Since there exists no exact algorithm for solving non-linear assignment problems in polynomial time, we propose to first recast the original problem [Eq. (5)] into an auxiliary linear assignment problem based on atom types. First, to reduce the complexity, we exclude monovalent atoms from the auxiliary problem. In this context, monovalent atoms are all atoms of an element for which all atoms are bonded to at most one other atom. Typically, this holds true for hydrogen and halogen atoms. It is sufficient if this applies only to one of the two structures as, e.g., a hydrogen atom can be bonded to two other atoms in a transition state of a proton transfer according to Eq. 4. For all other elements, we define atom types which are determined by the element and the number of bonds to monovalent atoms (e.g., CH 3 ). Auxiliary connectivtiy matrices A and B are then constructed by counting the bonds to these atom types. Hence, the auxiliary linear assignment problem reads