Spin-forbidden dehydrogenation of methoxy cation: a statistical view

Abstract

A non-adiabatic version of RRKM theory is applied to predicting the microcanonical rates for different mechanisms of spin-forbidden dissociation of methoxy cation and its isotopically substituted derivatives, to formyl cation and dihydrogen. The predictions are in agreement with experimental results on this system, and in particular with the occurrence of a “direct’' mechanism for dissociation, rather than of an indirect one via hydroxymethyl cation. Abinitio computations were used throughout to provide the parameters needed to apply the non-adiabatic RRKM theory, and the success of this strategy is shown to be promising for other applications in polyatomic systems. Finally, the kinetic energy release distribution for loss of hydrogen from methoxy and hydroxymethyl cations are computed using abinitio “direct dynamics’' classical trajectories at the HF/6-31G** level, their similarity is also in agreement with experiment.

References

1. M. Aschi, J. N. Harvey, C. A. Schalley, D. Schröder and H. Schwarz, Chem. Commun., 1998, 531.
2. As mentioned below, there is in fact an analytical PES available for the singlet system (see ref. 32). However, from the way this surface was constructed, it is unlikely to be truly global, in that it probably does not describe the regions close to the triplet methoxy minimum very accurately.
3. (a) J. C. Lorquet and B. Leyh-Nihant, J. Phys. Chem., 1988, 92, 4778; (b) F. Remacle, D. Dehareng and J. C. Lorquet, J. Phys. Chem., 1988, 92, 4784.
4. For one example among many see Y. Zeiri, G. Katz, R. Kosloff, M. S. Topaler and D. G. Truhlar, Chem. Phys. Lett., 1999, 300, 523.
5. M. Ben-Nun and T. J. Martinez, J. Chem. Phys., 1998, 108, 7244; X. Sun, H. Wang and W. H. Miller, J. Chem. Phys., 1998, 109, 7064; C. D. Schwieters and G. A. Voth, J. Chem. Phys., 1999, 111, 2869.
6. J. C. Tully, J. Chem. Phys., 1990, 93, 1061 and references cited thereinSee also M. S. Topaler Topaler, M. D. Hack, T. C. Allison, Y.-P. Liu, S. L. Mielke, D. W. Schwenke and D. G. Truhlar, J. Chem. Phys., 1997, 106, 8699; Y. L. Volobuev, M. D. Hack and D. G. Truhlar, J. Phys. Chem. A, 1999, 103, 6225.
7. (a) For reviews on statistical rate theories, see, e.g., W. Forst, Theory of Unimolecular Reactions, Academic Press, New York, 1973; (b) D. G. Truhlar, W. L. Hase and J. T. Hynes, J. Phys. Chem., 1983, 87, 2664; (c) R. G. Gilbert and S. C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell Scientific Publications, Oxford, UK, 1990; (d) T. Baer and W. L. Hase, Unimolecular Reaction Dynamics, Oxford University Press, Oxford, UK, 1996; (e) D. G. Truhlar, B. C. Garrett and S. J. Klippenstein, J. Phys. Chem., 1996, 100, 12771; (f) W. L. Hase, Acc. Chem. Res., 1998, 31, 659.
8. (a) J. B. Delos, J. Chem. Phys., 1973, 59, 2365; (b) J. C. Tully, J. Chem. Phys., 1974, 61, 61; (c) G. E. Zahr, R. K. Preston and W. H. Miller, J. Chem. Phys., 1975, 62, 1127; (d) E. J. Heller and R. C. Brown, J. Chem. Phys., 1983, 79, 3336; (e) A. J. Marks and D. L. Thompson, J. Chem. Phys., 1992, 96, 1911; (f) S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys., 1995, 103, 8528; (g) M. S. Topaler and D. G. Truhlar, J. Chem. Phys., 1997, 107, 392; (h) D. K. Sahm and D. L. Thompson, Chem. Phys. Lett., 1993, 210, 175.
9. (a) Q. Cui, K. Morokuma and J. M. Bowman, J. Chem. Phys., 1999, 110, 9469; (b) K. Morokuma, Q. Cui and Z. Liu, Faraday Discuss., 1998, 110, 71; (c) Q. Cui and K. Morokuma, Theor. Chem. Acc., 1999, 102, 127.
10. The work described in ref. 9 also uses ab initio calculations to determine the parameters needed for applying a non-adiabatic statistical rate theory. Our approach, developed before publication of these papers, is very similar except for the point discussed below in ref. 21.
11. (a) N. Koga and K. Morokuma, Chem. Phys. Lett., 1985, 119, 371; (b) A. Farazdel and M. Dupuis, J. Comput. Chem., 1991, 12, 276; (c) F. Jensen, J. Am. Chem. Soc., 1992, 114, 1596; (d) D. R. Yarkony, J. Phys. Chem., 1993, 97, 4407; (e) M. J. Bearpark, M. A. Robb and H. B. Schlegel, Chem. Phys. Lett., 1994, 223, 269; (f) K. M. Dunn and K. Morokuma, J. Phys. Chem., 1996, 100, 123; (g) J. M. Anglada and J. M. Bofill, J. Comput. Chem., 1997, 18, 992.
12. J. N. Harvey, M. Aschi, H. Schwarz and W. Koch, Theor. Chem. Acc., 1998, 99, 95.
13. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in Fortran 77, Cambridge University Press, Cambridge, UK, 1996.
14. See for example, (a) D. R. Yarkony, J. Am. Chem. Soc., 1992, 114, 5406; (b) J. E. Stevens, Q. Cui and K. Morokuma, J. Chem. Phys., 1998, 108, 1544; (c) A. A. Korkin, M. Nooijen, R. J. Bartlett and K. O. Christe, J. Phys. Chem. A, 1998, 102, 1837; (d) D. R. Yarkony, J. Phys. Chem. A, 1998, 102, 5305; (e) S. Wilsey, F. Bernardi, M. Olivucci, M. A. Robb, S. Murphy and W. Adam, J. Phys. Chem. A, 1999, 103, 1669; (f) A. L. Kaledin, Q. Cui, M. C. Heaven and K. Morokuma, J. Chem. Phys., 1999, 111, 5004; (g) M. R. Manaa and C. F. Chabalowski, Chem. Phys. Lett., 1999, 300, 619.
15. (a) J. N. Harvey, D. Schröder and H. Schwarz, Bull. Soc. Chim. Belg., 1997, 106, 447; (b) C. A. Schalley, J. N. Harvey, D. Schröder and H. Schwarz, J. Phys. Chem. A, 1998, 102, 1021; (c) C. A. Schalley, S. Blanksby, J. N. Harvey, D. Schröder, W. Zummack, J. H. Bowie and H. Schwarz, Eur. J. Org. Chem., 1998, 1, 987; (d) M. Aschi, F. Grandinetti and V. Vinciguerra, Chem. Eur. J., 1988, 4, 2366; (e) D. Schröder, C. Heinemann, H. Schwarz, J. N. Harvey, S. Dua, S. J. Blanksby and J. H. Bowie, Chem. Eur. J., 1998, 4, 2550; (f) C. Rue, P. B. Armentrout, I. Kretzschmar, D. Schröder, J. N. Harvey and H. Schwarz, J. Chem. Phys., 1999, 110, 7858; (g) M. Aschi and J. N. Harvey, J. Chem. Soc., Perkin Trans. 2, 1999, 1059; (h) M. Aschi and F. Grandinetti, J. Chem. Phys., 1999, 111, 6759; (i) K. M. Smith, J. N. Harvey and R. Poli, Organometallics, submitted.
16. For studies of reaction mechanisms involving conical intersections, see e.g. M. Garavelli, B. Frabboni, M. Fato, P. Celani, F. Bernardi, M. A. Robb and M. Olivucci, J. Am. Chem. Soc., 1999, 121, 1537; D. R. Yarkony, Acc. Chem. Res., 1998, 31, 511; F. Bernardi, M. Olivucci and M. A. Robb, Chem. Soc. Rev., 1996, 321.
17. K. Ohta and K. Morokuma, J. Phys. Chem., 1987, 91, 401; A. Farazdel, M. Dupuis, E. Clementi and A. Avitam, J. Am. Chem. Soc., 1990, 112, 4206; O. Kitao, H. Ushiyama and N. Miura, J. Chem. Phys., 1999, 110, 2936.
18. W. H. Miller, N. C. Handy and J. E. Adams, J. Chem. Phys., 1980, 72, 99.
19. If the MECP is truly a minimum within the seam of crossing, these frequencies are all positive and real. We note that this is not, in general, true of frequencies obtained by diagonalising the projected hessians of the two PESs. Using these hessians is equivalent to ignoring the curvature of the seam. As well as leading to two different sets of frequencies, one obtained from H₁ and one from H₂, this approach can also lead to imaginary frequencies even for a minimum on the seam. Our tests found this to be the case for the CH₃O⁺ MECPs studied here, but not for the HC + N₂ MECP studied in ref. 9, where only real frequencies are obtained. This is only by chance, however.
20. See, e.g. refs. 8a–c,e,h; (a) A. J. Lorquet, J. C. Lorquet and W. Forst, Chem. Phys., 1980, 51, 253; (b) A. H. H. Chang and D. R. Yarkony, J. Chem. Phys., 1993, 99, 6824.
21. N. Nakamura and S. Kato, J. Chem. Phys., 1999, 110, 9937.
22. For leading references, see (a) M. M. Bursey, J. R. Hass, D. J. Harvan and C. A. Parker, J. Am. Chem. Soc., 1979, 101, 5485; (b) P. C. Burgers and J. L. Holmes, Org. Mass Spectrom., 1984, 19, 452; (c) S.-C. Kuo, Z. Zhang, R. B. Klemm, J. F. Liebman, L. J. Stief and F. L. Nesbitt, J. Phys. Chem., 1994, 98, 4026.
23. For other calculations on the [C,H₃,O]⁺ system, see ref. 14a, L. A. Curtiss, L. D. Kock and J. A. Pople, J. Chem. Phys., 1991, 95, 4040.
24. T. H. Dunning Jr., J. Chem. Phys., 1989, 90, 1007.
25. The values reported in ref. 1 are in each case the magnitude of the two identical non-zero singlet-triplet matrix elements, which explains the apparent diefference with the rms values mentioned here.
26. L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov and J. A. Pople, J. Chem. Phys., 1998, 109, 7764.
27. For an example of an RRKM calculation using anharmonic vibrational energy levels, see K. M. Christoffel and J. M. Bowman, J. Phys. Chem. A, 1999, 103, 3020.
28. J. Villà, J. C. Corchado, A. González-Lafont, J. M. Lluch and D. G. Truhlar, J. Phys. Chem. A, 1999, 103, 5061 and references therein.
29. J. J. Wang, D. J. Smith and R. Grice, J. Phys. Chem. A, 1997, 101, 3293 and references therein.
30. B. Leyh-Nihant and J. C. Lorquet, J. Chem. Phys., 1988, 88, 5606.
31. For a discussion of such cases, see L. Salem and C. Rowland, Angew. Chem., Int. Ed. Engl., 1972, 11, 92.
32. T. G. Lee, S. C. Park and M. S. Kim, J. Chem. Phys., 1996, 104, 4517 see also Y. M. Rhee, T. G. Lee, S. C. Park and M. S. Kim, J. Chem. Phys., 1997, 106, 1003.
33. Gamess-USA (version of 1st December 1998), M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. J. Su and T. L. Windus together with M. Dupuis and J. A. Montgomery, J. Comput. Chem., 1993, 14, 1347.
34. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, UK, 1989.
35. R. Schinke, Photodissociation Dynamics, Cambridge University Press, Cambridge, UK, 1993, ch. 5, and references thereinAlso see R. Schinke, J. Phys. Chem., 1988, 92, 3195.
36. It is to be noted that the Wigner-generated initial conditions correspond to initial energies well above the MECP and the TS. Also, there does not appear to be a very high barrier on the singlet surface separating the MECP region from the CH₂OH⁺ minimum. Accordingly, 59 of the 400 trajectories started at the MECP, and 67 of those started at the TS, were observed to enter this CH₂OH⁺ minimum. The KER results are derived from the remaining 341 (333) trajectories.
37. E. Uggerud and T. Helgaker, J. Am. Chem. Soc., 1992, 114, 4265.
38. G. Hvistendahl and E. Uggerud, Org. Mass. Spectrom., 1991, 26, 67.
39. For a review on choosing initial conditions for classical trajectories, see G. H. Peslherbe, H. Wang and W. L. Hase, Adv. Chem. Phys., 1999, 105, 171.
40. W. Chen, W. L. Hase and H. B. Schlegel, Chem. Phys. Lett., 1994, 228, 436.