Enumeration of Primary, Secondary, and Tertiary Monosubstituted Alkanes as Stereoisomers

Shinsaku FUJITA

Department of Chemistry and Materials Technology, Kyoto Institute of Technology
Matsugasaki, Sakyo-ku, Kyoto, 606-8585 Japan
e-mail: fujitas@chem.kit.ac.jp

(Received: September 26, 2006; Accepted for publication: December 5, 2006; Published on Web: March 2, 2007)

Monosubstituted alkanes are counted as stereoisomers by means of Fujita's proligand method (Fujita S (2005) Theor. Chem. Acc. 113:73-79, 113:80-86, Fujita S (2006) Theor. Chem. Acc. 115:37-53), where the numbers of primary, secondary, and tertiary ones are calculated after deriving respective functional equations. The procedures of counting are programmed by means of the Maple programming language. They are executed and the results collected up to carbon content 100 in a tabular form. By omitting the sphericities of the recursive functions a(x), c(x2), and b(x) so as to give a single dummy variable r(x), such functional equations with sphericity are transformed into Polya's functional equations without sphericity, which are applied to the enumeration of primary, secondary, and tertiary monosubstituted alkanes as graphs (chemically, constitutional isomers). The results of Fujita's proligand method are compared with those based on Polya's theorem in connection with several cases of pseudoasymmetry.

Keywords: Monosubstituted alkane, Primary, Secondary, Tertiary, Stereoisomer, Enumeration, Sphericity

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