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. Our method gives a clear physical understanding of the behaviour of tunneling splittings in the presence of rotations, and scales linearly with system size.