Unimolecular phase space theory rates by inversion of angular momentum-conserved partition function

Abstract

A simplified phase space theory (PST) of angular momentum-conserving microcanonical rate constant at specified total angular momentum J in unimolecular fragmentation under a central potential is proposed via the reverse association of fragments. Angular momentum-conserved rotational–translational sum/density of states of fragments is approximated by interpolation between "‘high-J'' and ""low-J'' states (Chem. Phys. Lett., 1996, 262, 539), from which is obtained in closed form the corresponding J-conserved partition function Q_xi(J); this represents the core result of this work [eqn. (20)]. A relatively simple numerical Laplace inversion routine of the product of Q_xi(J) and the vibrational partition function accomplishes in a single stroke the inversion that leads immediately to the microcanonical rate constant k(E,J)_PST. Averaging of Q_xi(J) over J leads directly to the canonical (thermal) PST rate constant for dissociation. The procedure is checked against available more elaborate PST results and is illustrated on cases representing five different combinations of fragment symmetries: linear+atom, sphere+atom, linear+linear, sphere+linear and sphere+sphere. The method requires minimal computational effort and is particularly efficient for calculations involving large molecules and large angular momenta.

References

1. P. Pechukas and J. C. Light, J. Chem. Phys., 1965, 42, 3281; P. Pechukas, J. C. Light and C. Rankin, J. Chem. Phys., 1966, 44, 794.
2. (a) W. J. Chesnavich and M. T. Bowers, J. Am. Chem. Soc., 1976, 98, 8301; (b) J. Chem. Phys., 1977, 66, 2306; (c) J. Am. Chem. Soc., 1977, 99, 1705; (d) J. Chem. Phys., 1978, 68, 901; J. Troe, J. Chem. Phys., 1983, 79, 6017 Appendix C.
3. T. Baer and W. L. Hase, Unimolecular Reaction Dynamics, Oxford University Press, New York, 1996, Ch. 7.4.
4. C. E. Klots, J. Phys. Chem., 1971, 75, 1526; Z. Naturforsch., Teil A, 1972, 27, 553.
5. W. Forst, Theory of Unimolecular Reaction, Academic Press, New York, 1973, Ch. 6.
6. J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1967, Ch. 13.
7. W. Forst, Chem. Phys. Lett., 1996, 262, 539.
8. C. E. Klots and J. Polach, J. Phys. Chem., 1995, 99, 15396 Cf. also M. Olzmann and J. Troe, Ber. Bunsenges. Phys. Chem., 1992, 96, 1327; ibid. 1984, 98, 1562.
9. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, NBS Washington, 1972, p. 297.
10. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1965, p. 649, item 6.284.
11. W. Forst, J. Comput. Chem., 1996, 17, 954.
12. JANAF Thermochemical Tables, NSRDS-NBS 37, Washington, 2nd edn., 31971.
13. H. Katagiri and S. Kato, J. Chem. Phys., 1993, 99, 8805.
14. B. M. Toselli and J. R. Barker, J. Chem. Phys., 1989, 91, 2239.
15. W. Forst, Chem. Phys. Lett., 1994, 231, 43.
16. D. M. Wardlaw and R. A. Marcus, J. Chem. Phys., 1985, 83, 3462.
17. W. Tsang and J. T. Herron, J. Phys. Chem. Ref. Data, 1991, 20, 609.
18. R. Atkinson, D. L. Baulch, R. A. Cox, R. F. Hampson, J. A. Kerr and J. Troe, J. Phys. Chem. Ref. Data, 1992, 21, 1125.
19. L. B. Harding, Ber. Bunsenges. Phys. Chem., 1997, 101, 363.
20. M. Brouard, M. T. Macpherson and M. J. Pilling, J. Phys. Chem., 1989, 93, 4047.
21. W. Forst, J. Phys. Chem., 1991, 95, 3612.
22. D. L. Baulch, C. J. Cobos, R. A. Cox, C. Esser, P. Frank, Th. Just, J. A. Kerr, M. J. Pilling, J. Troe, R. W. Walker and J. Warnatz, J. Phys. Chem. Ref. Data, 1992, 21, 411.
23. C. J. Cobos and J. Troe, Z. Phys. Chem., 1990, 167, 129.
24. W. Tsang and R. F. Hampson, J. Phys. Chem. Ref. Data, 1986, 15, 1087.
25. P. H. Stewart, G. P. Smith and D. M. Golden, Int. J. Chem. Kinet., 1989, 21, 923.
26. L. R. Khundkar, J. L. Knee and A. H. Zewail, J. Chem. Phys., 1987, 87, 77.
27. S. J. Klippenstein, L. R. Khundkar, A. H. Zewail and R. A. Marcus, J. Chem. Phys., 1988, 89, 4761.
28. I. Nadler, J. Pfab, H. Reisler and C. Wittig, J. Chem. Phys., 1984, 81, 653.
29. W. Tsang, J. Phys. Chem. Ref. Data, 1992, 21, 753.
30. I. R. Sims and I. W. M. Smith, J. Chem. Soc., Faraday Trans., 1993, 89, 1; Cf. D. L. Yang and M. C. Lin, in The Chemical Dynamics and Kinetics of Small Radicals, ed. K. Liu, A. Wagner, World Scientific, Singapore, 1995, Ch. 5.
31. S. J. Klippenstein and R. A. Marcus, J. Chem. Phys., 1989, 91, 2280.
32. E. D. Potter, M. Gruebele, L. R. Khundkar and A. H. Zewail, Chem. Phys. Lett., 1989, 164, 463.
33. S. K. Kim, E. R. Lovejoy and C. B. Moore, J. Chem. Phys., 1995, 102, 3202.
34. D. M. Wardlaw and R. A. Marcus, J. Phys. Chem., 1986, 90, 5383.
35. S. H. Robertson, M. J. Pilling, D. L. Baulch and N. J. B. Green, J. Phys. Chem., 1995, 99, 13452.
36. J. P. Hessler and P. J. Ogren, J. Phys. Chem., 1996, 100, 984.
37. A. F. Wagner and D. M. Wardlaw, J. Phys. Chem., 1988, 92, 2462.
38. P. H. Stewart, C. W. Larson and D. M. Golden, Combust. Flame, 1989, 75, 25.
39. J. Troe, J. Chem. Phys., 1983, 79, 6017.
40. J. Troe, (a) Ber. Bunsenges. Phys. Chem., 1997, 101, 438; J. Chem. Soc., Faraday Trans.; (b) 1991, 87, 2299; (c) 1997, 93, 885.
41. C. J. Cobos and J. Troe, J. Chem. Phys., 1985, 83, 1010.
42. W. Forst, Comput. Chem., 1996, 20, 419.