Systems

Simulating nonadiabatic quantum dynamics in complex condensed-phase systems is computationally challenging due to the high dimensionality of the nuclear environment. To address this, we introduce the multilayer multistate reaction coordinate (ML-MRC) model, a general hierarchical transformation of the multistate harmonic (MSH) Hamiltonian that maps the complex bath into a structured chain of collective modes. We demonstrate that the ML-MRC framework allows the MSH model to be reformulated into hierarchies of arbitrary depth, from single-layer reaction coordinates to full-chain representations, while maintaining rigorous mathematical equivalence. This flexibility is validated across diverse physical systems, including the spin-boson model, the Frenkel exciton model for the photosynthetic light-harvesting Fenna–Matthews–Olson complex, and a realistic photoinduced charge transfer model for a carotenoid-porphyrin-fullerene triad in tetrahydrofuran. Furthermore, this hierarchical structure enables a robust dimensionality reduction strategy, where truncating the chain yields low-dimensional effective Hamiltonians that accurately reproduce the nonadiabatic dynamics of the untruncated model at a reduced computational cost. Finally, the ML-MRC model reveals valuable mechanistic insights through reaction coordinate trajectories, which are shown to synchronize remarkably with electronic population dynamics across multiple systems.