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Coherent state mapping ring polymer molecular dynamics for non-adiabatic quantum propagations.

We introduce the coherent-state mapping ring polymer molecular dynamics (CS-RPMD), a new method that accurately describes electronic non-adiabatic dynamics with explicit nuclear quantization. This new approach is derived by using coherent-state mapping representation for the electronic degrees of freedom (DOF) and the ring-polymer path-integral representation for the nuclear DOF. The CS-RPMD Hamiltonian does not contain any inter-bead coupling term in the state-dependent potential and correctly describes electronic Rabi oscillations. A classical equation of motion is used to sample initial configurations and propagate the trajectories from the CS-RPMD Hamiltonian. At the time equivalent to zero, the quantum Boltzmann distribution (QBD) is recovered by reweighting the sampled distribution with an additional phase factor. In a special limit that there is one bead for mapping variables and multiple beads for nuclei, CS-RPMD satisfies detailed balance and preserves an approximate QBD. Numerical tests of this method with a two-state model system show very good agreement with exact quantum results over a broad range of electronic couplings.