Bimodal distribution of lifetimes for an intermediate from a quasiclassical dynamics simulation

Journal of the American Chemical Society

Volumn 118, Issue 42, 1996, Pages 10329-10330

  Carpenter, Barry K ^a  

^a Department of Molecular Biology and Genetics   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPUTER SIMULATION; MOLECULAR DYNAMICS;

EID: 0029905871     PISSN: 00027863     EISSN: None     Source Type: Journal    
DOI: 10.1021/ja9617707     Document Type: Article

References (34)

1. Pelzer H.; Wigner E. Z. Phys. Chem. 1932, B15, 445. Glasstone S.; Laidler K. J.; Eyring H. Theory of Rate Processes; McGraw-Hill: New York, NY, 1940.
2. Pelzer H.; Wigner E. Z. Phys. Chem. 1932, B15, 445. Glasstone S.; Laidler K. J.; Eyring H. Theory of Rate Processes; McGraw-Hill: New York, NY, 1940.
3. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1927, 49, 1617. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1928, 50, 617. Kassel, L. S. J. Phys. Chem. 1928, 32, 225. Kassel, L. S. J. Phys. Chem. 1928, 32, 1065. Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894. Marcus, R. A. J. Chem. Phys. 1952, 20, 359, Robinson, P. J.; Holbrook, K. A. Unimolecular Reaction; Wiley: New York, NY, 1971. Forst, W. Unimolecular Reactions; Academic Press: New York, NY, 1973.
4. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1927, 49, 1617. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1928, 50, 617. Kassel, L. S. J. Phys. Chem. 1928, 32, 225. Kassel, L. S. J. Phys. Chem. 1928, 32, 1065. Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894. Marcus, R. A. J. Chem. Phys. 1952, 20, 359, Robinson, P. J.; Holbrook, K. A. Unimolecular Reaction; Wiley: New York, NY, 1971. Forst, W. Unimolecular Reactions; Academic Press: New York, NY, 1973.
5. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1927, 49, 1617. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1928, 50, 617. Kassel, L. S. J. Phys. Chem. 1928, 32, 225. Kassel, L. S. J. Phys. Chem. 1928, 32, 1065. Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894. Marcus, R. A. J. Chem. Phys. 1952, 20, 359, Robinson, P. J.; Holbrook, K. A. Unimolecular Reaction; Wiley: New York, NY, 1971. Forst, W. Unimolecular Reactions; Academic Press: New York, NY, 1973.
6. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1927, 49, 1617. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1928, 50, 617. Kassel, L. S. J. Phys. Chem. 1928, 32, 225. Kassel, L. S. J. Phys. Chem. 1928, 32, 1065. Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894. Marcus, R. A. J. Chem. Phys. 1952, 20, 359, Robinson, P. J.; Holbrook, K. A. Unimolecular Reaction; Wiley: New York, NY, 1971. Forst, W. Unimolecular Reactions; Academic Press: New York, NY, 1973.
7. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1927, 49, 1617. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1928, 50, 617. Kassel, L. S. J. Phys. Chem. 1928, 32, 225. Kassel, L. S. J. Phys. Chem. 1928, 32, 1065. Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894. Marcus, R. A. J. Chem. Phys. 1952, 20, 359, Robinson, P. J.; Holbrook, K. A. Unimolecular Reaction; Wiley: New York, NY, 1971. Forst, W. Unimolecular Reactions; Academic Press: New York, NY, 1973.
8. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1927, 49, 1617. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1928, 50, 617. Kassel, L. S. J. Phys. Chem. 1928, 32, 225. Kassel, L. S. J. Phys. Chem. 1928, 32, 1065. Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894. Marcus, R. A. J. Chem. Phys. 1952, 20, 359, Robinson, P. J.; Holbrook, K. A. Unimolecular Reaction; Wiley: New York, NY, 1971. Forst, W. Unimolecular Reactions; Academic Press: New York, NY, 1973.
9. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1927, 49, 1617. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1928, 50, 617. Kassel, L. S. J. Phys. Chem. 1928, 32, 225. Kassel, L. S. J. Phys. Chem. 1928, 32, 1065. Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894. Marcus, R. A. J. Chem. Phys. 1952, 20, 359, Robinson, P. J.; Holbrook, K. A. Unimolecular Reaction; Wiley: New York, NY, 1971. Forst, W. Unimolecular Reactions; Academic Press: New York, NY, 1973.
10. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1927, 49, 1617. Rice, O. K.; Ramsperger, H. C. J. Am. Chem. Soc. 1928, 50, 617. Kassel, L. S. J. Phys. Chem. 1928, 32, 225. Kassel, L. S. J. Phys. Chem. 1928, 32, 1065. Marcus, R. A.; Rice, O. K. J. Phys. Colloid Chem. 1951, 55, 894. Marcus, R. A. J. Chem. Phys. 1952, 20, 359, Robinson, P. J.; Holbrook, K. A. Unimolecular Reaction; Wiley: New York, NY, 1971. Forst, W. Unimolecular Reactions; Academic Press: New York, NY, 1973.
11. See, for example: Lehr, R. E.; Marchand, A. P. In Pericyclic Reactions; Marchand, A. P.; Lehr, R. E., Eds.; Academic Press: New York, NY, 1977; Vol. 1.
12. Since the AM1 and PM3 semiempirical methods are calibrated against experimental heats of formation, they calculate enthalpies rather than potential energies. The surface used for the dynamics was thus strictly an enthalpy surface rather than a potential energy surface, but it is assumed that the error arising from equating relative enthalpy and relative potential energy is small, compared to the overall errors in the semiempirical methods.
13. Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902.
14. Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209.
15. Calculations were carried out with Revision 2 of the MOPAC93 package (J. J. P. Stewart, Fujitsu Limited, Tokyo, Japan, 1993).
16. Salem, L.; Rowland, C. Angew. Chem., Int. Ed. Engl. 1972, 11, 92.
17. It is perhaps useful to emphasize that the point of the present work is to compare the predictions from two different kinetic models on the same potential energy surfaces. Whether the surface itself is accurate for the particular reaction selected is an important question when one comes to compare theory with specific experiments, but not important for the purpose of comparing the kinetic models or addressing general behavior of reactive intermediates.
18. For an example and key references, see: Liu, Y.-P.; Lu, D.; Gonzalez-Lafont, A.; Truhlar, D. G.; Garrett, B. C. J. Am. Chem. Soc. 1993, 115, 7806.
19. Animations of one direct trajectory and one "statistical" trajectory can be viewed by the interested reader on the World Wide Web (http:// www.chem. cornell.edu/∼bkc1/dynamics.html).
20. A somewhat similar procedure for mixing exact classical dynamics and statistical approximations can be found in: Hamilton and Brumer (Hamilton, I.; Brumer, P. J. Chem. Phys. 1985, 82, 1937), although the criterion for distinguishing between "statistical" and "nonstatistical" populations in that work is different from the one used here. It should be noted that the "lifetimes" computed for the two subsets of trajectories in the present work have somewhat different meanings. For the direct trajectories, the lifetimes are defined as the times required for each trajectory to evolve from its starting state to a state in which the carbon atoms whose bonding serves to close the four-membered ring of compound 1 approach each other within the sum of their covalent radii. For the "statistical" set the distribution of lifetimes comes from the reciprocal of the RRKM microcanonical rate constant for each indvidual starting state. Errors in relative lifetime of the two populations that arise from this difference in definition cannot be large enough to recombine the two subsets into a single population.
21. RRKM calculations were performed with the program by: Hase, W. L.; Bunker, D. L. QCPE 1975, No. 234.
22. Klärner, F.-G.; Drewes, R.; Hasselman, D. J. Am. Chem. Soc. 1988, 110, 297.
23. Berson, J. A.; Nelson, G. L. J. Am. Chem. Soc. 1967, 89, 5502. Berson, J. A.; Nelson, G. L. J. Am. Chem. Soc. 1970, 92, 1096. Baldwin, J. E.; Belfield, K. D. J. Am. Chem. Soc. 1988, 110, 296.
24. Berson, J. A.; Nelson, G. L. J. Am. Chem. Soc. 1967, 89, 5502. Berson, J. A.; Nelson, G. L. J. Am. Chem. Soc. 1970, 92, 1096. Baldwin, J. E.; Belfield, K. D. J. Am. Chem. Soc. 1988, 110, 296.
25. Berson, J. A.; Nelson, G. L. J. Am. Chem. Soc. 1967, 89, 5502. Berson, J. A.; Nelson, G. L. J. Am. Chem. Soc. 1970, 92, 1096. Baldwin, J. E.; Belfield, K. D. J. Am. Chem. Soc. 1988, 110, 296.
26. Carpenter, B. K. J. Am. Chem. Soc. 1995, 117, 6336.
27. For example: Woodward, R. B.; Hoffmann, R. The Conservation of Orbital Symmetry; Verlag Chemie: Weinheim, Germany, 1970.
28. N2 reaction: Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Sco. 1989, 111, 2349. Hase, W. L. Science, 1994, 266, 998. There appears to have been no prior discussion of the difference in selection of product exit channels by direct and statistical trajectories.
29. N2 reaction: Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Sco. 1989, 111, 2349. Hase, W. L. Science, 1994, 266, 998. There appears to have been no prior discussion of the difference in selection of product exit channels by direct and statistical trajectories.
30. N2 reaction: Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Sco. 1989, 111, 2349. Hase, W. L. Science, 1994, 266, 998. There appears to have been no prior discussion of the difference in selection of product exit channels by direct and statistical trajectories.
31. N2 reaction: Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Sco. 1989, 111, 2349. Hase, W. L. Science, 1994, 266, 998. There appears to have been no prior discussion of the difference in selection of product exit channels by direct and statistical trajectories.
32. N2 reaction: Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Sco. 1989, 111, 2349. Hase, W. L. Science, 1994, 266, 998. There appears to have been no prior discussion of the difference in selection of product exit channels by direct and statistical trajectories.
33. N2 reaction: Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Sco. 1989, 111, 2349. Hase, W. L. Science, 1994, 266, 998. There appears to have been no prior discussion of the difference in selection of product exit channels by direct and statistical trajectories.
34. N2 reaction: Vande Linde, S. R.; Hase, W. L. J. Am. Chem. Sco. 1989, 111, 2349. Hase, W. L. Science, 1994, 266, 998. There appears to have been no prior discussion of the difference in selection of product exit channels by direct and statistical trajectories.