Molecular point symmetry and the phase of the electronic wave function: Tools for the prediction of critical points of potential energy surfaces

By combining a well-known theorem of Longuet-Higgins on the phase changes of electronic wave functions along loops encircling a conical intersection of potential surfaces, and a recently proven “vertical symmetry theorem” on the relative distributions of point symmetry groups and potential surface critical points in configuration space, a new result is obtained, suitable for the prediction of the presence of a critical point within a domain of configurations.