exo-1,5,5-trimethylbicyclo[2.1.1]hexane-6-carboxylic acid. Ring contractions have been used extensively to build strained ring systems, as ring size does not impede the Wolff rearrangement, but often impedes other reactions. There are many examples where the Wolff rearrangement is used to contract cyclopentanone to cyclobutane. The rearrangement is commonly used to form strained bicyclic and ring-fused systems. There exist a handful of examples of ring contractions from cyclobutanones to cyclopropanes. The Wolff rearrangement is capable of contracting cyclohexanones to cyclopentanes, but is infrequently used to do so, because the Favorskii rearrangement accomplishes this transformation and the Wolff precursor is often more challenging to synthesize. However, an example of a cyclohexanone ring contraction using deformylative diazo transfer, followed by a Wolff rearrangement, is Keiichiro Fukumoto's synthesis of (±)-∆9(12)-capnellene. Cycloaddition reactions Ketene intermediates produced via the Wolff rearrangement are well known to undergo [2 + 2] thermal cycloadditions with olefins to form four-membered rings in both intermolecular and intramolecular reactions, examples of both are shown below. Ketenes are able to undergo what is normally considered a forbidden [2 + 2] cycloaddition reaction because the ketene acts in an antarrafactial manner, leading to the Woodward-Hoffmann allowed [πs2 + πa2] cycloaddition. Ketene [2 + 2] cycloadditions can be difficult reactions and give poor yields due to competing processes. The high energy aldoketene is very reactive and will cyclize with the diazo ketone starting material to produce butenolides and pyrazoles. Ketene [2 + 2] cycloaddition reactions have been used in many total syntheses since Corey's use of the [2 + 2] cyclization in synthesizing the prostaglandins. Robert Ireland's synthesis of (±)-aphidicolin uses the Wolff rearrangement to do a tandem ring-contraction, and [2 + 2] cycloaddition. The Danheiser benzannulation photolyses α-diazo ketones and traps with an alkyne, which undergoes a pericyclic cascade, to ultimately form versatilely substituted phenols. The first step in the benzannulation is the photolysis of an α-diazo ketone to form a vinylketene. The vinylketene then undergoes a [2 + 2] cycloaddition with an alkyne to form a 2-vinylcyclobutenone, which does a 4π electrocyclic ring-opening to generate a dienylketene. The dienylketene subsequently undergoes a 6π electrocyclic ring-closure followed by tautomerization, to form the phenolic benzannulated product. Vinylogous Wolff rearrangements The vinylogous Wolff rearrangement consists of a β,γ-unsaturated diazo ketone undergoing a Wolff rearrangement, and a formal 1,3-shift of the CH2CO2R group. The vinylogous Wolff rearrangement yields a γ,δ-unsaturated carboxylic acid derivative, which is the same retron as