Since the number of elementary reactions is typically greater than or equal to the number of chemical species, i.e., m ≥ n, there exists a direct mapping between E and H r . Yet, no obvious mapping exists in the opposite direction since this is an under-constrained linear system of equations. The Moore-Penrose 209-211 pseudo-inverse of the stoichiometry matrix M + can be used to construct the inverse mapping. To solve this inverse mapping, it is first necessary to select anchor species for each element from the mechanism, e.g., A =[C 2 H 6 , CO, H 2 O, Pt(111)]. We can separate the stoichiometry matrix M into the anchor species M A and non-anchor species M, leading to Eq. (73).