On symmetry properties of reaction coordinates

We discuss relationships between reaction coordinates, normal coordinates, and symmetry coordinates, defined at an arbitrary point on an adiabatic energy surface. Using simple group theoretical arguments, we prove that the points representing nuclear configurations with symmetry elements other than the identity element are located in valleys (or on ridges or shelves; all abbreviated as BGV) of the adiabatic electronic energy surface. We illustrate with examples complexities such as the bifurcation of a BGV or a transition from a valley into a ridge, for which motion along the reaction coordinate is not totally symmetric at every point, nor is the symmetry of nuclear configuration necessarily conserved during the reaction.