Non-adiabatic ring polymer molecular dynamics with spin mapping variables

We present a new non-adiabatic ring polymer molecular dynamics (NRPMD) method based on the spin mapping formalism, which we refer to as spin-mapping NRPMD (SM-NRPMD) approach. derive path-integral partition function expression using coherent state basis for electronic states and formalism nuclear degrees of freedom (DOFs). This provides an efficient sampling quantum statistics. Using basic property Stratonovich-Weyl transformation, Hamiltonian propose dynamical propagation coupled variables polymer. The accuracy SM-NRPMD is numerically demonstrated by computing position population auto-correlation functions model systems. results from agree very well with exact results. main advantage over harmonic oscillator demonstrated, where former nearly time-independent expectation values physical observables systems under thermal equilibrium, latter can not preserve initial Boltzmann distribution. also explicitly demonstrate that invariant upon various ways partitioning state-dependent state-independent potentials.