Dedicated to Paul von Ragué Schleyer, friend and mentor, on the occasion of his 80th birthday A computational study on the rearrangement of 2,2-diphenyl-1-[(E)-2-phenylethenyl]cyclopropane (1) is presented, using density functional theory (DFT), (U)B3LYP with the 6-31G* basis set (DFT1) and (U)M05-2X with the 6-311 þ G** basis set (DFT2). In agreement with a biradical character of the transition structure (TS) or intermediate, the potential-energy hypersurface is lowered by the influence of three conjugated Ph groups. Surprisingly, two conformations of the geminal diphenyl group (different twist angles) induce two different minimum-energy pathways for the rearrangement. Independent of the functional used, the first hypersurface harbors true biradical intermediates, whereas the second energy surface is a flat, slightly ascending slope from the starting material to the TS. The functional (U)M05-2X with the basis set 6-311 þ G** provides realistic energies which seem to be close to experiment. The activation energy for racemization of enantiomers of 1 is lower than that of rearrangement by 2.5 kcal mol
À1, in agreement with experiment.1. Introduction. -The rearrangement of vinylcyclopropane and its derivatives to substituted cyclopentenes has played an important role in the development of mechanistic and theoretical organic chemistry. Ever since the discovery of this reaction, independently by Vogel [1], and by Overberger and Borchert [2], it has been studied experimentally and theoretically. It played a role in the presentation of the WoodwardÀHoffmann rules [3], was recognized early as involving biradical intermediates [3 -5], and was analyzed by quantum-chemical calculations [6] [7]. A critical review on mechanistic aspects of this rearrangement was provided by Baldwin [8].The reaction exhibits both aspects, that of a concerted and a stepwise mechanism. However, calculations on the potential-energy surface of the unsubstituted system display only one transition structure (TS) for rearrangement and no intermediate [6]. The potential-energy surface is rather flat and diradical in nature. The TS is a biradical which undergoes ring closure to cyclopentene. The results of Houks group closely resemble those of Davidson and Gajewski [7], who took a slightly different approach. Both studies agree on the biradical nature of the rearrangement and on the preference for the si-stereochemistry of rearrangement suggested by the WoodwardÀHoffmann rules [3]. For the unsubstituted system, two more TSs, slightly (0.3 -1.1 kcal mol À1 )