The Deductive Solution of Chemical Problems by Computer Programs on the Basis of a Mathematical Model of Chemistry

A mathematical model of constitutional chemistry is described which is well suited as a theoretical basis for the deductive solution of a variety of chemical problems by computer programs. Within this framework the chemical constitution of molecules and ensembles of molecules (EM) is represented by BE-matrices, whose rows and columns are assigned to the considered atomic cores, and whose entries represent covalent bonds and free valence electrons. Chemical reactions are represented by transforming the BE-matrix B of the beginning EM into the BE-matrix E of the end EM by addition of an R-matrix R according to the master equation B + R = E of the present theory. With a given initial matrix B, those R-matrices R whose addition to B represent chemical reactions can be generated mathematically without any information on individual chemical reactions. The applications of this approach are synthesis design and the prediction of the products which may conceivably be formed from combinations of listed chemical compounds. When the basis elements of the R-matrices are used in a successive mode in this context, results may be obtained which take into account mechanistic aspects of chemical reacttions. A pair (B, E) representing the beginning and end EM of any chemical reaction, or a sequence of chemical reactions yields a difference matrix E - B = R = ∑R whose components Rv may be used to generate networks of reaction pathways that lead from EM(B) to EM (E). This may also be used for synthesis design, or for the elucidation of reaction mechanisms. From given R-matrices R one may generate those pairs (B, E) which satisfy B + R = E, and thus systematically “invent” chemical reactions. The deductive approach yields unprecedented conceivable solutions to chemical problems. These can be screened through selection rules which are based on general chemical experience.