J. Am. Chem. SOC. 1988, I IO, 2089-2092 for a pronounced shortening of the C,-OCH3 bond. This shortening is increased by Coulomb effects involving the strongly positively charged C1 atom and the three adjacent 0 atoms. Electrostatic effects between methyl hydrogens and the 0 atoms of the ring also play a role since they add to the stability of the endo form.
Acknowledgment. This work was supported by Grants CHE8303615 and CHE-8603834 from the National Science Foundation. Support at the Universitat Kiiln was provided by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen
2089
Industrie. Helpful discussions on various aspects of this research with Dr. Kurt W. Hillig I1 are gratefully acknowledged. We thank Professor H. D. Rudolph and Dr. V. Typke of Ulm University for the program Z F A P ~which was invaluable throughout this entire project.
Supplementary Material Available: Tables S1-S 17 listing transition frequencies and centrifugal distortion constants for the ground vibrational states of the normal and isotopic species and observed and calculated Stark coefficients (18 pages). Ordering information is given on any current masthead page.
Transition Structures for Homodienyl 1,5-Sigmatropic Hydrogen Shifts: Origin of the High Endo Stereoselectivity Richard J. Loncharich and K. N. H o d * Contribution from the Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90024- 1569. Received August 17, I987
Abstract: The endo and exo transition structures for the homodienyl hydrogen shift of 1-methyl-2-vinylcyclopropanehave been obtained with ab initio quantum mechanical calculations. The difference in energy between the endo and ex0 transition states is estimated to be 17 kcal/mol, favoring the endo mode of reaction, as compared to Berson's estimate of at least 12 kcal/mol made on the basis of experimental data. The transition structures are compared to that obtained earlier for the simplest ene reaction of propene with ethylene. Orbital overlap factors, which lead to the endo preference, are discussed.
The best understood stereoelectronic imperative is that developed by Woodward and Hoffmann, differentiating thermally allowed and forbidden reactions.' Among the thermally allowed pericyclic reactions, there are stereoisomeric variants that have activation energy differences as large as those between allowed and forbidden reactions.2 These are understood in a few cases, but general rules have not yet emerged. W e have been investigating such reactions theoretically, and here we describe theoretical studies of an especially well-documented spectacular reaction of this type. In connection with our study of the ene reaction? we have undertaken a study of the intramolecular retro-ene reaction of cis- 1-methyl-2-vinylcyclopropane(1). This transformation is also known as the homodienyl 1,s-hydrogen shift. It can occur in two stereochemically distinct modes, endo or exo, both of which are thermally allowed. The endo transition state gives cis-l,4-hexadiene (2) while the exo transition state gives rram-lP-hexadiene (3), as shown in Scheme I. Daub and Berson4 estimated that the endo transition state is at least 12 kcal/mol lower in energy than the exo transition state. This free energy difference was estimated from experiments on substituted derivatives. Activation energies were measured for compounds having tert-butyl substitution at the terminal vinyl position of l,l-dimethyl-2-vinylcyclopropane (4). The trans-substituted system (4, R2 = t-Bu) .C h
-4
Scheme I
Ha 1-endo
-%1.exo
3
Table I. Energetics of the Retro-Ene Reactions of cis-1-Methyl-2-vinylcyclopropane(Theoretical Results Are Obtained with the 3-21GBasis Set)o adduct E. AH* A s * AH,.. T.K endo 48.8 45.3 -6.4 -11.0 exo 65.9 62.0 -6.1 -12.7 exptl Ib 31.3 -5.2' 543 exptl IId 3 1.2 f 0.7 -4.7 439-493 exptl 111' 31.1 30.2 f 0.6 -3.1 443-463
@Absoluteenergies (au) of the reactant, endo transition structure, exo transition structure, cis product, and trans product are -231.67544,-231.59670,-231.57047,-231.69302,and -231.69512, respectively. Reference 4. Reference 10. Reference 8c,d.
Reference 8b.
I Rz 4
6
(1) Woodward, R. B.;Hoffmann, R. The Conseruurionof Orbital Symmetry, Academic: New York,1970. (2)See,for example: (a) Rondan,N. G.; Houk, K. N. J . Am. Chem. Soc. 1985,107,2099.(b) K i m , W.; Rondan, N. G.; Houk, K. N. J. Am. Chcm. SOC.1984,106,7989.
(3)Loncharich, R. J.; Houk, K. N. J . Am. Chem. Soc. 1987,109,6947. (4)Daub, J. P.;Berson, .I. A. TetruhedronLeu. 1984,25, 4463.
leads to a 7.0 kcal/mol lower activation energy than the cisterr-butyl system (4, R, = t-Bu), which corresponds to a AAG* of 6.5 kcal/mol; and the cis-tert-butyl system gives a cis to trans product ratio of 99.4:0.6, which corresponds to a AAG* of 5.5 kcal/mol. Thus, the formation of the cis product occurs with a rate that is over 5 orders of magnitude faster than the rate of formation of the trans product. Berson, following an earlier suggestion by W i n ~ t e i n proposed ,~ that this rate difference 'is
0002-7863/88/1510-2089$01.50/00 1988 American Chemical Society
Loncharich and Houk
2090 J. Am. Chem. Soc., Vol. 110, No. 7, 1988
TS-endo
TS-em
exo-I
-37.8 -59.4 11.2
-13.6 -55.4 5.8
-8.5 -65.6 -23.7
-1.5
96.2 156.6 103 2 110.6 IW.6 119.3
95.3 147.1 103.6 114.9 107.0
91.0 149.4 104.6 109 7 104.7
124.2
120.1
c5c6
2.110
1392 1.373 1.480 1.351 1.401 2.006
1.398 1374 1.453
ClCI
I 402 1.374 1.349 1.447 1.397
5 c4c5c6cl
H&CIH6 H,C,CsH, CIC2C3 CzHA HIC&S c4cSc6
C5C&, c6clc2
c,c2 c,c6
CzH3 W
4
111.9 121.8 121.1 124.6
1.318 1.478
1.446
1.395 1.987
1516 1.523
Figure 1. 3-21G geometries of the reactant, endo and ex0 transition
structures of the homodienyl 1,5-hydrogen shift of cis-l-methyl-2vinylcyclopropane. For comparison,the geometry of the prototype ene reaction of propene with ethylene is also shown.
D
ex
