On transition-state theory and the classical mechanics of collinear collisions

We consider classical transition-state theory of collinear atom-diatom reactions. There are (many) potential surfaces for which this theory is exact provided all trajectories with energy above some fixed value are disregarded; the energy cutoff of course depends on the surface. We develop a simple criterion for recognizing or constructing such surfaces, and discuss examples. We also show that if a surface has a proper transition state, as defined below, then transition-state theory is exact unless collision complexes exist.