Multi-state harmonic models with globally shared bath for nonadiabatic dynamics in the condensed phase

Model Hamiltonians constructed from quantum chemistry calculations and molecular dynamics simulations are widely used for simulating nonadiabatic dynamics in the condensed phase. The most popular two-state spin-boson model could be built by mapping the all-atom anharmonic Hamiltonian onto a two-level system bilinearly coupled to a harmonic bath using the energy gap time correlation function. However, for more than two states, there lacks a general strategy to construct multi-state harmonic (MSH) models since the energy gaps between different pairs of electronic states are not entirely independent and need to be considered consistently. In this paper, we extend the previously proposed approach for building three-state harmonic models for photoinduced charge transfer to the arbitrary number of electronic states with a globally shared bath and the system-bath couplings are scaled differently according to the reorganization energies between each pair of states. We demonstrate the MSH model construction for an organic photovoltaic carotenoid-porphyrin-C₆₀ molecular triad dissolved in explicit tetrahydrofuran solvent. Nonadiabatic dynamics was simulated using mixed quantum-classical techniques, including the linearized semiclassical and symmetrical quasiclassical dynamics with the mapping Hamiltonians, mean-field Ehrenfest, and mixed quantum-classical Liouville dynamics in two-state, three-state, and four-state harmonic models of the triad system. The MSH models are shown to provide a general and flexible framework for simulating nonadiabatic dynamics in complex systems.