A global characterization and similarity analysis of two‐dimensional potential energy surfaces

Potential energy surfaces can be classified into combinatiorial equivalence classes, based on their partitioning into catchment regions. Two classification theorems are proven: one for reaction spheres and another for reaction tori. A method for constructing all possible equivalence classes of reaction spheres and reaction tori is presented. As illustration of the general results, it is shown that not all the two‐dimensional reaction spheres are combinatorially equivalent to polyhedra in the three‐dimensional Euclidean space. As examples, several reaction spheres are calculated by using the RHF method at the 3‐21G* level, describing the interactions between a series of polyatomic ions and H+. The calculations show that the potential energy surface of the CO …︁H+ interaction, combinatorially equivalent to that of the NO−3 …︁H+ interaction, is not combinatorially equivalent to any polyhedron in 3‐space; however, the combinatorially different potential energy surface of the PO …︁ H+ interaction is equivalent to a polyhedron in 3‐space. The topological classification scheme is proposed for the study of similarities between various families of chemical reactions.