J. Org. Chem. 1995,60, 4653-4656 4653 Kinetic Isotope Effects as a Guide to strength on the position of the transition structure along Transition State Geometries for the the reaction pathway for this five-membered Ei mech- Intramolecular Cope and Wide Eliminaion anism. Both reactants, although dipolar in nature, afford Reactions. An ab Initio MO Study neutral elimination products, which simplifies the overall theoretical treatment. Prior experience7with zwitterionic structures such as Robert D. Bach,* Carlos Gonzalez, Jose L. Andres, and H. Bernard Schlegel water oxide (HzO+-O-) suggested that the MP2/6-31G* level of theory would provide adequate geometries for Department of Chemistry, Wayne State University, dipolar reactants 1,3,and 5 (Figures 1and 218 Classical Detroit, Michigan 48202 barrier heights for TS-2 and TS-4 are predicted to be 28.2 and 10.8 kcal/mol, respectively, at the MP2/6-31G* level Received February 6, 1995 of theory. Activation barriers of 29.1 and 11.4 kcaumol were found for these two elimination reactions, respec- The quality of geometries given by electronic structure tively, using full fourth-order Moller-Plesset perturba- calculations may be readily verified by direct comparison tion theory The bar- with experimental data. Excellent agreement between (MP4SDTQ/6-31G*//MP2/6-3lG*). rier for the Cope elimination is consistent with experiment theory and experiment is commonplace even at the (AH$= 24.3-29.4 kcal/mol for 2-phenylethyldimethyl- Hartree-Fock level of theory provided that an adequate amine oxide)."" The lower barrier (AM* = 17.7 kcal/ basis set is employed. When post-Hartree-Fock methods mol) for the ylide mechanism is a consequence of the more are included, the energetics of a great many reactions highly basic carbon atom that is reflected in a much may be accurately determined, as confirmed by matching earlier transition state. Accordingly, the Cope elimina- with experimentally derived thermochemistry. In the tion is endothermic by 4.9 kcal/mol, while the overall gas phase, calculated activation barriers are also found ylide reaction affording isolated products is exothermic to be quite reliable. However, an assessment of the by 45.1 kcal/mol. The C,j-H1 bond elongation is only 6% accuracy of transition state geometries remains a pri- in TS-4 compared to 27% in the Cope elimination. In mary goal of the applied quantum chemist. An experi- both transition structures the internal bond angles mentally determined kinetic isotope effect (KIE) is one involving hydrogen abstraction are noticeably smaller of the few available tools that can probe the geometry of than the anticipated -108" H-0-N and H-C-N bond a transition state.' A number of studies have been angles (Figure 1).lb The percent C-N bond stretch in reported in which theoretically calculated KIE have been TS-2 (34%) and TS-4 (18%) also gives an indication of used in an effort to predict transition state structures.2 the position of the TS along the reaction coordinate, as In this paper we describe a direct comparison of calcu- does the extent of double-bond formation indicated by the lated KIE to experimental values for several intra- change in bond distances. Another indication in molecular elimination reactions to evaluate the accuracy C-C the amount of double-bond character in the TS is the of transition state geometries determined by ab initio approach toward planarity at and C,j as measured by methods. C, the sum of the three valence angles (28,)of the incipient The intramolecular Cope elimination (TS-2),involving alkene (Figure 1). The 20" change experienced by C, in the thermal decomposition of an amine oxide, provides the cope elimination indicates a change in rehybridization an ideal test case for theoretical study of both primary nearly twice as large as that in the ylide reaction. and secondary isotope effects. Stereochemical3and iso- topic labeling studies4have established this reaction to The secondary KIE, attending the change in hybridiza- be an intramolecular syn-elimination. Deuterium label- tion from sp3 to sp2, is still thought to be primarily a ing studies5 have also established a syn-periplanar consequence of the change in out-of-plane bending fre- transition state for the related Wittig modification6 of the Cope elimination. Comparison with the corresponding (7)(a) Bach, R. D.; Owensby, A. L.; Gonzalez, C.; Schlegel, H. B.; ylide pathway (TS-4)provides a probe of the effect of base McDouall, J. J. W. J. Am. Chem. SOC.1991, 113, 6001. (b) Bach, R. D.; Andres, J. L.; Owensby, A. L.; Schlegel, H. B.; McDouall, J. J. W. J.Am. Chem. SOC.1992,114,7207. (c)Bach, R. D.; Su, M.-D.; Schlegel, (1)ia) Shiner, V. J., Jr. In Isotope Efects in Chemical Reactions; H. B. J. Am. Chem. SOC.1994, 116, 5379. Collins, C. J., Bowman, N. S.,Eds.; Van Nostrand Reinhold: New York, (8)All geometriesga given in the figures utilized gradient geometry 1970; Chapter 2. ib) Melander, L.; Saunders, W. H., Jr.Reaction Rates optimationgbat both HF and MP2 levels of theory. Analytical second of Isotopic Molecules; Wiley: New York, 1980. (c) Gajewski, J. J. derivatives and vibrational frequencies at the HF/6-31G* and MP2/ Isotopes in Organic Chemistry, Vol. 7 Secondary and Solvent Isotope 6-31G* levels were computed using Gaussianga and CADPAC,gc Effects;Buncel, E., Lee, C. C., Eds.; Elsevier: Amsterdam, 1987. respectively. The rate constants were calculated without scaling by (2)(a) Dewar, M. J. S.; Ford, G. P. J.Am. Chem. SOC.1977,99,8343. using nonvariational transition state theorylo8 including Wigner's ib) Saunders, M.; Laidig, K. E.; Wolfsberg, M. J. Am. Chem. SOC.1989, tunneling correction.lOb 111, 8989. (c)Chantranupong, L.; Wildman, T. A. J. Am. Chem. SOC. (9) (a)Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. 1990, 112, 4151. (d) Wolfe, S.; Hoz, S.; Kim, C.-K.; Yang, K. J. Am. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.; Chem. SOC.1990, 112, 4186. (e) Axelsson, B. S.; Matsson, 0.; Gonzalez, C.; Defrees, D. J.; Fox,-D. J.; Whiteside, R. A,; Seeger, R.; Langstrom, B. J.Am. Chem. SOC.1989,112,6661. (DJensen, F.; Houk, Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; K. N. J. Am. Chem. SOC.1987,109, 3139. Topiol, S.; Pople, J. A. Gaussian 90; Gaussian: Pittsburgh, PA 1990. (3)(a) Cram, D. J.;McCarty, J. E. J.Am. Chem. SOC.1964, 76,5740. tb) Schlegel, H. B. J. Comput. Chem. 1982, 3, 214. (c)Amos, R. D.; ib) Cope, A. C.; LeBel, N. A. J. Am. Chem. SOC.1960, 82, 4656. (c) Rice, J. E. CADPAC: Cambridge Analytic Derivatives Package, Issue Saunders, W. H., Jr.; Cockerill, A. F. Mechanisms of Elimination 4, Cambridge, 1988. Reactions; Wiley-Interscience: New York, 1973. (10)(a) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical (4)ia) Bach, R. D.; Andrzejewski, D.; Dusold, L. R. J. Org. Chem. Kinetics and Dynamics; Prentice Hall: Englewood Cliffs, NJ, 1989. 1973, 38, 1742. (b) Bach, R. D.; Braden, M. L. J. Org. Chem. 1991, ib)Wigner, E. P. 2. Phys. Chem. 1932, B19, 203. (c)Bell, R. P. Trans. 56, 7194. Faraday SOC.1969, 55, 1. id) Bell, R. P. The Proton in Chemistry, (5)(a) Bach, R. D.; Knight, J. W.; Braden, M. L. J.Am. Chem. SOC. 2nd ed.; Chapman and Hall: London, 1973; Chapter 12. 1991,113,4712. ib) Bach, R. D.; Bair, K. W.; Andrzejewski, D. J.Am. ( 11)(a) Chiao, W.-B.; Saunders, W. H., Jr. J. Am. Chem. SOC.1978, Chem. SOC.1972, 94, 8608. (c)Bach, R. D.; Andrzejewski, D. J. Am. 100, 2802. (b) Wright, D. R.; Sims, L. B.; Fry, A. J. Am. Chem. SOC. Chem. SOC.1971,93, 7118. 1983,105, 3714. ic) Lewis, D. E.; Sims, L. B.; Yamataka, H.; Mckenna, (6)Witting, G.; Polster, R. JustusLiebigs Ann. Chem. 1967, 612, J. J.Am. Chem. SOC.1980,102, 7411. (d)Miller, D. J.;Subramanian, 102. Rm.; Saunders, W. H., Jr. J. Am. Chem. SOC.1981, 103, 3519. 0022-3263/95/1960-4653$09.00/00 1995 American Chemical Society 4654 J. Org. Chem., Vol. 60, No. 14, 1995 Notes H0OLNHz -t HpCZCHz zei =329.430 <H,CpC, = 108.35' <ONC C =0.05" <H C C N = -174.63" <HICgta!l = 0.00" <Oh8 e! - 58.95O <HICgka!l-= -51.55" E~pp-209.63556 E~pp-209.59066 .hE*~p2=26.2 E~p4=-209.65452 Eyp4~-209.60752 AE*MP~=29.1 cH~C~C,= 107.77" <CNC C = 15.67' CH C C N = -172.13' <H1Cp?&h = -11 .Ole <Ck8 8 = 67.91" <HICpkak = -51.55' EMpz= -1 73.73893 Eyp2= -1 73.721 78 AE*~pzs10.8 EMPI= -1 73.78776 E~p4=-173.74344 AE*~prs11.4 Figure 1. Geometries (MP2/6-31G*)for the starting materials and transitions states of the Cope elimination reaction (TS-2) and its respective ylide elimination (TS-4) with experimental conditions shown over the arrow. Total energies are in au, and activation barriers at the level indicated given in kcaymol. E~pz- -286.77435 E~pp-286.73340 AEL~pp25.7 Figure 2. Geometry and transition state (MP2/6-31G*)for the Cope elimination reaction (TS-6) affording 1,3-butadiene and hydroxylamine. Energies are in au and relative energies in kcaymol. Bond distances are in A and angles in degrees. quency.12 The above analysis of the geometry of the two agreement with the secondary KIE is particularly grati- transition structures is quite consistent with the mag- fying.