The 16 kcal/mol Anomaly: Alteration of [2 + 2 + 2] Cycloaddition Rates by Through-Bond Interactions Dorota Sawicka, Sarah Wilsey, and K. N. Houk* Department of Chemistry and Biochemistry UniVersity of California Los Angeles, California 90095-1569 ReceiVed December 22, 1997 ReVised Manuscript ReceiVed NoVember 21, 1998 The [2 + 2 + 2] retro-cycloaddition reactions of bridged cyclohexanes show an enormous acceleration of cleavage of cyclopropane-bridged systems compared to cyclobutane-bridged systems. 1 The reactions of simple derivatives of 1 occur readily at 60 °C; 1 has an estimated activation energy of about 25 kcal/ mol. 1 The ring-opening reaction of 2 is only 7 kcal/mol less exothermic but only occurs above 400 °C, with an activation energy of over 50 kcal/mol! 2 The patterns found for this and other 3 systems show a general preference for cleavage of odd-membered rings. An anomalously high rate of cyclopropane cleavage has also been noted by Ingold and Beckwith in several radical systems 4 and by Stirling and co- workers in anionic systems. 5,6 Semiempirical 5,6 and ab initio 7 calculations led these authors to the conclusion that the strain energy in cyclopropane is released more efficiently than in cyclobutane rings. Berson has suggested that orbital interactions involving bent bonds favor the [2 + 2 + 2] cycloreversion of 3,4-diazabicyclo[4.1.0]hept-3-enes over 3,4-diazabicyclo[4.2.0]- oct-3-enes. 8 We have found that symmetry-imposed differences in through-bond coupling can have very large effects on rate. We investigated bond cleavage reactions in the [2 + 2 + 2] cycloreversions of systems 1, 2, 3 and related mono- and bis- substituted cyclohexanes using the hybrid density functional theory method, B3LYP, and the complete active space SCF methods, CASSCF. The 6-31G* basis set was used with both methods. All computations were carried out using GAUSSIAN 94. 9 Reactants, transition structures, and products were fully optimized in each case. Frequency calculations were performed on all structures except the CASSCF transition structure for the cycloreversion of 2 due to computational expense. To assess the aromatic properties of the transition states, NICS (nucleus- independent chemical shift) 10 values were calculated with GIAO- SCF/6-31G* on B3LYP/6-31G* geometries. The transition structures for the [2 + 2 + 2] cycloreversions involving cyclohexanes bridged by three three-, four- and five- membered rings are shown in Figure 1. 11 The mono- and bis- bridged analogues of systems 1, 2, and 3 and the tris- cyclobutenacyclohexane were also studied. These reactions are all essentially synchronous concerted processes. The ∆E rxn are plotted against ∆E ‡ for all cases (Figure 2 and Table 1). CASSCF values for several systems give the same relative activation energies. The activation energy is related to the energy of reaction by ∆E ‡ ) 0.86∆E rxn + 55.8: the more exothermic the reaction, the lower the activation energy. Deviations below this line indicate that the activation energy is anomalously low for that energy of reaction. Deviations above the line suggest that the transition state is less stable than expected from the energy of reaction. The parent reaction and those involving cleavage of five-membered rings lie within a few kcal/mol of the least-squares line. The mono-, bis-, and tris-cyclobutacyclohexanes and tris-cyclobutenacyclo- hexane lie above the line, with deviations corresponding to activation energies 5-11 kcal/mol higher than expected. The mono-, bis-, and tris-cyclopropacyclohexanes lie below the line; (1) (a) Spielmann, W.; Fick, H.-H.; Meyer, L.-U.; de Meijere, A. Tetrahedron Lett. 1976, 45, 4057. (b) Rucker, C.; Muller-Botticher, H.; Braschwitz, W.-D.; Prinzbach, H.; Reifenstahl, U.; Irngartinger, H. Liebigs Ann./Recueil 1997, 967. (c) Zipperer, B.; Muller, K.-H.; Gallenkamp, B.; Hildebrand, R.; Fletschinger, M.; Burger, D.; Pillat, M.; Hunkler, D.; Knothe, L.; Fritz, H.; Prinzbach, H. Chem Ber. 1988, 121, 757. (2) Maas, M.; Lutterbeck, M.; Hunkler, D.; Prinzbach, H. Tetrahedron Lett. 1983, 24, 2143.; Mohler, D. L.; Vollhardt, P. C.; Wolff, S. Angew. Chem., Int. Ed. Engl. 1990, 29, 1151 (3) Wilsey, S.; Dowd, P.; Houk, K. N., to be submitted for publication. (4) (a) Ingold, K. U.; Maillard, B.; Walton, J. C. J. Chem. Soc., Perkin Trans. 2 1981, 970. (b) Beckwith, A. L. J.; Ingold, K. U. Rearrangements in Ground and Excited States; de Mayo, P., Ed.; Academic Press: New York, 1980; and references therein. For an example where stereoelectronic effects override this preference, see: Beckwith, A. L. J.; Moad, G. J. Chem. Soc., Perkin Trans. 2 1980, 1083. (5) (a) Stirling, C. J. M. Tetrahedron 1985, 41, 1613. (b) Stirling, C. J. M. Pure and Appl. Chem. 1984, 56, 1781 and references therein. (6) (a) Earl, H. A.; Marshall, D. R.; Stirling, C. J. M. J. Chem. Soc., Perkin Trans. 2 1983, 779. (b) Earl, H. A.; Stirling, C. J. M. J. Chem. Soc., Perkin Trans. 2 1987, 1273. (c) Bury, A.; Earl, H. A.; Stirling, C. J. M. J. Chem. Soc., Perkin Trans. 2 1987, 1281. (7) Tonachini, G., Bernardi, F.; Schlegel, H. B.; Stirling, C. J. M. J. Chem. Soc., Perkin Trans. 2 1988, 705. (8) Berson, J. A.; Olin, S. S.; Petrillo, E. W., Jr.; Pickart, P. Tetrahedron 1974, 30, 1639. (9) GAUSSIAN 94 (Revision B2) Frisch, M. J. et al. Gaussian Inc., Pittsburgh, PA, 1995. (10) (a) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; Hommes, N. J. R. v. E. J J. Am. Chem. Soc. 1996, 118, 6317. (b) Jiao, H. and Schleyer, P. v. R., submitted for publication. (11) The [2 + 2 + 2] cycloreversion of 1 has been calculated using MINDO/3, see: Spanget-Larsen J.; Gleiter, R. Angew. Chem., Int. Ed. Engl. 1978, 17, 441. Figure 1. B3LYP/6-31G* and (CASSCF) optimized geometries of the transition structures for [2 + 2 + 2] cycloreversion reactions of cyclohexane bridged by three (a) cyclopropane, (b) cyclobutane and (c) cyclopentane rings. Figure 2. Plot of activation energy (∆E ‡ ) against energy of reaction (∆Erxn) for [2 + 2 + 2] cycloreversion reactions of unbridged and bridged cyclohexane systems. Deviations from the least-squares line are given next to the horizontal lines. 864 J. Am. Chem. Soc. 1999, 121, 864-865 10.1021/ja974322n CCC: $18.00 © 1999 American Chemical Society Published on Web 01/16/1999