The use of elementary reaction coordinates in the search for conical intersections

A method to locate conical intersections between the ground-state potential surface and the first electronically excited states of polyatomic molecules is described. It is an extension of the Longuet-Higgins sign-change theorem and uses reaction coordinates of elementary reactions as the starting point of the analysis. It is shown that the complete molecular landscape can be partitioned into 2-D domains, each bordered by a Longuet-Higgins loop formed from reaction coordinates of elementary reactions. A domain may contain a conical intersection and if it does, it contains only one (the uniqueness theorem), whose energy is higher than the neighboring minima or transition states. The method can be helped by symmetry, but applies also to systems having no symmetry elements. It is demonstrated for some simple cases. The presence of a conical intersection is manifested by the nature of ground-state thermal reactions, as shown for instance by the fact that the transition state in the ring opening of the cyclopropyl radical is nonsymmetric.