Comparison of Atom Maps

The computation of reliable, chemically correct atom maps from educt/product pairs has turned out to be a difficult problem in cheminformatics because the chemically correct solution is not necessarily an optimal solution for combinatorial formulations such as maximum common subgraph problems. As a consequence, competing models have been devised and compared in extensive benchmarking studies. Due to isomorphisms among products and educts it is not immediately obvious, however, when two atom maps for a given educt/product pairs are the same. We formalize here the equivalence of atom maps and show that equivalence of atom maps is in turn equivalent to the isomorphism of labeled auxiliary graphs. In particular, we demonstrate that Fujita's Imaginary Transition State can be used for this purpose. Numerical experiments show that practical feasibility. Generalizations to the equivalence of subgraph matches, double pushout graph transformation rules, and mechanisms of multi-step reactions are discussed briefly.