Systematic Search for New Types of Chemical Interconversions: Mathematical Models and Some Applications

According to Formal − Logical Approach to Organic Reactions, the systematical search for new, unprecedented types of chemical interconversions needs the complete sets of symbolic, reaction, structural, and skeletal equations to be generated. In this paper, the generation problems are shown to be reduced to graph labeling problems and, more precisely, to constructive enumeration problems for orbit representatives of induced permutation groups acting on certain sets of vertex or edge labelings of well-defined graphs. The suggested combinatorial models make it possible to take into account formal charges and unshared electrons (needed to describe ionic, radical, and oxidation−reduction processes) and unchanged bonds forming cycles (included in cyclic structures of educts and products and needed to describe, e.g., degenerate rearrangements). The basic ideas of the effective generating algorithms, some results of the corresponding analytical enumeration techniques, and several new reaction types found by computer programs are also discussed.