Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limiting, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer. A multiscale integrator for the infinite swapping limit is also proposed to enable practical sampling based on the limiting dynamics, avoiding the enumeration of all possible surface index configurations, which grows exponentially with respect to the number of beads in the ring polymer. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path integral molecular dynamics with surface hopping.