The Pathway of Minimum Steps for the Bulivalene Automerlzation It was in 1962, in a journal scarcely available in the West, that the structural consequences of a rapid and degenerate Cope rearrangement in bullvalene (tricycl0[3.3.2.0~~~1deca-3,6,9-triene)
@ bullvalene
were first pointed out by William Doering.' A full discussion by Doering and Roth of the evolution of the concept of bullvalene appeared in 1963in a far more accessible place.2 Accounts of syntheses of this fascinatiqg molecule rapidly followed,34and its properties have been a subiect of intensive interest ever since." ~ d l v a l e nis e capable of Guming any of its 10!/3 = 1,209,600forms. In order to demonstrate this possibilityof fluxionality, Doering and Roth developed a scheme whereby an adjacent pair of carbon atoms (carbons 1and 2) was interchanged through a sequence of some 47 Cope rearrangements. Although no claim waa made that this represented a'minimum or even short sequence, the discovery of such has remained an object of substantial interest. We have used an exhaustive computer search to determine that the path of minimum steps for interconvemion of carbons of types I and I1 involves 17 Cope rearrangements. One sequence is shown below. We have retained the notation of Doering and Roth and used their devices of clockwise and counterclockwise rotation (CWrot and CCWrot) and of a-7eaehange.2
These proceaees require 2 and 7 Cope rearrangements, respectively. At the heart of the path we have discovered is the eachange, in 15 steos, of two cvclonroovl (4 and 5). Entw to this seauence as well as eeress from it is achieved hv . . .. oositions . ,asimpie Cope rearrangement, thus requiring the total of 17 for 1,iinterconvemion (0-8exchange). Of the 1.29 X 1OSpossihle 17-step sequences, only 24 are productive! Interchanges of carbonsof type I1 and I11 or Ill and IV ran also beachieved but only in more than I: steps."
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'von E. Doering, W., Zh. Vsesoyuz. Khim. Obshchestuo imD. I. Mendeleem, 7,308 (1962). %on E. Doering, W., and Roth, W. R., Tetrahedron, 19,715 (1963); von E. Doering, W., and Roth, W. R., Angew. Chem. Inter. Ed., 2.115 (1963). %chrger, G., Angew. Chem. Inter. Ed., 2,481 (1963). 'von E. Doering, W., Ferrier, B. M., Foasel, E. T., Hartenatein, J. H., Jones, Jr., M., Klumpp, G.,Rubin, R. M., and Saunders, M., Tetrahedron, 23,3943 (1967). 'Scott, L. T., and Jones, Jr., M., Chem. Revs., 72,181 (1972);S c M e r , G.,and Otb, J. F.M., Angew. Chem.Int. Ed. Engl., 6,414 (1967). 6We thank the Department of Chemistry a t Princeton University for funds for computer time. Princeton University Princeton, New Jersey 08540
Karl E. Bennett Allan Fisher
