Isomers Enumeration and Generation

1 Isomers Enumeration and Generation. - During the last two years there seems to have been a degree of activity in the area of isomer characterization, more so with articles devoted to methodology development. There have been 

Knopfinacher and Warlimont, following earlier work, use much more esoteric mathematical machinery (concerning semi-groups of polynomial-like structures) to develop methods to determine the asymptotic (large-A) form of isomer counts for A-atom alkanes. Polya in fact developed asymptotic results, but Knopfinacher and Warlimont are interested in extensions, particularly to obtain asymptotics for the numbers of generalized isomers , viewed as sets of molecules such that different sets as a whole have the same elemental composition. Their main result is a theorem on the asymptotic number of ways in which a mixture of molecules may be realized when the total number of particular kind of atoms is fixed, and the asymptotic results for ordinary single-molecule isomers is already known. Examples of application to mixtures of alkanes, alkenes, substituted alkanes and achiral alkanes and alkanols are given. 

Baraldi and Vanossi, also following up on earlier formal work, use (in a fairly conventional manner) the general Polya-theoretic machinery to enumerate substitutional isomers for several cychc or polyhedral skeletons. They conclude with enumerations for icosahedral-symmetry skeletons, both for an icosahedron and for a truncated icosahedron, such as have become of some degree of popularity (as in ref. 86) over the last decade or so because of the elegantly beautiful truncated-icosahedral structure of buckminsterfullerene. 

Special efficiency in generating libraries of isomer slructures is addressed. Another suite of programs due to Kerber s group may be found at  

Hopefully such publicly available resources should find notable use by a wide community of chemists. 

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