Abstract
Based on the total π-electron energies Eπs of Hückel Molecular Orbital (HMO) method for all the possible isomers of conjugated acyclic polyenes (C2nH2n+2) up to n = 7, the structure–stability relation of the possible isomers was analyzed. It was shown that the mean length of conjugation L can roughly predict the ordering of stability among isomers, while the Z-index, or Hosoya-index, can almost perfectly reproduce their stability. Further, the genealogy of the conjugated acyclic polyene family was obtained by drawing systematic diagrams connecting these isomers of different n, and governed by several simple rules. Namely, the stability change of a given isomer in the genealogy connecting n and n + 1 polyenes can be classified into three different modes of vinyl addition (elongation, inner and outer branching) and horn growing, i.e., substitution of –HC=CH– moiety with –HC(=CH2)–C(=CH2)H–. By using the Z-index, we can extend this type of discussion to polyene radicals and even to “cross-conjugated” cyclic polyenes containing only one odd-membered cycle, such as radialene and fulvene.
Highlights
The successful isolation and identification of the tremendously large family of organic compounds, even limited to hydrocarbons, seems to have established the logical structure of the kingdom of organic chemistry, which is opening its open gates to other fields of science spanning from biology to astronomy, information technology, and general physics
Understanding of the structure–activity relationship and mathematics underlying the whole family of conjugated acyclic polyenes is rather low
In order to steer towards the right direction, the present author has published several papers aimed at understanding and justifying the organic electron theory, mainly involving conjugated polyenes by using the graph-theoretical molecular orbital (GTMO) method
Summary
The successful isolation and identification of the tremendously large family of organic compounds, even limited to hydrocarbons, seems to have established the logical structure of the kingdom of organic chemistry, which is opening its open gates to other fields of science spanning from biology to astronomy, information technology, and general physics. In order to steer towards the right direction, the present author has published several papers aimed at understanding and justifying the organic electron theory, mainly involving conjugated polyenes by using the graph-theoretical molecular orbital (GTMO) method. The classical concept of cross-conjugation, if properly appreciated with a slight modification, will play an important role for understanding the correct part of the conventional organic electron theory [1,2,3,4,5,6]. The genealogy and mathematical structure of the whole family of conjugated acyclic polyene molecules are explained in various levels of logic from high school chemistry (without wavefunction) to sophisticated mathematical chemistry (with perturbation theory) only by using the Molecules 2017, 22, 896; doi:10.3390/molecules22060896 www.mdpi.com/journal/molecules. Hosoya-index) [13,14]
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