{"id":5834,"date":"2011-12-11T10:12:36","date_gmt":"2011-12-11T10:12:36","guid":{"rendered":"http:\/\/www.ch.imperial.ac.uk\/rzepa\/blog\/?p=5834"},"modified":"2011-12-11T11:39:14","modified_gmt":"2011-12-11T11:39:14","slug":"violations-there-are-none","status":"publish","type":"post","link":"https:\/\/www.ch.ic.ac.uk\/rzepa\/blog\/?p=5834","title":{"rendered":"Violations. There are none!"},"content":{"rendered":"
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Thus famously wrote Woodward and Hoffmann (WH) in their\u00a0classic monograph<\/a> about the conservation of orbital symmetry in pericyclic reactions. But they also note that the “fantastic” hydrocarbon (number 85<\/strong> in their review) shown below presents a situation of great interest <\/em>in having a half life of ~30 minutes<\/a> at 353K (a free energy barrier of ~ 26.2 kcal\/mol). Here I investigate if it might actually be such a violation.<\/p>\n

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I should first note that WH expect that violating reactions are likely to comport themselves via<\/em> a non-concerted reaction path involving discrete intermediates.1<\/sup> Which in the above case would be a biradical. But why is it an interesting example? Because, as a 4n (n=2) electron electrocyclic reaction (involving the bonds shown in red above), it must involve one\u00a0antarafacial<\/em> component. This is apparently rendered impossible (so WH claim) by the very rigid geometry of the system. However, an alternative, and geometrically more viable reaction involving only suprafacia<\/em>l components would indeed be be a violation according to their definition, if it were to be concerted, without (biradical) intermediates. So if a concerted pathway with no antarafacial<\/em> components could<\/em> be found, it would constitute a violation.<\/p>\n

To model this system, the benzo groups (blue) are first removed. A transition state for the reaction is found<\/a> [\u03c9B97XD\/6-311g(d)] with \u0394G\u2020<\/sup> 21.5 kcal\/mol and an intrinsic reaction coordinate<\/a> (IRC) that shows a concerted profile, albeit one with quite unusual features revealed in the gradient norm along the IRC.<\/p>\n\n\n\n
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  1. One might first note that the calculated barrier is similar to that measured for the real reaction (albeit with benzo groups). Although this does not prove that a lower energy process (such as involving biradicals) does not occur, it does at least suggest that the concerted pathway is not unreasonable given the observed kinetics of the reaction.<\/li>\n
  2. The geometry up to the transition state (IRC=0.0 above) retains a plane of symmetry, and there is no hint of any axis of symmetry developing that might be associated with twisting due to an antarafacial<\/em> component (click on the graphic below to inspect this geometry). However, the length of the cleaving bond (2.85\u00c5) is unusually long for a transition state involving C-C cleavage, and the double bond (green above) is still intact (1.33\u00c5). There is however an asymmetry developing, in which one of the 6-rings is moving faster than the other.<\/li>\n
  3. At an IRC value of +5 (well past the transition state), something unexpected starts to happen; it is best seen as a very prominent feature in the gradient norm. Only now does the C=C bond start to lengthen to that typical of a pericyclic transition state (~1.40\u00c5).<\/li>\n
  4. By IRC +8, the erstwhile C=C bond has reached 1.43\u00c5, but the geometry still retains most of its plane of symmetry. At IRC +10, this suddenly and abruptly breaks, and one trans\u00a0<\/em>alkene starts to form in the rhs ring. You can see this in the animation below, where one hydrogen suddenly accelerates its motion to fully assimilate the trans<\/em> position (this phenomenon is a feature of so-called valley-ridge inflection points<\/a>) and the other reverses its own motion. Prior to this, the trans\u00a0<\/em>component had been divided amongst two C=C bonds in the forming product, thus preserving the plane of symmetry.\n
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    Animation of the geometry along the IRC. Click for 3D.<\/p><\/div><\/div>\n<\/li>\n

  5. The product of this IRC is thus a biphenyl where one of the phenyl rings sustains a trans\u00a0<\/em>component, a M\u00f6bius benzene in fact! Appropriately, the bond lengths in this (antiaromatic) ring alternate, whereas they are all equal in the other (aromatic) ring.
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    Click to invoke Jmol<\/th>\nRotate with mouse<\/th>\n<\/tr>\n
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    A M\u00f6bius benzene. Click for 3D<\/p><\/div><\/td>\n