Fig. 7.

A illustrates how the interconversion of rings, in this case a five- and seven-membered ring, result in concerted PT. On the y axis, the symmetrized PT coordinates for the concerted PT events, , , and (corresponding to the black, red, and green curves, respectively) are shown. (B) Coupling between the ring interconversions and the umbrella inversion mode of the hydronium during PT events. The data series shows the umbrella inversion mode coordinate on the y axis along with four snapshots from the molecular dynamics trajectory. The purple triangle is formed by the base of three protons, which is used to illustrate the role of the inversion mode. The inversion coordinate is defined by the perpendicular distance between the oxygen atom of the hydronium ion and the plane formed by the hydrogen atoms. In the first example (A), the inversion mode does not change and hence does not play a role in the PT. However, in the second example, the inversion mode changes, which facilitated the formation and breakage of a 4M ring and is coupled to PT. For clarity, we note that in the first 2 ps the oxygen lies below the triangular blue base, whereas between 2 and 6 ps the oxygen lies above the triangular base.