Efficient Algorithms to Enumerate Isomers and Diamutamers with More Than One Type of Substituent

Journal of Chemical Information and Computer Sciences

Volumn 40, Issue 4, 2000, Pages 956-966

  Van Almsick, Markus ^a   Dolhaine, Hans ^b   Hönig, Helmut ^c  

^a Henkel KGaA ^*  (Germany)

^b HENKEL KGAA   (Germany)

^c GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001053421     PISSN: 00952338     EISSN: None     Source Type: Journal    
DOI: 10.1021/ci990121m     Document Type: Article

References (24)

1. IUPAC Commission on Nomenclature of Organic Chemistry, Section E: Pure And Applied Chemistry; Pergamon Press: Oxford, 1976; Vol. 45, pp 11-30.
2. ISOMERS.M ftp site and pointers to related Web sites are located at http://vvww-orgc.tu-graz.ac.at/hoegroup.
3. Pólya, G. Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und Chemische Verbindungen. Acta Math. 1937, 68. Stockholm 145-254. In English: Pólya, G. Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds; Springer: New York, 1987.
4. Pólya, G. Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und Chemische Verbindungen. Acta Math. 1937, 68. Stockholm 145- 254. In English: Pólya, G. Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds; Springer: New York, 1987.
5. Wolfram, S. The Mathematica Book, 4th ed.; Wolfram Media/Cambridge University Press: Cambridge, U.K., 1999.
6. Pilati, T.; Forni, A. SYMMOL: a program to find the maximum symmetry group in an atom cluster, given a prefixed tolerance. J. Appl. Crystallogr. 1998, 31, 503-504.
7. n stands for an n-fold rotation axis, which represents a group cycle of length n.
8. 4.
9. n/q, if q is a common denominator for n and p.
10. Schoenflies, A. Theorie der Kristallstruktur, Bomtraeger: Berlin, 1923.
11. Kerber, A. Applied Finite Group Actions; Algorithms & Combinatorics 19; Springer-Verlag: New York, 1999; Chapter 2.
12. The distributative law of Boolean logic is a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c). Note the analogy to basic algebra: a·(b + c) = a·b + a·c.
13. One can include vacant substituent sites in an isomer enumeration by simply introducing a vacant substituent type, typically hydrogen.
14. 60 fullerene.
15. Dolhaine, H. A Computer Program for the Enumeration of Substitutional Isomers. Comput. Chem. 1981, 5, 41-48. See also the note by Dolhaine, H.; Garavelli, J. S.; Leonard, J. E. Comments on Papers Concerning Computer Enumeration of Permutation Isomers. Comput. Chem. 1986, 10, 239-240.
16. Dolhaine, H. A Computer Program for the Enumeration of Substitutional Isomers. Comput. Chem. 1981, 5, 41-48. See also the note by Dolhaine, H.; Garavelli, J. S.; Leonard, J. E. Comments on Papers Concerning Computer Enumeration of Permutation Isomers. Comput. Chem. 1986, 10, 239-240.
17. Leonard, J. E. Isomer Numbers of Nonrigid Molecules, The Cyclohexane Case. J. Phys. Chem. 1977, 81 (23), 2212.
18. i should render the number of substituent sites. Consistency checks for isomer enumerations: The number of diamutamers should be the number of diastereoisomers plus the number of enantiomeric pairs. The number of diastereoisomers should be the number of enantiomeric pairs plus the number of achiral diamutamers.
19. Dolhaine, H.; Hönig, H.; van Almsick, M. Sample Applications of an Algorithm for the Calculation of the Number of Isomers With More Than One Type of Achiral Substituent, MATCH communication in mathematical and in computer chemistry, March 1999, Vol. 39, pp 21-37, http://www.mathe2.uni-bayreuth.de/match.
20. See e.g.: Balasubramanian, K. Applications of Combinatorics and Graph Theory to Spectroscopy and Quantum Chemistry. Chem. Rev. 1985, 85, 599-618.
21. http://www.combmatorial.com/.
22. http://www-orgc.tu-graz.ac.at/institut/softnew.htm.
23. Fujita, S. Unit Subduced Cycle indices with and without Chirality Fittingness for Ih Group. An Application to Systematic Enumeration of Dodecahedrane Derivatives. Bull. Chem. Soc. Jpn. 1990. 21, 141-157.
24. All calculations and benchmarks were performed on a 300 MHz PC x86 Pentium processor under Windows NT.