We present a novel nonadiabatic ring polymer molecular dynamics method (N-RPMD) based on a spin mapping (SM) formalism recently introduced that can accurately describe both electronic non-adiabatic dynamics as well as nuclear quantum effects. The RPMD method is based on the isomorphism between the partition function of a quantum particle and a classical ring polymer. It consists in classical dynamics in an extended phase space hence providing the numerical efficiency of classical MD including nuclear dynamical quantum effects (tunneling, zero-point energy). In this work, we use the SM representation to map the electronic states onto the spin coherent state basis as opposed to the widely used MMST representation. Contrarily to the latter, the dimensionality of the mapping variables (MVs) is exactly the same as the electronic subspace, preserving the size of the Hilbert subspace. The spin MVs defining the electronic states on the Bloch sphere, the total electronic population is bounded by its radius. Hence, the total population is conserved to be unitary and there is no inverted potential problem, those two being major issues of MMST MVs.<br/>Motivated by these advantages, we developed a spin mapping N-RPMD method (SM-NRPMD) by deriving a partition function to sample the initial quantum Boltzmann distribution (QBD) and a Hamiltonian used for dynamics propagation. Our method is compared to a previous MMST based N-RPMD method (NRPMD) and to exact calculations by computing correlation functions for 1D spin-boson models ranging from adiabatic to highly nonadiabatic. The SM-NRPMD method provides accurate results throughout the entire range. Contrarily to the MMST based N-RPMD methods, our method seems to conserve the QBD even for low number of beads, which is its main advantage with its independence to the splitting between state dependent and independent part of the Hamiltonian.

Non-adiabatic ring polymer molecular dynamics with spin mapping variables: A novel method to study nonadiabatic dynamics

ACS Fall 2021

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