The rotational spectrum of a highly vibrationally mixed quantum state. II. The eigenstate-resolved spectroscopy analog to dynamic nuclear magnetic resonance spectroscopy

Journal of Chemical Physics

Volumn 110, Issue 4, 1999, Pages 1990-1999

  Pate, Brooks H ^a  

^a UNIVERSITY OF VIRGINIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMATIONS; EIGENVALUES AND EIGENFUNCTIONS; ELECTRONIC DENSITY OF STATES; ISOMERIZATION; MATHEMATICAL MODELS; MOLECULAR DYNAMICS; MOLECULAR VIBRATIONS; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; SPECTROSCOPY; SPECTRUM ANALYSIS; TIME DOMAIN ANALYSIS;

BLOCH EQUATIONS; COHERENT MICROWAVE EXCITATION; EIGENSTATE RESOLVED SPECTROSCOPY; STRUCTURAL LOCALIZATION DECAYS;

QUANTUM THEORY;

EID: 0033593152     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.477864     Document Type: Article

References (50)

1. P. J. Robinson and K. A. Holbrook, Unimolecular Reactions (Wiley-Interscience, New York, 1972), Chap. 4.
2. T. Baer and W. L. Hase, Unimolecular Reaction Dynamics (Oxford University Press, New York, 1996).
3. I. Oref and B. S. Rabinovitch, Acc. Chem. Res. 12, 166 (1979).
4. D. B. Borchardt and S. H. Bauer, J. Chem. Phys. 85, 4980 (1986).
5. K. V. Reddy and M. J. Berry, Chem. Phys. Lett. 66, 223 (1979).
6. D. M. Leitner and P. G. Wolynes, Chem. Phys. Lett. 280, 411 (1997).
7. S. Nordholm, Chem. Phys. 137, 109 (1989).
8. S. H. Northrup and J. T. Hynes, J. Chem. Phys. 73, 2700 (1980).
9. H. Gunther, NMR Spectroscopy, 2nd ed. (Wiley, New York, 1995), Chap. 9, Appendix Sec. 9.
10. H. S. Gutowsky and C. Holm, J. Chem. Phys. 25, 1228 (1956).
11. H. S. Gutowsky, D. W. McCall, and C. P. Slichter, J. Chem. Phys. 21, 279 (1953).
12. H. M. McConnell, J. Chem. Phys. 28, 430 (1958).
13. E. Hudspeth, D. A. McWhorter, and B. H. Pate, J. Chem. Phys. 107, 8189 (1997).
14. D. A. McWhorter, E. Hudspeth, and B. H. Pate, J. Chem. Phys. 110, 2000 (1999), following paper.
15. P. M. Felker and A. H. Zewail, J. Chem. Phys. 82, 2975 (1985).
16. P. M. Felker and A. H. Zewail, J. Chem. Phys. 82, 2994 (1985).
17. P. M. Felker and A. H. Zewail, J. Chem. Phys. 82, 3003 (1985).
18. J. Kommandeur, W. A. Majewski, W. L. Meerts, and D. W. Pratt, Annu. Rev. Phys. Chem. 38, 443 (1987).
19. C. E. Hamilton, J. L. Kinsey, and R. W. Field, Annu. Rev. Phys. Chem. 37, 493 (1986).
20. K. K. Lehmann, G. Scoles, and B. H. Pate, Annu. Rev. Phys. Chem. 45, 241 (1994).
21. D. J. Nesbitt and R. W. Field, J. Phys. Chem. 100, 12735 (1996).
22. The example measurement outlined here is a simple example to illustrate the capabilities of time-domain spectroscopy. More sophisticated time-domain measurements that can be used to study isomerization have been developed; P. Hamm, M. Lim, and R. M. Hochstrasser, J. Chem. Phys. 107, 10523 (1997); P. J. Reid, S. J. Doig, S. D. Wickham, and R. A. Mathies, J. Am. Chem. Soc. 115, 4754 (1993).
23. The example measurement outlined here is a simple example to illustrate the capabilities of time-domain spectroscopy. More sophisticated time- domain measurements that can be used to study isomerization have been developed; P. Hamm, M. Lim, and R. M. Hochstrasser, J. Chem. Phys. 107, 10523 (1997); P. J. Reid, S. J. Doig, S. D. Wickham, and R. A. Mathies, J. Am. Chem. Soc. 115, 4754 (1993).
24. B. H. Pate, J. Chem. Phys. 109, 4396 (1998).
25. D. Green, R. Holmberg, C. Y. Lee, D. A. McWhorter, and B. H. Pate, J. Chem. Phys. 109, 4407 (1998).
26. K. F. Freed and A. Nitzan, J. Chem. Phys. 73, 4765 (1980).
27. A. M. de Souza, D. Kaur, and D. S. Perry, J. Chem. Phys. 88, 4569 (1988).
28. A. McIlroy and D. J. Nesbitt, J. Chem. Phys. 92, 2229 (1990).
29. B. H. Pate, K. K. Lehmann, and G. Scoles, J. Chem. Phys. 95, 3891 (1991).
30. C. L. Brummel, S. W. Mork, and L. A. Philips, J. Chem. Phys. 95, 7041 (1991).
31. X.-P. Jiang and P. Brumer, J. Chem. Phys. 94, 5833 (1991).
32. D. S. Perry, J. Chem. Phys. 98, 6665 (1993).
33. n|bright). The initial decay is defined by the first two terms. The second moment is the sum of the squares of the matrix elements connecting the bright state to the bath. Because the second moment is the sum of the matrix elements, the total initial rate can be separated into the two contributions given in the text.
34. E. Hudspeth, D. A. McWhorter, and B. H. Pate, J. Chem. Phys. 109, 4316 (1998).
35. D. Green, S. Hammond, J. Keske, and B. H. Pate, J. Chem. Phys. 110, 1979 (1999), preceding paper.
36. eff = 1/2(B + C).
37. D. A. McWhorter and B. H. Pate, J. Phys. Chem. A 102, 8795 (1998).
38. This line width is chosen to add clarity to the ligures in this paper. In our experiments, the linewidth is 300 kHz for saturation spectroscopy (Ref. 24) and 6 MHz, for measurements using the Autler-Townes splitting technique (Ref. 14). 18 We choose to consider the rotational spectrum in the Type I frequency region so that we can compare the eigenstate rotational spectrum to the vibrational spectrum. Of course, there is also a spectrum in the frequency region for the Type II states. The results presented in this section are equally valid for spectroscopy in the Type II frequency range.
39. 1 definition is analogous to the spin-lattice relaxation time; A. Abragam, Principles of Nuclear Magnetism (Oxford University Press, New York, 1961).
40. C. Cohen-Tanoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, New York, 1977), Vol. 2, pp. 1299-1301.
41. The decay rates are actually twice the value given by Eq. (6). The factor of 2 can be understood by comparison to relaxation kinetics techniques. A differential equation approach shows that when a reaction is perturbed away from equilibrium, it relaxes at the sum of the forward and reverse reaction rates. Eigenstate rotational spectroscopy is analogous to relaxation methods. The eigenstate is initially at "conformational equilibrium" because it is composed of both Type I and Type II basis states. Coherent rotational excitation takes the molecule away from equilibrium by causing structure relocalization. The decay of the total Type I probability [Eq. (8)] occurs at the sum of the forward and reverse isomerization rates. In these calculations, the forward and reverse rates are equal; M. J. Pilling and P. W. Seakins, Reaction Kinetics (Oxford University Press, New York, 1995), Chap. 8.
42. The determination of the initial state created by coherent excitation of the eigenstate rotational spectrum. ψ(0), follows the same formulation that is used for the vibrational spectrum (Refs. 28 and 30). The initial state is a superposition of the J + 1 eigenstates. The amplitude of each eigenstate in the coherent state is determined by the rotational transition moment for the eigenstate-to-eigenstate transition.
43. G. A. Bethardy, X. Wang, and D. S. Perry, Can. J. Chem. 72, 652 (1994).
44. D. S. Perry, G. A. Bethardy, and X. Wang, Ber. Bunsenges. Phys. Chem. 99, 530 (1995).
45. A. McIlroy and D. J. Nesbitt, J. Chem. Phys. 101, 3421 (1994).
46. I-II) contribute to the fourth moment of the spectrum. As a result, fast bath isomerization leads to a slowing of the decay as seen in Fig. 8(c). This effect is an example of motional narrowing; P. W. Anderson, J. Phys. Soc. Jpn. 9, 888 (1954).
47. C. P. Slichter, Principles of Magnetic Resonance, 3rd ed. (Springer, New York, 1996), Appendix F.
48. For example, direct vibrational transitions between vibrational states of two different conformations are generally much weaker than vibrational transitions that maintain conformational structure.
49. R. S. Ruoff, T. J. Kulp, and J. D. McDonald, J. Chem. Phys. 81, 4414 (1984).
50. F. D. Lewis, P. A. Teng, and E. Weltz, J. Phys. Chem. 87, 1666 (1983).