We present a novel nonadiabatic ring polymer molecular dynamics (NRPMD) method based on a spin mapping (SM) formalism recently introduced, that can accurately describe both electronic nonadiabatic 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 molecular dynamics including nuclear dynamical quantum effects (tunnelling, 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 is the same as the electronic subspace, preserving the Hilbert subspace. The SM variables are used to define the electronic state on the Bloch sphere, so the total population is unitary and there is no inverted potential problem contrarily to the MMST representation.
Motivated by these advantages, we developed a SM-NRPMD method by deriving a partition function to sample the initial quantum Boltzmann distribution and a Hamiltonian used for dynamics propagation. Using our recent derivation of general formula to obtain the structure constants of the su(N) Lie algebra, we obtained equations of motion for the SM variables. Our method is compared to an MMST-NRPMD method and to exact calculations by computing correlation functions for one-dimensional spin-boson models ranging from adiabatic to highly nonadiabatic regimes. Our novel method provides accurate results throughout the entire range. Contrarily to the MMST method, ours seems to conserve the quantum Boltzmann distribution even for low number of beads, which is its main advantage.

Position and population correlation functions

Position and population expectation values

Duncan Bossion

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