Multistate Reaction Coordinate Model for Charge and Energy Transfer Dynamics in the Condensed Phase

Abstract

Constructing multistate model Hamiltonians from all-atom electronic structure calculations and molecular dynamics simulations is crucial for understanding charge and energy transfer dynamics in complex condensed phases. The most popular twolevel system model is the spin-boson Hamiltonian, where the nuclear degrees of freedom are represented as shifted normal modes. Recently, we proposed the general multistate nontrivial extension of the spin-boson model, i.e., the multistate harmonic (MSH) model, which is constructed by extending the spatial dimensions of each nuclear mode so as to satisfy the all-atom reorganization energy restrictions for all pairs of electronic states. In this work, we propose the multistate reaction coordinate (MRC) model with a primary reaction coordinate and secondary bath modes as in the Caldeira-Leggett form but in extended spatial dimensions. The MRC model is proven to be equivalent to the MSH model and offers an intuitive physical picture of the nuclear-electronic feedback in nonadiabatic processes such as the inherent trajectory of the reaction coordinate. The reaction coordinate is represented in extended dimensions, carrying the entire reorganization energies and bilinearly coupled to the secondary bath modes. We demonstrate the MRC model construction for photoinduced charge transfer in an organic photovoltaic caroteniod-porphyrin-C 60 molecular triad dissolved in tetrahydrofuran as well as excitation energy transfer in a photosynthetic light-harvesting Fenna-Matthews-Olson complex. The MRC model provides an effective and robust platform for investigating quantum dissipative dynamics in complex condensed-phase systems since it allows a consistent description of realistic spectral density, state-dependent system-bath couplings, and heterogeneous environments due to static disorder in reorganization energies.

All-Atom Photoinduced Charge Transfer Dynamics in Condensed Phase via Multistate Nonlinear-Response Instantaneous Marcus Theory

“…A quantitative description of the distances between different electronic states could be achieved by mapping the all-atom Hamiltonian to the multistate reaction coordinate (MRC) model Hamiltonian. 66 The time-dependent energy gap variance σ jk 2 (t) is obtained with eq 18, and the results of Confs. 3 and 5 are presented in Figures 5 and S6, respectively.…”

“…The time evolution of the energy gap reflects the nonequilibrium effect due to the initial nuclear preparation on the ground state, and the amount of the energy-gap change is related to how far the initial electronic state of the transition is away from the equilibrium position on the ground electronic state. A quantitative description of the distances between different electronic states could be achieved by mapping the all-atom Hamiltonian to the multistate reaction coordinate (MRC) model Hamiltonian …”

“…3 65 and Conf. 5 66 shown in Figure 1, which were selected from the landmark structure database 67 to exhibit population transfer dynamics among all three excited states in the first few picoseconds after the photoexcitation. For each conformation, four electronic states including ππ*, CT1, CT2, and ground state (g) were parametrized.…”