substrates. Johnson–Claisen and Ireland–Claisen rearrangements of ketene acetals 4 have been used a number of times to prepare allenic esters and acids. Reactions of vinyl ethers 5 (the Saucy–Marbet rearrangement) give allene aldehydes, while propargylic sulfenates 6 give allene sulfoxides. Allenes can also be prepared by nucleophilic substitution in 9 and 10 (nucleophile Nu− can be a hydride anion), 1,2-elimination from 8, proton transfer in 7, and other, less general, methods. Use and occurrence Use The reactivity of allenes is rich and opens wide possibilities for discovery. The two π-bonds are located at the 90° angle to each other, and thus require a reagent to approach from somewhat different directions. With an appropriate substitution pattern, allenes exhibit axial chirality as predicted by van’t Hoff as early as 1875. Such compounds are now extensively investigated. Protonation of allenes gives cations 11 that undergo further transformations.56 Reactions with soft electrophiles (e.g. Br+) deliver positively charged onium ions 13. Transition-metal-catalysed reactions proceed via allylic intermediates 15 and have attracted significant interest in recent years. Numerous cycloadditions are also known, including [4+2]-, (2+1)-, and [2+2]-variants, which deliver, e.g., 12, 14, and 16, respectively. Occurrence Numerous natural products contain the allene functional group. Noteworthy are the pigments fucoxanthin and peridinin. Little is known about the biosynthesis, although it is conjectured that they are often generated from alkyne precursors. Allenes serve as ligands in organometallic chemistry. A typical complex is Pt(η2-allene)(PPh3)2. Ni(0) reagents catalyze the cyclooligomerization of allene. Using a suitable catalyst (e.g. Wilkinson's catalyst), it is possible to reduce just one of the double bonds of an allene. Delta convention Many rings or ring systems are known by semisystematic names that assume a maximum number of noncumulative bonds. To unambiguously specify derivatives that include cumulated bonds (and hence fewer hydrogen atoms than would be expected from the skeleton), a lowercase delta may be used with a subscript indicating the number of cumulated double bonds from that atom, e.g. 8δ2-benzocyclononene. This may be combined with the λ-convention for specifying nonstandard valency states, e.g. 2λ4δ2,5λ4δ2-thieno[3,4-c]thiophene. See also Compounds with three or more adjacent carbon–carbon double bonds are called cumulenes. References Further reading Brummond, Kay M. (editor). Allene chemistry (special thematic issue). Beilstein Journal of Organic Chemistry 7: 394–943. External links Synthesis of allenes Jacobus Henricus van 't Hoff