Figure 2: Distortion symmetry of the PF5 pseudorotation.
The PF5 molecule undergoes pseudorotation from the λ=−1 state (left inset in a, blue atom is P and yellow atoms are F), through a transition state at λ=0 (middle inset in a), to the λ=+1 state (right inset in a). Pairs of static images at λ and −λ are related by a fourfold rotation along the PF1 bond (see inset in b for atom labels). The orange (light blue) arrows represent portions of the pathway going in the direction of increasing (decreasing) λ. The path segment over an infinitesimal path segment, Δλ to the left of λ=0 is transformed under 4 into the path segment −Δλ to the right of λ=0. The displacements of atoms between consecutive images on the left can be related to the displacements of atoms between consecutive images on the right. Thus 4 transforms images between λ and −λ and also the atomic displacements between consecutive images in such a way that the overall distortion path remains invariant. The set of all such operations that leave this pathway invariant form the complete distortion-symmetry group of this pathway, 4mm, where starred symmetries are distortion reversing and are highlighted by blue colour. The blue circles in a are energies from NEB calculations and the black line is the symmetrized fit as guaranteed by the 4mm symmetry group. The PF1 bond length (labelled in the inset in b, which shows the superimposed images of the molecule along the distortion path) as a function of λ for the NEB calculated path is plotted in b as blue circles; it is also guaranteed to be an even function with respect to λ, as is consistent with the symmetrized fit (blue line). Similarly, the PF2 (green circles and line) and PF3 (red circles and line) bond lengths are required by the 4mm symmetry to be mirror images of each other; this is consistent with the plot in b.
