these respective transitions. Triplet sensitizers result in non-Wolff carbene byproducts, and thus are not useful in synthetic applications of the Wolff rearrangement. However, they have been used to probe the mechanism of the Wolff rearrangement. Synthetic uses The Wolff rearrangement has a few retrons, depending on the reaction out of the ketene intermediate. A carboxylic acid derivative with an α-methylene group is a retron for an Arndt-Eistert type homologation. An acid in which the α-carbon belongs to a ring is a retron for a Wolff rearrangement ring contraction. Homologation reactions In the Arndt-Eistert homologation reaction, a carboxylic acid and thionyl chloride are reacted to generate an acid chloride. The acid chloride then reacts with diazomethane (R2 = H), or occasionally a diazoalkyl, via the Arndt-Eistert procedure, to generate an α-diazo ketone, which will undergo a metal-catalyzed or photolyzed Wolff rearrangement, to give a ketene. The ketene can be trapped with any weak acid, such as an alcohol or amine, to form the ester or amide. However, trapping with water, to form the acid is the most common form. In the most basic form, where R2= H, RXH=H2O, the reaction lengthens the alkyl chain of a carboxylic acid by a methylene. However, there is great synthetic utility in the variety of reactions one can carry out, by varying the diazoalkyl and weak acid. The migrating group, R1 migrates with complete retention. A very useful application of the Arndt-Eistert homologation forms the homologated aldehyde by either trapping the ketene with N-methyl aniline and reducing with lithium aluminum hydride, or trapping the ketene with ethanethiol and reducing with Raney nickel. There exist many hundreds of examples of the Arndt-Eistert homologation in the literature. Prominent examples in natural product total synthesis include the syntheses of (−)-indolizidine and (+)-macbecin. A recent example of the Arndt-Eistert homologation is a step in the middle stage of Sarah Reisman's synthesis of (+)-salvileucalin B. Ring contractions If the reactant is a cyclic α-diazo ketone, then Wolff-rearrangement products will be the one-carbon ring-contracted product. These reactions are generally concerted due to the s-cis conformation, and are photocatalyzed. The reaction below shows the concerted mechanism for the ring contraction of α-diazocyclohexanone, followed by trapping of the ketene with a weakly acidic nucleophile. The first known example is the ring contracted Wolff rearrangement product of α-diazocamphor, and subsequent kinetic hydration of the ketene from the more sterically accessible "endo" face, to give