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.
supported by Deutsche Forschungsgemeinschaft (grant Ke 11)
supported by Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
N.L. Allinger. MM2. A Hydrocarbon Force Field Utilizing V1 and V2 Torsional Terms. J. Amer. Chem. Soc., 99, S. 8127–8134, 1977.
N.L. Biggs, K.E. Lloyd, and R.J. Wilson. Graph theory 1736–1936. Clarendon Press, 1977.
A. Cayley. On the theory of the analytical forms called trees. Phil. Mag., 13, S. 172–176, 1857.
A. Cayley. On the analytical forms called trees, with application to the theory of chemical combinations. Rep. Brit. Assoc. Adv. Sci., 45, S. 257–305, 1875.
R. Grund. Symmetrieklassen von Abbildungen und die Konstruktion von diskreten Strukturen. Bayreuther Mathematische Schriften, 31, S. 19–54, 1990.
R. Grund. Konstruktion molekularer Graphen mit gegebenen Hybridisierungen und überlappungsfreien Fragmenten. Bayreuther Mathematische Schriften, 49, S. 1–113, 1994 (to appear).
R. Grund, A. Kerber, and L. Laue. Construction of discrete structures, especially isomers. to appear in Discr. Appl Math.
R. Grund, A. Kerber, and R. Laue. MOLGEN, ein Computeralgebra-System für die Konstruktion molekularer Graphen. MATCH, 27, S. 87–131, 1992.
R. Hager, A. Kerber, R. Laue, D. Moser, and W. Weber. Construction of orbit representatives. Bayreuther Mathematische Schriften, 35, S. 157–169, 1991.
A. von Humboldt Versuche über den gereizten Muskel-und Nervenfaser nebst Vermuthungen über den chemischen Prozess des Lebens. Decker und Compagnie, Leipzig, und Heinrich August Rottmann, Posen, 1797
A. Kerber. Algebraic Combinatorics Via Finite Group Actions. BI-Wissenschaftsverlag, Mannheim, Wien, Zürich, 1991.
R. Laue. Construction of combinatorial objects — a tutorial. Bayreuther Mathematische Schriften, 43, S. 53–96, 1993.
E. Luks. Isomorphism of graphs of bounded valence can be tested in polynomial time. J. Computer and System Sciences, 25, S. 42–65, 1982.
J.G. Nourse, D.H. Smith, R.E. Carhart, and C. Djerassi. Exhaustive generation of stereoisomers for structure elucidation. J. Am. Chem. Soc., 101, S. 1216–1223, 1979.
G. Pólya. Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen. Acta mathematica, 68, S. 145–253, 1937.
R.C. Read. Every one a winner. Ann. Discr. Math., 2, S. 107–120, 1978.
H.J. Redfield. The theory of group-reduced distributions. Am. J. Math., 49, S. 433–455, 1927.
D.H. Rouvray. The Origins of Chemical Graph Theory. In: D. Bonchev/D. h. Rouvray (eds.): Chemical Graph Theory, 1–39. Mathematical Chemistry Series, vol. 1, Abacus Press, 1991.
E. Ruch, W. Hässelbarth, B. Richter. Doppelnebenklassen als Klassenbegriff und Nomenklaturprinzip für Isomere und ihre Abzählung. Theoretica Chimica Acta, 19 (1970), 288–300.
E. Ruch, D. J. Klein. Double cosets in chemistry and physics. Theoretica Chimica Acta, 63 (1983), 447–472.
B. Schmalz. Verwendung von Untergruppenleitern zur Bestimmung von Doppelnebenklassen. Bayreuther Mathematische Schriften, 31, S. 109–143, 1990.
B. Schmalz. t-Designs zu vorgegebener Automorphismengruppe. Bayreuther Mathematische Schriften, 41, S. 1–164, 1992.
B. Schmalz. The t-designs with prescribed automorphism group, new simple 6-designs. J. Comb. Designs, 1, S. 125–146, 1993.
C.A. Shelley. Heuristic Approach for Displaying Chemical Structures. J. Chem. Inf. Comput. Sci., 23, S. 61–65, 1983.
C.C. Sims. Computation with Permutation Groups. In S.R. Petrick, Hrsg., Proc. of the Second Symposium on Symbolic and Algebraic Manipulation, S. 23–28. Assoc. Comput. Mach.
J.J. Sylvester. Chemistry and Algebra. Nature, 17, 1878.
Th. Wieland. Erzeugung, Abzählung und Konstruktion von Stereoisomeren. MATCH, 31, 1994 (submitted).
L. A. Zlatina. Mathematical Models of Generation of Stereoisomers and Building Space Models of Molecules. Dissertation, All-Union Research Institute of Organic Sythesis, Moskau, 1991.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Benecke, C., Grund, R., Hohberger, R., Kerber, A., Laue, R., Wieland, T. (1995). Chemical isomerism, a challenge for algebraic combinatorics and for computer science. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_2
Download citation
DOI: https://doi.org/10.1007/3-540-60114-7_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60114-2
Online ISBN: 978-3-540-49440-9
eBook Packages: Springer Book Archive