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"Exploration of the Accessible Chemical Space of Acyclic Alkanes" Paton, R. S.; Goodman, J. M. J. Chem. Inf. Model. 2007, 47, 2124-2132

A problem that has long interested chemists has been to calculate the number of isomers for an alkane of any given carbon content. Whilst there appears to be no simple mathematical relationship between the number of isomers and the carbon content, it is possible to calculate this number iteratively counting the number of isomers of each fragment into which the alkane can be decomposed. This approach has been encoded into an algorithm for calculating the number of isomers of large alkanes - It is estimated that C167H336 has more isomers than the universe has particles!

In fact not all structural isomers are possible - high level ab initio calculations show that highly branched C16 and C17 fragments, if they were synthesized, would be unstable andrapidly undergo homolytic dissociation at room temperature.

This factor has been taken into account in the development of IsoCount which disallows the unstable substructures. The Applet calculates the number of isomers removing any containing the C17 substructure, or using the more stringent condition of removing the C16 substructure. The java source code is available.

This analysis has implications for the synthesis of dendrimers.