Interdisciplinary Aspects of Organic Chemistry-cum-Graph Theory

Abstract

The distinction between interdisciplinarity, multidisciplinarity, and transdisciplinarity is emphasized. Chemistry evolved later as a science than physics, so that in the early 19th century renowned philosophers denied the possibility of mathematics being useful for chemical problems. Later, with the advent of quantum mechanics, chemistry was viewed as reducible to physics. It is argued, however, that mathematical chemistry – discrete mathematics and graph theory – can explain chemical phenomena and concepts without the intermediacy of physics. Isomer enumeration of cyclic and acyclic organic compounds (as molecular graphs) contributed to the birth of graph theory. Aromatic heterocyclic compounds can be described and enumerated according to three types of atoms forming the aromatic ring, according to the number (0, 1, or 2) of π-electrons in the non-hybridized orbital. Benzenoids and diamondoids can be classified, described and enumerated with the help of dualists. In polycyclic benzenoids, various π-electron partitions are possible, and among them the Clar-sextet partition is the most unequal. Topological indices that associate numbers with molecular structures are instruments for quantitative structure-property or structure-activity relationships (QSPR and QSAR, respectively) and drug design. Reaction graphs and synthon graphs are also mentioned. Reciprocal interaction – from chemistry to mathematics – accounts for the discovery of new (3,g)-cages and upper/lower bounds of various energy graphs or graph connectivities.