Supplemental Material

The supplementary material includes the following: character table of the $G_6$ molecular symmetry group, details of the transformation of bend eigenstates from ``bisector-$z$' coordinates employed for solving the Schr"odinger equation to ``H-bond coordinates' used in the present analysis, details of isolating the $G_6^\dagger$ region, selection rules and transformation properties corresponding to the $F_{K,L,M}^{(\Psi)}({\bf Q})$ amplitude functions, calculation of the Fourier amplitudes, assignment of ``upper' and ``lower' to $K=3$ and $K=6$ pseudorotation excitations, tables containing the composition of the 9D bend eigenstates and the assignment of the components.