Instanton theory of ground-state tunneling splittings with general paths.

We derive a multidimensional instanton theory for calculating ground-state tunneling splittings in Cartesian coordinates for general paths. It is an extension of the method by Mil'nikov and Nakamura [J. Chem.

Semiclassical analysis of the quantum instanton approximation.

We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths and find that two such paths dominate the expression. For symmetric barriers, these two paths join together to describe the semiclassical instanton periodic orbit.

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.

Rotation-tunneling spectrum of the water dimer from instanton theory.

We present an extension to the ring polymer instanton (RPI) method that includes overall rotations in the tunneling pathways, allowing a calculation of the full rotation-tunneling spectrum of the water dimer. Our method gives a qualitative description of the rotational and tunneling processes underpinning the spectrum, and shows the drastic reduction of the largest splitting with increasing rotational excitation. We show that this reduction is due to the strong coupling between the rotational motion about the principal axis and the acceptor tunneling motion (where the acceptor monomer rotates about the hydrogen bond), which results in a large increase in the path length and hence the quantum action.