Quantum dynamics of the trimethylene biradical Stereomutation of cyclopropane and unimolecular decay

Abstract

A reduced-dimensionality three degrees-of-freedom quantum dynamics calculation of the stereomutation of cyclopropane has been performed. In one set of calculations, wavepackets are initiated centered around stationary points on the conrotatory, disrotatory and single rotation (cis/trans conversion) pathways. The ratio of trans to cis isomer formed, R_tc, is shown to be highly dependent on the location, and average energy of the initial wavepacket as well as the initial orientation of the terminal methylene torsions. In a second set of calculations, wavepackets are initiated as ‘highly excited cyclopropane’, in one of the four possible isomeric configurations, designated as a trans configuration for the purposes of analysis. Here also, R_tc depends on the initial torsional orientation. Analysis of wavepacket density and the time constants for formation of product density indicate that that the contributing mechanisms range from direct, concerted conrotatorymotion to more statistical behavior. A ‘Boltzmann’ average at 695 K of theratio of ‘double’ to ‘single’ rotations, k₁₂/k₁, results in k₁₂/k₁=2R_tc=2.2. Wavepacket density is shown to orient preferentially along the conrotatory and disrotatory pathways rather than the higher energy single rotation(cis/trans conversion) pathway.

References

1. J. E. Baldwin, in The Chemistry of the Cyclopropyl Group, ed. Z. Rappoport, Wiley, Chichester, 1995, vol. 2, pp. 469–494; J. A. Berson, Science, 1994, 266, 1338; G. Boche and H. M. Walborksy, Cyclopropane Derived Reactive Intermediates, Wiley, Chichester, 1990; B. K. Carpenter, in The Chemistry of the Cyclopropyl Group, ed. Z. Rappoport, Wiley, Chichester, 1985, pt. 2, pp. 1027–1082; W. T. Borden, in Reactive Intermediates, ed. M. Jones and R. A. Moss, Wiley, New York, 1985, vol. 3, pp. 151–188; 1981, vol. 2, pp. 175–209.
2. C. Doubleday, Jr., J. Phys. Chem., 1996, 100, 3520; C. Doubleday, Jr., J. W. McIver, Jr. and M. Page, J. Phys. Chem., 1988, 92, 4367.
3. (a) S. J. Getty, E. R. Davidson and W. T. Borden, J. Am. Chem. Soc., 1992, 114, 2085; (b) W. T. Borden and E. R. Davidson, J. Am. Chem. Soc., 1980, 102, 5409.
4. Y. Yamaguchi, H. F. Schaefer III and J. E. Baldwin, Chem. Phys. Lett., 1991, 185, 143 (b) J. E. Baldwin, Y. Yamaguchi and H. F. Schaefer III, J. Phys. Chem., 1994, 98, 7513; J. E. Baldwin, T. B. Freedman, Y. Yamaguchi and H. F. Schaefer III, J. Am. Chem. Soc., 1996, 118, 10934.
5. F. T. Smith, J. Chem. Phys., 1958, 29, 235; J. Kollmar, J. Am. Chem. Soc., 1973, 95, 966.
6. R. J. Hoffmann, J. Am. Chem. Soc., 1968, 90, 1475.
7. S. W. Benson, J. Chem. Phys., 1961, 34, 521; H. J. O'Neal and S. W. Benson, J. Chem. Phys., 1968, 72, 1866.
8. Of course, any of the three carbon-carbon bonds can break.
9. J. A. Berson and L. D. Pedersen, J. Am. Chem. Soc., 1975, 97, 238; J. A. Berson, L. D. Pedersen and B. K. Carpenter, J. Am. Chem. Soc., 1976, 98, 122.
10. S. J. Cianciosi, N. Ragunathan, T. B. Freedman, L. A. Nafie, D. K. Lewis, D. A. Glenar and J. E. Baldwin, J. Am. Chem. Soc., 1991, 113, 1864; J. E. Baldwin, S. J. Cianciosi, D. A. Glenar, G. J. Hoffman, I. Wu and D. K. Lewis, J. Am. Chem. Soc., 1992, 114, 9408.
11. (a) C. Doubleday, Jr., K. Bolton, G. H. Peslherbe and W. L. Hase, J. Am. Chem. Soc., 1996, 118, 9922; (b) C. Doubleday, Jr., K. Bolton and W. L. Hase, J. Am. Chem. Soc., 1997, 119, 5251; (c) K. Bolton, W. L. Hase and C. Doubleday, Jr., Ber. Bunsen-Ges. Phys. Chem., 1997, 101, 414; (d) C. Doubleday, Jr., K. Bolton and W. L. Hase, J. Phys. Chem. A, 1998, 102, 3648.
12. D. A. Hrovat, S. Fang, W. T. Borden and B. K. Carpenter, J. Am. Chem. Soc., 1997, 119, 5253.
13. X. Chapuisat and Y. Jean, J. Am. Chem. Soc., 1975, 97, 6325.
14. E. M. Goldfield, unpublished work.
15. J. J. P. Stewart, MOPAC 7.0, A General Molecular Orbital Package, Quantum Chem. Program Exchange, 1993, 455; J. J. P. Stewart, J. Comput. Chem., 1989, 10, 209.
16. M. J. S. Dewar, J. A. Hashmall and C. G. Venie, J. Am. Chem. Soc., 1968, 90, 1953.
17. M. J. S. Dewar, E. G. Zoebisch, E. F. Healy and J. J. P. Stewart, J. Am. Chem. Soc., 1895, 107, 3902.
18. D. A. Hrovat and W. T. Borden, personal communication.
19. Mathematica, Wolfram Research, http://www.wolfram.com.
20. J. E. Hadder and J. H. Frederick, J. Chem. Phys., 1992, 97, 3500.
21. B. Podolsky, Phys. Rev., 1928, 32, 812.
22. D. Kosloff and R. Kosloff, J. Comput. Phys., 1983, 52, 35.
23. S. K. Gray and D. E. Manolopoulos, J. Chem. Phys., 1996, 104, 7099.
24. E. M. Goldfield and S. K. Gray, J. Chem. Soc., Faraday Trans., 1997, 93, 909; E. M. Goldfield and S. K. Gray, Chem. Phys. Lett., 1997, 276, 1; A. J. H. M. Meijer and E. M. Goldfield, J. Chem. Phys., 1998, 108, 5404.
25. P. Pernot and W. A. Lester, Jr., Int. J. Quantum Chem., 1991, 40, 577 see also, R. Heather and H. Metiu, J. Chem. Phys., 1987, 86, 5009.
26. D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys., 1994, 101, 3671.