Zero-point energy constraints in RRKM and non-RRKM molecules

Abstract

The TRAPZ method for zero-point energy (ZPE) preservation (Lim and McCormack, J. Chem. Phys., 1995, 102, 1705) is generalised to molecular systems of non-zero angular momentum. The method is shown to conserve linear momentum, angular momentum and total energy. It is also found to preserve the intrinsic Rice–Ramsperger–Kassel–Marcus (RRKM) behaviour of a dissociating Al₃ cluster. The TRAPZ rate coefficients are lower than those calculated for classical ensembles, since regions of phase space with less than ZPE can no longer react. As required, the RRKM rate coefficients are upper bounds to the TRAPZ rate coefficients. The TRAPZ reaction threshold is higher than the classical (asymptotic-limit) product ZPE due to fluctuations in instantaneous normal mode ZPEs. Rotationally hot Al₂ is produced as Al₃ ZPE bending motion is converted to Al₂ angular momentum. The TRAPZ method does not preserve the non-RRKM behaviour of HNC isomerisation.

References

1. D. L. Clark and M. A. Collins, J. Chem. Phys., 1987, 86, 6871.
2. D. L. Clarke and M. A. Collins, J. Chem. Phys., 1987, 87, 5312.
3. Y. Guan and D. L. Thompson, J. Chem. Phys., 1988, 88, 2355.
4. D.-H. Lu, W. L. Hase and R. J. Wolf, J. Chem. Phys., 1986, 85, 4422.
5. D.-H. Lu and W. L. Hase, J. Phys. Chem., 1988, 92, 3217.
6. D.-H. Lu and W. L. Hase, J. Chem. Phys., 1988, 89, 6723.
7. A. J. Stace and J. N. Murrell, J. Chem. Phys., 1978, 68, 3028.
8. K. F. Lim, J. Chem. Phys., 1994, 101, 8756.
9. K. F. Lim, J. Chem. Phys., 1994, 100, 7385.
10. G. Lendvay and G. C. Schatz, J. Chem. Phys., 1992, 96, 4356.
11. T. Lenzer, K. Luther, J. Troe, R. G. Gilbert and K. F. Lim, J. Chem. Phys., 1995, 103, 626.
12. R. G. Gilbert, Australian J. Chem., 1995, 48, 1787.
13. N. S. Swamy and W. L. Hase, J. Am. Chem. Soc., 1984, 106, 4071.
14. J. A. Miller, J. Chem. Phys., 1986, 84, 6170.
15. L. A. M. Quintales, A. J. C. Varandas and J. M. Alvarino, J. Phys. Chem., 1988, 92, 4552.
16. M. R. Pastrama, L. A. M. Quintales, J. Brandao and A. J. C. Varandas, J. Phys. Chem., 1990, 94, 8073.
17. J. Davidsson and G. Nyman, J. Chem. Phys., 1990, 92, 2407.
18. G. Nyman and J. Davidsson, J. Chem. Phys., 1990, 92, 2415.
19. U. Wilhelmsson and G. Nyman, J. Chem. Phys., 1992, 96, 1886.
20. A. J. C. Varandas and J. M. C. Marques, J. Chem. Phys., 1994, 100, 1908.
21. A. J. C. Varandas, Chem. Phys. Lett., 1994, 225, 18.
22. J. M. Bowman, B. Gazdy and Q. Sun, J. Chem. Phys., 1989, 91, 2859.
23. R. Alimi, A. Garcia-Vela and R. B. Gerber, J. Chem. Phys., 1992, 96, 2034.
24. G. H. Peslherbe and W. L. Hase, J. Chem. Phys., 1994, 100, 1179.
25. M. Ben-Nun and R. D. Levine, J. Chem. Phys., 1994, 101, 8768.
26. S. Kumar, N. Sathyamurthy and R. Ramaswamy, J. Chem. Phys., 1995, 103, 6021.
27. K. F. Lim and D. A. McCormack, J. Chem. Phys., 1995, 102, 1705.
28. Y. Guo, D. L. Thompson and T. D. Sewell, J. Chem. Phys., 1996, 104, 576.
29. D. Shen and H. O. Pritchard, J. Chem. Soc., Faraday Trans., 1996, 92, 1297.
30. D. L. Shen and H. O. Pritchard, J. Chem. Soc., Faraday Trans., 1996, 92, 4357.
31. K. F. Lim, J. Chem. Soc., Faraday Trans., 1997, 93, 669.
32. W. H. Miller, W. L. Hase and C. L. Darling, J. Chem. Phys., 1989, 91, 2863.
33. D. A. McCormack and K. F. Lim, J. Chem. Phys., 1995, 103, 1991.
34. D. A. McCormack and K. F. Lim, J. Chem. Phys., 1997, 106, 572.
35. M. Hénon and C. Heiles, Astron. J., 1964, 69, 73.
36. D. W. Noid and R. A. Marcus, J. Chem. Phys., 1977, 67, 559.
37. D. W. Noid, M. L. Koszykowski and R. A. Marcus, J. Chem. Phys., 1979, 71, 2864.
38. M. D. Feit and J. A. Fleck, J. Chem. Phys., 1984, 80, 2578.
39. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics, Springer, New York, 1990.
40. S. E. Koonin and D. C. Meredith, Computational Physics, Addison-Wesley, Reading MA, 1st edn., 1990, p. 639.
41. A. P. Fordy, Physica D, 1991, 52, 204.
42. M. Brack, R. K. Bhaduri, J. Law and M. V. N. Murthy, Phys. Rev. Lett., 1993, 70, 568.
43. D. A. McCormack and K. F. Lim, paper presented at Conference on the Dynamics of Molecular Collisions, Pacific Grove, USA, 1995; D. A. McCormack, Ph.D. Thesis, University of Melbourne, 1997.
44. G. H. Peslherbe and W. L. Hase, J. Chem. Phys., 1994, 101, 8535.
45. G. H. Peslherbe and W. L. Hase, J. Chem. Phys., 1996, 104, 9445.
46. T. D. Sewell, D. L. Thompson, J. D. Gezelter and W. H. Miller, Chem. Phys. Lett., 1992, 193, 512.
47. F. E. Budenholzer, M. Y. Chang and K. C. Huang, J. Phys. Chem., 1994, 98, 12501.
48. D. Shen, W. T. Chan and H. O. Pritchard, J. Chem. Soc., Faraday Trans., 1996, 91, 3747.
49. W. T. Chan, D. Shen and H. O. Pritchard, J. Chem. Soc., Faraday Trans., 1995, 91, 1717.
50. T. Keyes, J. Phys. Chem. A, 1997, 101, 2921.
51. W. H. Miller, N. C. Handy and J. E. Adams, J. Chem. Phys., 1980, 72, 99.
52. H. Goldstein, Classical Mechanics, Addison-Wesley, Reading, 1980.
53. T. W. B. Kibble, Classical Mechanics, Longman, London, 3rd. edn., 1985.
54. D. J. Evans and G. P. Morriss, Comput. Phys. Rep., 1984, 1, 297.
55. R. A. Edberg, D. J. Evans and G. P. Morriss, J. Chem. Phys., 1986, 84, 6933.
56. C. Eckart, Phys. Rev., 1934, 46, 383.
57. A. Sayvetz, J. Chem. Phys., 1939, 6, 383.
58. Dynamics of Molecular Collisions, ed. W. H. Miller, Plenum Press, New York, 1976.
59. J. H. Beynon and J. R. Gilbert, Applications of Transition State Theory to Unimolecular Reactions, Wiley, New York, 1984, p. 85.
60. M. J. Pilling, I. W. M. Smith, Modern Gas Kinetics: Theory, Experiment, and Application, Blackwell, Oxford, 1987.
61. J. I. Steinfeld, J. S. Francisco and W. L. Hase, Chemical Kinetics and Dynamics, Prentice Hall, Englewood Cliffs, 1989.
62. W. L. Hase, R. J. Duchovic, X. Hu, A. Komornicki, K. F. Lim, D.-H. Lu, G. H. Peslherbe, K. N. Swamy, S. R. Vande Linde, A. Varandas, H. Wang and R. J. Wolf, Quantum Chem. Program Exchange Bull., 1996, 16, 43.
63. W. L. Hase and D. Buckowski, Chem. Phys. Lett., 1980, 74, 284.
64. J. N. Murrell and S. Carter, J. Mol. Spectrosc., 1982, 93, 307.
65. S. J. Klippenstein and R. A. Marcus, J. Phys. Chem., 1988, 92, 5412.
66. J. Yu and S. J. Klippenstein, J. Phys. Chem., 1991, 95, 9882.
67. S. J. Klippenstein, J. Chem. Phys., 1991, 94, 6469.
68. S. J. Klippenstein, J. Chem. Phys., 1992, 96, 367.
69. R. G. Gilbert and S. C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell, Oxford, 1990.
70. C. Schlier, J. Chem. Phys., 1995, 103, 1989.
71. G. Z. Whitten and B. S. Rabinovitch, J. Chem. Phys., 1963, 38, 2466.
72. G. Z. Whitten and B. S. Rabinovitch, J. Chem. Phys., 1964, 41, 1883.