Chemical isomerism, a challenge for algebraic combinatorics and for computer science

Abstract

Chemical isomerism means that there do occur different molecules with the same atomic constitutents. For example, about 70 molecules have been found which consist of exactly six carbon and six hydrogen atoms, or, in formal terms, which have the chemical formula C6H6. The existence of chemical isomerism was stated by the end of the eighteenth century, it was verified a quarter of a century later and explained another half of a century afterwards. It stimulated the development of graph theory and gave birth to algebraic combinatorics. It is only now that efficient computers and the helpful methods of computer science can be used in order to solve the basic problem related to chemical isomerism and the corresponding molecular structure elucidation. This problem is the construction of all the molecular graphs which correspond to a given chemical formula and (optional) further conditions on prescribed and forbidden substructures etc. Here we therefore present MOLGEN, a software package which solves this problem in a redundancy free and efficient way. It is designed for research and education, and it finds applications in molecular structure elucidation, where a molecule has to be identified from experimental, usually from spectroscopic data. MOLGEN provides the full wealth of mathematically possible structures (multigraphs with given degree sequence, where the vertices are colored by atom names), from which further chemical tests allow to pick the correct solutions. From the mathematical point of view, MOLGEN is based on the constructive theory of discrete structures, and it clearly shows the success of the combination of algebraic and combinatorial methods for applications in sciences. Moreover, its efficiency is based on a careful use of data structures. MOLGEN is intensively used in chemical industry.