Coherent State Mapping Ring Polymer Molecular Dynamics for Nonadiabatic Quantum Propagations

Accuartely and efficiently simulating quantum dynamics effects is one of the central challenges in mordern theoretical chemistry. Direct simulations of the exact quantum dynamics remains to be computationally challenging. Here we propose to develop a classical trajectory based method to accurately describe electronic non-adiabatic dynamics as well as capture nuclear quantum effects. 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. 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 preserves detailed balance and an approximate QBD. Numerical tests of this method with a two-state model system show very good agreement with the exact quantum results. Besides the equlibrium regime, CS-RPMD also holds a very promising method to apply in non-equilibrium dynamics.