Numbers of Monosubstituted Alkanes as Stereoisomers

Shinsaku FUJITA

Department of Chemistry and Materials Technology, Kyoto Institute of Technology
Matsugasaki, Sakyo-ku, Kyoto, 606-8585 Japan

(Received: September 28, 2006; Accepted for publication: December 5, 2006; Published on Web: February 28, 2007)

Monosubstituted alkanes as stereoisomers, not as constitutional isomers, are regarded as planted three-dimensional (3D) trees, which are defined as a 3D extension of planted trees (graphs). They are thus recognized as 3D-objects (planted promolecules) and enumerated by 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). By starting from three kinds of sphericity indices, i.e., ad for homospheric cycles, cd for enantiospheric cycles, and bd for hemispheric cycles, cycle indices with chirality fittingness (CI-CFs) are obtained to enumerate planted 3D-trees or equivalently monosubstituted alkanes as stereoisomers. Functional equations a(x), c(x2), and b(x) for recursive calculations are derived from the CI-CFs and programmed in three ways by means of the Maple programming language. The three recursive procedures for calculating the numbers of planted 3D-trees are executed to give identical results, which are collected up to 100 carbon content in a tabular form. The results are compared with the enumeration of planted trees (as graphs).

Keywords: Monosubstituted alkane, Stereoisomer, Enumeration, Sphericity

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