Path Integral Energy Landscapes for Water Clusters

The energy landscapes for a discretized path integral representation of the water dimer, trimer and pentamer are characterized in terms of the localized (classical) and delocalized minima and transition states. The transition states are finite-temperature approximations to the exact instanton path, and they are typically used to calculate the tunneling splittings or reaction rates. The features of the path integral landscape are explored, thus elucidating procedures that could usefully be automated when searching for instantons in larger systems. Our work not only clarifies the role of minima and transition states in path integral calculations but also enables us to analyze the quantum-to-classical transition.