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The Lewis acid-promoted rearrangement of enol acetals to cyclic ethers, which involves an oxygen-to-carbon transposition, is known as the Petasis-Ferrier rearrangement. This reaction is generally referred to as the “Type II” Ferrier rearrangement.
Al(III), Hg(II), and Pd(II) reagents are often used for this reaction.
・Ferrier, R. J. J. Chem. Soc. Perkin Trans. 1 1979, 1455. DOI: 10.1039/P19790001455
・Petasis, N. A.; Lu, S.-P. J. Am. Chem. Soc. 1995, 117, 6394. DOI: 10.1021/ja00128a044
・Petasis, N. A.; Lu, S.-P. Tetrahedron Lett. 1996, 37, 141. doi:10.1016/0040-4039(95)02114-0
・Ferrier, R. J.; Middleton, S. Chem. Rev. 1993, 93, 2779. DOI: 10.1021/cr00024a008
Note the difference between this reaction and the Type I Ferrier reaction, which is the allylic substitution of 1,2-glycals.
An application in the total synthesis of phorboxazole A.
An interesting variant which effects one-carbon homologation.
The exo-olefin enol acetals are commonly prepared from β-hydroxycarboxylic acids and aldehydes, which form cyclic acetals, followed by olefination with the Petasis reagent.
 Smith, A. B., III; Minbiole, K. P.; Verhoest, P. R.; Schelhaas, M. J. Am. Chem. Soc. 2001, 123, 10942. DOI: 10.1021/ja011604l
 O’Neil, E.; Kingree, S. V.; Minbiole, K. P. C. Org. Lett. 2005, 7, 515. DOI: 10.1021/ol047426t