Ab Initio calculations of the potential surfaces for rearrangement of methylenecyclopropane and 2,2-difluoromethylenecyclopropane. Why do the geminal fluorines have little effect on lowering the activation energy? †

Abstract

(4/4)CASSCF and CASPT2 calculations with the 6-31G* basis set have been performed in order to understand the experimental observation that the geminal fluorines in 2,2-difluoromethylenecyclopropane (2) have only a small effect on lowering the activation energies for its degenerate and non-degenerate methylenecyclopropane rearrangements, relative to the activation energy for the rearrangement of the hydrocarbon (1). As expected from previous experimental and computational studies, the geminal fluorines are calculated to destabilize the three-membered ring in 2 thermodynamically. The small amount of kinetic destabilization of 2 is shown to be due to a nearly equal destabilization of the transition structures for its rearrangements. The high energies of the transition structures are attributed to the strong preference of a CF₂ group for a pyramidal geometry. This preference is found to destabilize the transition structures both for forming a σ bond to the fluorinated carbon in the degenerate methylenecyclopropane rearrangement of 2 and for making a π bond to this carbon in the non-degenerate rearrangement of 2 to (difluoromethylene)cyclopropane (4).

References

1. Reviews: (a) W. R. Dolbier, Jr., Acc. Chem. Res., 1981, 14, 195; (b) B. E. Smart, in Molecular Structure and Energetics, eds. J. F. Liebman and A. Greenberg, VCH, Deerfield Beach, FL, 1986; vol. 3, 141.
2. W. R. Roth, W. Kirmse, W. Hoffmann and H. W. Lennartz, Chem. Ber., 1982, 115, 2508.
3. A. Greenberg, J. Liebman, W. R. Dolbier Jr., K. S. Medinger and A. Skancke, Tetrahedron, 1983, 39, 1533.
4. (a) S. J. Getty, D. A. Hrovat, J. D. Xu, S. A. Barker and W. T. Borden, J. Chem. Soc., Faraday Trans., 1994, 90, 1689; (b) 2,2-difluoropropane was computed to be 5.9 kcal mol^–1 more stable than 1,1-difluoropropane at the RHF/6-31G^* level and 7.3 kcal mol^–1 more stable at the MP2/6-31G^* level. Thus, the strain released upon formation of the latter from 1,1-difluorocyclopropane was calculated to exceed that released by formation of propane from cyclopropane by 6.6 kcal mol^–1 at the RHF level and 6.3 kcal mol^–1 at MP2.
5. (a) W. R. Dolbier, Jr. and H. O. Enoch, J. Am. Chem. Soc., 1977, 99, 4532; (b) However, as predicted by ab initio calculations,^4,6 the E_a for racemization of optically active cis-1,1-difluoro-2-ethyl-3-methyl-cyclopropane by coupled conrotation has subsequently been found to be 8.4 kcal mol^–1 lower than the E_a for conversion of the cis-2,3-dimethyl fluorocarbon to the trans isomer.⁷.
6. S. J. Getty, D. A. Hrovat and W. T. Borden, J. Am. Chem. Soc., 1994, 116, 1521.
7. F. Tian, S. B. Lewis, M. D. Bartberger, W. R. Dolbier Jr. and W. T. Borden, J. Am. Chem. Soc., 1998, 120, 6187.
8. W. R. Dolbier, Jr. and S. F. Sellers, J. Am. Chem. Soc., 1982, 104, 2494.
9. W. R. Dolbier, Jr. and T. H. Fielder, Jr., J. Am. Chem. Soc., 1978, 100, 5577.
10. W. R. Dolbier, Jr., C. R. Burkholder, A. L. Chaves and A. Green, J. Fluorine Chem., 1996, 77, 31.
11. (a) S. J. Getty, E. R. Davidson and W. T. Borden, J. Am. Chem. Soc., 1992, 114, 2085; (b) J. E. Baldwin, Y. Yamaguchi and H. F. Schaefer III, J. Phys. Chem., 1994, 98, 7513.
12. P. C. Hariharan and J. A. Pople, Theor. Chim. Acta, 1973, 28, 213.
13. Gaussian 94, Revision B.3, M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez and J. A. Pople, Gaussian, Inc., Pittsburgh PA, 1995.
14. Review: W. T. Borden and E. R. Davidson, Acc. Chem. Res., 1996, 29, 87.
15. K. Andersson, P.-Å. Malmqvist and B. O. Roos, J. Chem. Phys., 1992, 96, 1218.
16. MOLCAS version 3, K. Andersson, M. R. A. Blomberg, M. P. Fülscher, V. Kellö, R. Lindh, P.-Å. Malmqvist, J. Noga, J. Olsen, B. O. Roos, A. J. Sadlej, P. E. M. Siegbahn, M. Urban and P.-O. Widmark, University of Lund, Sweden, 1994.
17. D. Feller, K. Tanaka, E. R. Davidson and W. T. Borden, J. Am. Chem. Soc., 1982, 104, 967.
18. Review: W. T. Borden, Chem. Commun., 1998, 1919.
19. (a) W. T. Borden and L. Salem, J. Am. Chem. Soc., 1973, 95, 932; (b) W. T. Borden, J. Am. Chem. Soc., 1975, 97, 2906; (c) E. R. Davidson and W. T. Borden, J. Am. Chem. Soc., 1977, 99, 2053.
20. (a) W. von E. Doering and H. D. Roth, Tetrahedron, 1970, 26, 2825; (b) J. C. Gilbert and J. R. Butler, J. Am. Chem. Soc., 1970, 92, 2168; (c) M. Jones, Jr., M. E. Hendrick, J. C. Gilbert and J. R. Butler, Tetrahedron Lett., 1970, 845; (d) W. von E. Doering and L. Birladeanu, Tetrahedron, 1973, 29, 449.
21. (a) In contrast to the (4/4)CASSCF results, (2/2)CASSCF calculations find that the disrotatory stationary point is a true transition structure, connecting 1 and 9; B. Ma and H. F. Schaefer III, Chem. Phys., 1996, 207, 31; (b) for the results of other recent calculations on trimethylenemethane see C. J. Cramer and B. A. Smith, J. Phys. Chem., 1996, 100, 9664.
22. J. P. Chesick, J. Am. Chem. Soc., 1963, 85, 2720.
23. Replacement of the remaining pair of ring hydrogens in 2 by fluorines has been computed to result in a 10 kcal mol^–1 larger increase in strain than replacing a pair of geminal ring hydrogens in 1 by fluorines; A. Skancke and U. Wahlgren, Acta Chem. Scand. A, 1983, 37, 771 It is generally the case in fluorocarbons that substitution of fluorine for hydrogen at carbons adjacent to CF₂ groups is destabilizing,¹ and this is probably the reason why the E_a for methylenecyclopropane rearrangement is 9 kcal mol^–1 smaller in 1,1,2,2-tetrafluoromethylenecyclopropane than in 2; W. R. Dolbier, Jr., S. F. Sellers, B. H. Al-Sader and B. E. Smart, J. Am. Chem. Soc., 1980, 102, 5398.
24. (a) S. Y. Wang and W. T. Borden, J. Am. Chem. Soc., 1989, 111, 7282; (b) H. Hammons, M. B. Coolidge and W. T. Borden, J. Phys. Chem., 1990, 94, 5468; (c) A. Nicolaides and W. T. Borden, J. Am. Chem. Soc., 1992, 114, 8682.
25. (a) The calculated CISD difference of 5.7 kcal mol^–1 between the energy required to twist a CH₂ group out of conjugation in allyl radical and the CF₂ group out of conjugation in 1,1-difluoroallyl radical^24b,c is, in fact, similar to the CASPT2 differences of 7.7 and 6.7 kcal mol^–1 between the energies of, respectively, 10 and 12 and 11 and 12; (b) the CISD energy of 12.7 kcal mol^–1 that is required to planarize the twisted CF₂ group in 1,1-difluoroallyl radical is also similar to the CASPT2 energy of 11.0 kcal mol^–1 required to planarize the CF₂ group in 12.
26. The pyramidalization angle, φ, is the angle between the plane of the CF₂ group and the extension of the C–C bond to it.
27. See, for example: (a) D. A. Hrovat, H. Sun and W. T. Borden, THEOCHEM, 1988, 163, 51; (b) W. T. G. Johnson and W. T. Borden, J. Am. Chem. Soc., 1997, 119, 5930; (c) P. N. Skancke, D. A. Hrovat and W. T. Borden, J. Phys. Chem. A, 1999, 103, 4043.
28. (a) H.-G. Korth, H. Trill and R. Sustmann, J. Am. Chem. Soc., 1981, 103, 4483; (b) D. A. Hrovat and W. T. Borden, J. Phys. Chem., 1994, 98, 10460 and references cited therein.
29. W. J. Hehre, J. A. Pople and A. J. P. Devaquet, J. Am. Chem. Soc., 1976, 98, 664.
30. The transition structure for methylene rotation in 1,1-difluoropropane-1,3-diyl has the CH₂ group rotated 90° from its conformation in 23. In the transition structure there is, therefore, no interaction between the CH₂ and CF₂ radical centers; and its (2/2)CASSCF energy is, consequently, 7.7 kcal mol^–1 higher than that of 23.⁶.