Instanton calculations of tunneling splittings for water dimer and trimer

Abstract

We investigate the ability of the recently developed ring-polymer instanton (RPI) method [J. O. Richardson and S. C. Althorpe, J. Chem. Phys. 134, 054109 (2011)] to treat tunneling in water clusters. We show that the RPI method is easy to extend to treat tunneling between more than two minima, using elementary graph theory. Tests of the method on water dimer and trimer yield a set of instanton periodic orbits which correspond to all known tunneling pathways in these systems. Splitting patterns obtained from the orbits are in good overall agreement with experiment. The agreement is closer for the deuterated than for the protonated clusters, almost certainly because the main approximation in the calculations is neglect of anharmonicity perpendicular to the tunneling path. All the calculations were performed on a desktop computer, which suggests that similar calculations will be possible on much larger clusters.

Investigation of Terahertz Vibration–Rotation Tunneling Spectra for the Water Octamer

“…Here we summarize the ring-polymer instanton method, 39,40 which was used to compute approximate tunneling splittings and tunneling pathways. The basis of the approach is that the tunneling splittings can be obtained from the limit 41−43 …”

“…The computation was straightforward for this system because none of the paths were found to involve significant rearrangements of the oxygen atoms. 40 The number of replicas, N, and imaginary timeduration, βℏ, were chosen to be large enough to converge the actions S λμ to within about 1%. This level of convergence was sufficient to determine the order of magnitude of the tunneling matrix elements h λμ , and hence the splitting patterns.…”

A Journey Through Chemical Dynamics

“…This type of approximation has been used for a variety of applications involving tunneling phenomena. A recent and impressive example is work by Stuart Althorpe and colleagues (30) treating the tunneling splitting patterns in water clusters.…”

Efficient algorithms for semiclassical instanton calculations based on discretized path integrals

“…To obtain the reliable single kink path, several variants on the least action approach have been proposed. 20,21,[35][36][37][38][39][40][41][42][43][44][45] To describe the sina) Authors to whom correspondence should be addressed. Electronic addresses: kawatsu@fukui.kyoto-u.ac.jp and smiura@mail.kanazawau.ac.jp.…”