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Reference found in article:  Wadsworth, W. S.; Emmons, W. D. J. Am.  Chem. Soc. 1961, 83, 1733-1738.
A key  component of the transformation of molecule 3 to molecule 4 is the  Horner-Wadsworth-Emmons reaction. This paper, written by Wadsworth and Emmons,  details this mechanism in depth, in collaboration with ideas from a previous  paper written by Emmons. In the first step of the reaction, a phosphonate anion  adds to an aldehyde or ketone, forming an alkoxide intermediate. This  intermediate is in equilibrium with a four-membered ring. The molecule then  undergoes fragmentation yielding a phosphate anion and a newly formed double  bond in the product. The paper discusses the benefits of using a phosphonate  anion, because it reacts without reverse addition and can be used effectively  with all ketones, even those that are sterically hindered. The phosphonate  anion has three contributing resonance structures, giving the P=O bond some  single bond character, which aid in its ability to react under mild conditions.  The first step in the mechanism, where an aldehyde or ketone is added to the  carbonyl group, yields an intermediate that is in equilibrium with a  four-membered ring. These equilibrating structures then undergo fragmentation  to yield the product and phosphate anion. Phosphonate anions can be used in  conjunction with the Horner-Wadsworth-Emmons mechanism to yield a variety of different  reaction products. For instance, they can react with alkyl halides to give  α-substituted phosphonates, which will react with a hydride reagent and an  aldehyde or ketone to give olefins, which is a type of synthetic fiber.  Additionally, halogenation of a phosphonate anion with subsequent addition of  an aldehyde or ketone will produce vinyl halides.



