Editing Allenes (section)

===Symmetry===
[[File:Allene symmetry.png|none|300px]]
The symmetry and isomerism of allenes has long fascinated organic chemists.<ref>{{March6th}}</ref> For allenes with four identical substituents, there exist two twofold axes of rotation through the central carbon atom, inclined at 45° to the CH<sub>2</sub> planes at either end of the molecule. The molecule can thus be thought of as a two-bladed [[propeller]]. A third twofold axis of rotation passes through the C=C=C bonds, and there is a mirror plane passing through both CH<sub>2</sub> planes. Thus this class of molecules belong to the D<sub>2d</sub> [[point group]]. Because of the symmetry, an unsubstituted allene has no net [[bond dipole moment|dipole moment]], that is, it is a non-polar molecule.
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| footer    = ''R'' and ''S'' configurations are determined by precedences of the groups attached to the axial section of the molecule when viewed along that axis. The front plane is given higher priority over the other and the final assignment is given from priority 2 to 3 (i.e. the relationship between the two planes).
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An allene with two different substituents on each of the two carbon atoms will be [[chirality (chemistry)|chiral]] because there will no longer be any mirror planes. The chirality of these types of allenes was first predicted in 1875 by [[Jacobus Henricus van 't Hoff]], but not proven experimentally until 1935.<ref>{{cite journal |title= Experimental Demonstration of the Allene Asymmetry |first1= Peter |last1= Maitland |first2= W. H. |last2= Mills |journal= Nature |volume= 135 |pages= 994 |year= 1935 |issue= 3424 |doi= 10.1038/135994a0 |bibcode= 1935Natur.135Q.994M |s2cid= 4085600 |doi-access= free }}</ref> Where '''A''' has a greater priority than '''B''' according to the [[Cahn–Ingold–Prelog priority rules]], the configuration of the [[axial chirality]] can be determined by considering the substituents on the front atom followed by the back atom when viewed along the allene axis. For the back atom, only the group of higher priority need be considered.

Chiral allenes have been recently used as building blocks in the construction of organic materials with exceptional chiroptical properties.<ref>{{cite journal|title=Allenes in Molecular Materials|last1=Rivera Fuentes|first1=Pablo|last2=Diederich|first2=François|journal=Angew. Chem. Int. Ed. Engl.|date=2012|volume=51|issue=12|pages=2818–2828|doi=10.1002/anie.201108001|pmid=22308109|doi-access=free}}</ref> There are a few examples of drug molecule having an allene system in their structure.<ref>{{Cite journal|last1=Celmer|first1=Walter D.|last2=Solomons|first2=I. A.|title=The Structure of the Antibiotic Mycomycin|date=1952|url=http://dx.doi.org/10.1021/ja01127a529|journal=Journal of the American Chemical Society|volume=74|issue=7|pages=1870–1871|doi=10.1021/ja01127a529|issn=0002-7863}}</ref>  Mycomycin, an antibiotic with tuberculostatic properties,<ref>{{Cite journal|last=Jenkins|first=D.E.|date=1950|title=Mycomycin: a new antibiotic with tuberculostatic properties.|journal=J Lab Clin Med|volume=36|issue=5|pages=841–2|pmid=14784717}}</ref> is a typical example. This drug exhibits enantiomerism due to the presence of a suitably substituted allene system.

Although the semi-localized textbook [[Sigma-pi separation|σ-π separation]] model describes the bonding of allene using a pair of localized orthogonal π orbitals, the full molecular orbital description of the bonding is more subtle.  The symmetry-correct doubly-degenerate HOMOs of allene (adapted to the D<sub>2d</sub> point group) can either be represented by a pair of orthogonal MOs ''or'' as twisted helical linear combinations of these orthogonal MOs.  The symmetry of the system and the degeneracy of these orbitals imply that both descriptions are correct (in the same way that there are infinitely many ways to depict the doubly-degenerate HOMOs and LUMOs of benzene that correspond to different choices of eigenfunctions in a two-dimensional eigenspace).  However, this degeneracy is lifted in substituted allenes, and the helical picture becomes the only symmetry-correct description for the HOMO and HOMO–1 of the C<sub>2</sub>-symmetric {{ill|2,3-Pentadiene|lt=1,3-dimethylallene|de|2,3-Pentadien}}.<ref>{{Cite journal|last1=H. Hendon|first1=Christopher|last2=Tiana|first2=Davide|last3=T. Murray|first3=Alexander|last4=R. Carbery|first4=David|last5=Walsh|first5=Aron|date=2013|title=Helical frontier orbitals of conjugated linear molecules|journal=Chemical Science|language=en|volume=4|issue=11|pages=4278–4284|doi=10.1039/C3SC52061G|doi-access=free|hdl=10044/1/41564|hdl-access=free}}</ref><ref>{{Cite journal|last1=Garner|first1=Marc H.|last2=Hoffmann|first2=Roald|last3=Rettrup|first3=Sten|last4=Solomon|first4=Gemma C.|author-link4=Gemma Solomon|date=2018-06-27|title=Coarctate and Möbius: The Helical Orbitals of Allene and Other Cumulenes|url=|journal=ACS Central Science|volume=4|issue=6|pages=688–700|doi=10.1021/acscentsci.8b00086|issn=2374-7943|pmc=6026781|pmid=29974064}}</ref> This qualitative MO description extends to higher odd-carbon cumulenes (e.g., 1,2,3,4-pentatetraene).
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