The hierarchic classification of chemical reactions

A hierarchic classification of chemical reactions is implied by the theory of the BE-and R-matrices (ref. 9). This classification is a powerful device in the deductive computer assisted solution of chemical problems. 

Chemical reactions are first classified according to the minimal number of valence electrons that must be redistributed during the conversion of the educts into the products this is their minimal chemical distance (MCD). The determination of the MCD of a chemical reaction (ref. 5-7) yields also an atom-by-atom mapping of the educts and the products, and it also identifies the reactive centers whose union is the socalled core of the reaction. 

A category of reactions with a characteristic irreducible R-matrix is a set of basis reactions. The basis reactions correspond to the traditional classification of organic reactions . A basis reaction is best characterized in graph theoretical terms (ref. 13). The educts and the products of a basis reaction are expressed by a graph (see Fig. 7.2) whose nodes correspond to the reactive centers and whose lines indicate the bond orders of the covalent bonds that are directly affected by the reaction. The 

Down the hierarchy of chemical reactions, the basis reactions are further partitioned by specifying the chemical elements at the reactive centers. 

Finally we reach the individual reactions by stating the covalent bonds and atoms outside the core of the reaction. A more formalistic classification of the basis reactions is achieved through their T-matrices (ref. 14). 

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Now all of the BE-pairs (B,E) are generated by exhaustive combination of the valence schemes that had been elaborated for the rows/columns. Within the hierarchic classification of chemical reactions, thus the level of basis reactions is reached. Subsequently chemical elements are assigned to the rows/columns of (B,E), and finally the unused valences of the reactive centers are supplied with residues as specified by the user. 

The hierarchic classification of chemical reactions provides also criteria forjudging the degree of novelty of unprecedented reactions. Among the new reactions that have been discovered by IGOR, and have been experimentally realized, the conversion of 4 + 5 via 6 into 7 has, up to now, the highest degree of novelty (Fig. 7.8). The reaction 4 + 5—- 6 —< 7 is a realization of the above abstract scheme. 

This hierarchic classification of chemical reactions by their R- and BE-matrices may not only serve as a means of formal ordering of reactions and as a basis of documentation systems, but can also serve as a device in the systematic computer-assisted deductive search for new chemical reactions, by an algorithm which finds all of the mathematically and chemically fitting pairs (B, E) of BE-matrices for a representation R-matrix of an R-category. 

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