The atom sequence mapping is a necessary step when the corresponding model reaction TSs are extracted from the database and the mapping information between the input reaction and the model reaction is not known. In particular, it is possible that multiple mappings are consistent with the application of the model reaction and so all relevant mappings need to be enumerated (e.g., consider a symmetric model reaction graph that could map in either direction to a larger asymmetric reactant). In such a case, the model reaction is regenerated with an atom-mapping that is consistent with the user-specified reaction. Two lists of atom hash values are computed from the reactant and product graphs, respectively, providing two hash values for each atom. Each hash represents the graphical uniqueness of each atom based on its element, its bonded neighbors, their bonded neighbors, and so on out to the full span of the model reactant and product. An atom with a unique hash-value pair means that there are no other degenerate atoms and, therefore, it can be used to anchor a unique atom mapping between the model reaction and the inputted reaction. If there are degenerate atoms that share the same pair of hash values, all consistent atom mappings are enumerated.