The numbers of chiral and achiral alkanes and monosubstituted alkanes
dc.contributor.author | Robinson, R. W. | en_US |
dc.contributor.author | Harry, F. | en_US |
dc.contributor.author | Balaban, A. T. | en_US |
dc.date.accessioned | 2006-04-07T16:32:47Z | |
dc.date.available | 2006-04-07T16:32:47Z | |
dc.date.issued | 1976 | en_US |
dc.identifier.citation | Robinson,, R. W., Harry, F., Balaban, A. T. (1976)."The numbers of chiral and achiral alkanes and monosubstituted alkanes." Tetrahedron 32(3): 355-361. <http://hdl.handle.net/2027.42/21904> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6THR-42K6J86-40/2/cd6c889961d34dbaaef154721c17c7b8 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/21904 | |
dc.description.abstract | Whereas the theory for the enumeration of the optical isomers of the lakyl radicals and the alkanes has long been understood, this is not the case for the corresponding archiral isomers. We present for the first time recurrence formulae for counting the number of archiral isomers of the alkyl radicals and the alkanes. For chiral and archiral alkanes and monosubstituted alkanes, numerical results up to C14 are tabulated.After presenting the history of the problem and the necessary definitions, we proceed to derive functional equations on the various generating functions, which readily yield the more explicit recurrence formulae usefule for numerical calculations. In the process, we first re-derive Polya's expression for planted steric trees using his classical enumeration theorem. This result is then extended to the enumeration of free steric trees using the now standard tree-counting method due to Otter and known as a dissimilarity characteristic equation.By definition, a steric tree is a quartic tree (all points having degree 1 or 4) in which the four neighbors of every carbon point are given a tetrahedral configuration. Building on the methods of the first two authors for counting chiral and archiral trees in the plane, we obtain the formula for counting achiral steric trees, thus setting a problem first enunciated by van't Hoff and Le Bel in 1874. | en_US |
dc.format.extent | 741356 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | The numbers of chiral and achiral alkanes and monosubstituted alkanes | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Materials Science and Engineering | en_US |
dc.subject.hlbsecondlevel | Chemistry | en_US |
dc.subject.hlbsecondlevel | Chemical Engineering | en_US |
dc.subject.hlbsecondlevel | Biological Chemistry | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.subject.hlbtoplevel | Health Sciences | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI 48104, U.S.A. | en_US |
dc.contributor.affiliationother | Department of Mathematics, University of Newcastle, New South Wales, 2308, Australia | en_US |
dc.contributor.affiliationother | Institute of Atomic Physics, P.O. Box 5206,m Bucharest, Romania | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/21904/1/0000311.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0040-4020(76)80049-X | en_US |
dc.identifier.source | Tetrahedron | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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