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My textbook (Klein) describes the mechanism for the Wittig reaction as a [2+2] cycloaddition, followed by a collapse of the ring.

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As far as I'm aware, [2+2] cycloadditions are symmetry forbidden, unless the reaction is light-initiated, which the text does not mention. Is the book wrong? If not, what is going on here?

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    $\begingroup$ What if the reaction is not concerted? ;) $\endgroup$ Commented Nov 25, 2016 at 20:09
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    $\begingroup$ Then the reaction is not a cycloaddition and a completely different mechanism is needed? (I learned that pericyclic reactions are always concerted, but I may be wrong...) $\endgroup$
    – roymend
    Commented Nov 25, 2016 at 20:17
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    $\begingroup$ Very interesting question! I'd like to point out that a thermal $[2_\mathrm{s} + 2_\mathrm{s}]$ cycloaddition is Woodward-Hoffmann forbidden, but a $[2_\mathrm{s} + 2_\mathrm{a}]$ cycloaddition is (e.g. the reaction of a ketene with an alkene proceeds in this manner). See: Why is the Wittig reaction syn stereoselective? Also, Grossman talks about this a bit in his book The Art of Writing Reasonable Reaction Mechanisms. I've attached the relevant pages here. $\endgroup$ Commented Nov 25, 2016 at 20:33
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    $\begingroup$ The other question to ask is: what is the symmetry of the orbitals on the phosphorus ylide? $\endgroup$
    – Zhe
    Commented Nov 25, 2016 at 20:38
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    $\begingroup$ I think, the simplest explanation here is that the reaction is not concerted. But then remember that the Wittig ylide is not exactly identical to your average alkene either. $\endgroup$
    – Jan
    Commented Nov 25, 2016 at 23:03

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