Pseudorotation

The IUPAC defines pseudorotation as "a conformational change resulting in a structure that appears to have been produced by rotation of the entire initial molecule and is superimposable on the initial one, unless different positions are distinguished by substitution or isotopic labeling. No angular momentum is generated by this motion; this is the reason for the term."

Introduction
It is difficult to appreciate pseudorotation without access to molecular models or molecular graphics. In its purest sense it refers to symmetrical molecules, often with symmetry axes of higher order than 2. A small displacement of the atomic positions leads to a loss of symmetry, and then suddenly the symmetry reappears in a different orientation. Although not formally required, pseudorotation normally involves displacements along low-energy pathways. There are several well-known and intensively studied systems.

Berry mechanism
The Berry mechanism refers to the facile interconversion of axial and equatorial ligand in MX5 complexes. A molecule such as PF5 has D3h symmetry. Small movement of atoms can maintain C2v symmetry (a subgroup of D3h) and after a surprisingly small change, a new configuration with D3h symmetry is found.

Cyclopentane
A molecular model of cyclopentane is not flat, but puckered. An arbitrary configuration has no symmetry (C1) but there are special conformations with Cs (envelope) and C2 (twist) symmetry. These can be set out as a graph with 10 nodes, alternating between boat and twist. The graph itself has C5 permutation symmetry (check this).

Cyclohexane
The most stable conformation of cyclohexane is the chair, which is relatively inflexible and, when built from molecular models, is provably rigid. This conformation can be flipped through higher energy intermediates to a flexible system. These conformations all have C2 symmetry, but there are special points with higher symmetry: C2v (boat) and D2 (twist-boat).

Pseudorotation