Lu, J; Zhou, Z, *Path integral molecular dynamics with surface hopping for thermal equilibrium sampling of nonadiabatic systems.*,
The Journal of Chemical Physics, vol. 146 no. 15
(April, 2017),
pp. 154110 [doi] .
**Abstract:**

*In this work, a novel ring polymer representation for a multi-level quantum system is proposed for thermal average calculations. The proposed representation keeps the discreteness of the electronic states: besides position and momentum, each bead in the ring polymer is also characterized by a surface index indicating the electronic energy surface. A path integral molecular dynamics with surface hopping (PIMD-SH) dynamics is also developed to sample the equilibrium distribution of the ring polymer configurational space. The PIMD-SH sampling method is validated theoretically and by numerical examples.*