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Communications to the Editor MIND0/2 Study of Aromatic (“Allowed”) Electrocyclic Reactions of Cyclopropyl and Cyclobutene
Sir: Electrocyclic reactions are of especial interest since it was a process of this kind that initiated the classic studies of Woodward and Hoffmann.’ The experimental facts are now well known and several theoretical treatments have appeared.’-12 Here we report a study of the electrocyclic ring opening of cyclopropyl cation, anion, and radical (1-3) and of cyclobutene (4), using the M I N D 0 / 2 m e t h ~ d , ’ ~with , ’ ~ modified parameters13 that give better estimates of molecular geometries, in particular C H bond lengths. In 1-3, the reaction coordinate was taken t o be the apical angle 8 (see l),in 4 the length ( R ) of the bond undergoing rupture. The reaction path was calculated for successive increments of the reaction coordinate; the geometry at each point was calculated by an iterative procedure using a program (SIMPLEX) written by D r . A. Brown and modified by Dr. D. H . Lo, the initial gometry being that for the previous point.
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Cyclopropyl Cation (1). We predict the ring opening to be disrotatory, in agreement with qualitative theories, 1,-4 experiment, l6 and calculations by EH,6 C N D O / 2 (with CI),j and ab initio SCF7methods. We predict the reaction t o require activation, in disagreement with the EH6 and ab initio’ results; n o value was quoted in ref 5. A t first sight this may seem t o be at variance with the evidence16 that rearrangement of the nascent cyclopropyl cation acts as a driving force in the solvolysis of cyclopropyl esters; here, howeker, the nascent cation is formed with a pyramidal ( I ) R. B. Woodward and R. Hoffmann, Angew. Chem., Int. Ed. Engl., 8, 781 (1969). (2) H . C. Longuet-Higgiiis and F. W. Abrahamsoii, J . Amer. Chem. Soc., 87, 2045 (1965). (3) H . E. Zimmerman, ibid., 88, 1564 (1966). (4) M. J. S. Dewar, Tetrahedron, Suppl., 8 (l), 75 (1966); “The Molecular Orbital Theory of Organic Chemistry,” McGraw-Hill, New York, N. Y . , 1969, p 325; Aizgew. Chem., in press. (5) D. T. Clark and G . Smale, Tetrahedron, 25, 13 (1969). (6) W. Kutzelnigg, Tetrahedron Lett., 4965 (1967). (7) D . T. Clark and D . R . Armstrong, Theor. Chim. Acta, 13, 365 ( 1969). (8) D. T. Clark and G . Smale, Tetrahedron Lett., 3673 (1968). (9) D. T. Clark and D. R . Armstrong, Theor. Chim. Acta, 14, 370 (1969). ( I O ) W. Th. A. M. van der Lugt and L. J. Oosterhoff, J . Amer. Chem. Soc., 91, 6042 (1969). (11) I
