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Garner MH, Hoffmann R, Rettrup S, Solomon GC. Coarctate and Möbius: The Helical Orbitals of Allene and Other Cumulenes. ACS Cent Sci 2018; 4:688-700. [PMID: 29974064 PMCID: PMC6026781 DOI: 10.1021/acscentsci.8b00086] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Indexed: 05/24/2023]
Abstract
As brought to the attention of the community by Hendon et al. and noted by previous workers, the π orbitals of the equilibrium geometry odd-carbon (even number of double bonds = n) [n]cumulenes may be written in either rectilinear or helical form. We trace the origins and detailed composition of the helical orbitals of cumulenes, which emerge in the simplest Hückel model and are not much modified in advanced computations. For the α,ω-disubstituted even [n]cumulenes, the helical representation is obligatory as the symmetry is reduced from D2d to C2. A relationship is apparent between these helical orbitals of the even [n]cumulenes, seen as a Herges coarctate system, and the corresponding Möbius cyclic polyene orbitals. The twist of the orbitals varies in interesting ways along the helix, and so does the contribution of the component atomic orbitals. Though the electronic structures of even [n]cumulenes and Möbius cyclopolyenes are closely related, they differ for higher n in intriguing ways; these are linked to the constrained rotation of the basis orbitals along the helical twist itinerary. Relations are constructed between the level patterns of the π-systems of even [n]cumulenes and ideas of Hückel and Möbius aromaticity.
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Affiliation(s)
- Marc H. Garner
- Department of Chemistry and Nano-Science Center, University
of Copenhagen, Universitetsparken
5, DK-2100, Copenhagen
Ø, Denmark
- Department
of Chemistry and Chemical Biology, Cornell
University, Ithaca, New York 4850, United
States
| | - Roald Hoffmann
- Department
of Chemistry and Chemical Biology, Cornell
University, Ithaca, New York 4850, United
States
| | - Sten Rettrup
- Department of Chemistry and Nano-Science Center, University
of Copenhagen, Universitetsparken
5, DK-2100, Copenhagen
Ø, Denmark
| | - Gemma C. Solomon
- Department of Chemistry and Nano-Science Center, University
of Copenhagen, Universitetsparken
5, DK-2100, Copenhagen
Ø, Denmark
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Affiliation(s)
- Alicia C. Voukides
- Department
of Chemistry University of New Hampshire, Durham, New Hampshire 03824, United States
| | - Katharine J. Cahill
- Department
of Chemistry University of New Hampshire, Durham, New Hampshire 03824, United States
| | - Richard P. Johnson
- Department
of Chemistry University of New Hampshire, Durham, New Hampshire 03824, United States
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Christl M, Groetsch S, Günther K. The Dimerization of Chiral Allenes: Pairs of Enantiomers and Pairs of Homomers Furnish Different Diastereomers Cycloallenes, Part 14. This work was supported by the Deutsche Forschungsgemeinschaft, by the Fonds der Chemischen Industrie, and by CHEMETALL GmbH. Part 13: M. Christl, S. Groetsch, Eur. J. Org. Chem. 2000, 1871-1874. Angew Chem Int Ed Engl 2000; 39:3261-3263. [PMID: 11028070 DOI: 10.1002/1521-3773(20000915)39:18<3261::aid-anie3261>3.0.co;2-t] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- M Christl
- Institut für Organische Chemie der Universität Am Hubland, 97074 Würzburg (Germany)
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Witt O, Mauser H, Friedl T, Wilhelm D, Clark T. Reactions of the Lithium Salts of the Tribenzylidenemethane Dianion, Diphenylacetone Dianion, and Related Compounds. J Org Chem 1998. [DOI: 10.1021/jo971113c] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ortrun Witt
- Institut für Organische Chemie I der Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestrasse 42, D-91054 Erlangen, Germany
| | - Harald Mauser
- Institut für Organische Chemie I der Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestrasse 42, D-91054 Erlangen, Germany
| | - Thomas Friedl
- Institut für Organische Chemie I der Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestrasse 42, D-91054 Erlangen, Germany
| | - Dieter Wilhelm
- Institut für Organische Chemie I der Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestrasse 42, D-91054 Erlangen, Germany
| | - Timothy Clark
- Institut für Organische Chemie I der Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestrasse 42, D-91054 Erlangen, Germany
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Affiliation(s)
- Holger F. Bettinger
- Institut für Organische Chemie, Friedrich-Alexander Universität Erlangen-Nürnberg, Henkestr. 42, D-91054 Erlangen, Germany, Institut für Organische Chemie, Georg-August Universität Göttingen, Tammannstr. 2, D-37077 Göttingen, Germany, and the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602
| | - Paul v. R. Schleyer
- Institut für Organische Chemie, Friedrich-Alexander Universität Erlangen-Nürnberg, Henkestr. 42, D-91054 Erlangen, Germany, Institut für Organische Chemie, Georg-August Universität Göttingen, Tammannstr. 2, D-37077 Göttingen, Germany, and the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602
| | - Peter R. Schreiner
- Institut für Organische Chemie, Friedrich-Alexander Universität Erlangen-Nürnberg, Henkestr. 42, D-91054 Erlangen, Germany, Institut für Organische Chemie, Georg-August Universität Göttingen, Tammannstr. 2, D-37077 Göttingen, Germany, and the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602
| | - Henry F. Schaefer
- Institut für Organische Chemie, Friedrich-Alexander Universität Erlangen-Nürnberg, Henkestr. 42, D-91054 Erlangen, Germany, Institut für Organische Chemie, Georg-August Universität Göttingen, Tammannstr. 2, D-37077 Göttingen, Germany, and the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602
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Affiliation(s)
- Marcus S. Brody
- Contribution from the Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901
| | - Robin M. Williams
- Contribution from the Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901
| | - M. G. Finn
- Contribution from the Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901
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Affiliation(s)
- Holger F. Bettinger
- Institut für Organische Chemie, Friedrich-Alexander Universität Erlangen-Nürnberg, Henkestr. 42, D-91054 Erlangen, Germany, and the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602
| | - Peter R. Schreiner
- Institut für Organische Chemie, Friedrich-Alexander Universität Erlangen-Nürnberg, Henkestr. 42, D-91054 Erlangen, Germany, and the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602
| | - Paul v. R. Schleyer
- Institut für Organische Chemie, Friedrich-Alexander Universität Erlangen-Nürnberg, Henkestr. 42, D-91054 Erlangen, Germany, and the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602
| | - Henry F. Schaefer
- Institut für Organische Chemie, Friedrich-Alexander Universität Erlangen-Nürnberg, Henkestr. 42, D-91054 Erlangen, Germany, and the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602
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Valtazanos P, Ruedenberg K. The ring opening of substituted cyclopropylidenes to substituted allenes: the effects of steric and long-range electrostatic interactions. ACTA ACUST UNITED AC 1991. [DOI: 10.1007/bf01112347] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Valtazanos P, Elbert ST, Xantheas S, Ruedenberg K. The ring opening of cyclopropylidene to allene: global features of the reaction surface. ACTA ACUST UNITED AC 1991. [DOI: 10.1007/bf01112344] [Citation(s) in RCA: 50] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Semenov SG, Tulub AV. Investigation of the electrical properties of molecules in the presence of accidental degeneracy. Calculation of 1,3-diphenylallene in the CNDO approximation. J STRUCT CHEM+ 1986. [DOI: 10.1007/bf00754142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Fujisawa T, Iida S, Sato T. A convenient synthesis of allenes by the reaction of propargyl alcohols with grignard reagents using 1-chloro-2-methyl-n,n-tetramethylenepropenylamine. Tetrahedron Lett 1984. [DOI: 10.1016/0040-4039(84)80052-0] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Ruch E, Runge W, Kresze G, Ruch E. Experimentelle Prüfung von Näherungsansätzen für Chiralitätsfunktionen am Beispiel der optischen Aktivität von Allen-Derivaten im Transparenzgebiet. Angew Chem Int Ed Engl 1973. [DOI: 10.1002/ange.19730850103] [Citation(s) in RCA: 38] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Ruch E, Runge W, Kresze G. Semiempirical Use of Chirality Functions for the Description of the Optical Activity of Allene Derivatives in the Transparent Region. ACTA ACUST UNITED AC 1973. [DOI: 10.1002/anie.197300201] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Baker R, Garratt P, Nicolaou K, Sondheimer F. Diastereomeric monocyclic diallenes. The stereochemistry of formation of racemic and meso-3,4,9,10-cyclodecatetraene-1,7-dione. Tetrahedron Lett 1972. [DOI: 10.1016/s0040-4039(01)94062-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Schöllkopf U, Fellenberger K, Rizk M. 1.2-Wanderungen zum Atom mit freiem Elektronenpaar, VIII.ortho-Isomerisation bei anionisierten Äthern und Wanderungsmechanismus eines Propargyl-Restes bei der Wittig-Umlagerung. ACTA ACUST UNITED AC 1970. [DOI: 10.1002/jlac.19707340111] [Citation(s) in RCA: 36] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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