Multiphonon vibrational relaxation in liquids: Should it lead to an exponential-gap law

Journal of Chemical Physics

Volumn 121, Issue 22, 2004, Pages 11217-11226

  Ma, Ao ^a   Stratt, Richard M ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INTERMOLECULAR SPECTRA; INTERMOLECULAR VIBRATIONS; VIBRATIONAL ENERGY; VIBRATIONAL RELAXATION;

BESSEL FUNCTIONS; CRYSTALLINE MATERIALS; MOLECULAR DYNAMICS; NATURAL FREQUENCIES; QUANTUM THEORY; RELAXATION PROCESSES; RESONANCE;

MOLECULAR VIBRATIONS;

EID: 11144256588     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1819873     Document Type: Article

References (34)

1. R. M. Stratt, in Ultrafast Infrared and Roman Spectroscopy, edited by M. D. Fayer (Marcel Dekker. New York, 2001).
2. P. Moore, A. Tokmakoff, T. Keyes, and M. D. Fayer, J. Chem. Phys. 103, 3325 (1995).
3. R. E. Larsen and R. M. Stratt, J. Chem. Phys. 110, 1036 (1999).
4. Y. Deng, B. M. Ladanyi, and R. M. Stratt, J. Chem. Phys. 117, 10752 (2002).
5. A. Ma and R. M. Stratt, J. Chem. Phys. 119, 6709 (2003).
6. R. E. Larsen and R. M. Stratt, Chem. Phys. Lett. 297, 211 (1998).
7. S. Califano, V. Schettino, and N. Neto, Lattice Dynamics of Molecular Crystals (Springer, Berlin, 1981), Chap. 5.
8. V. M. Kenkre, A. Tokmakoff, and M. D. Fayer, J. Chem. Phys. 101, 10618 (1994).
9. A. Nitzan, S. Mukamel, and J. Jortner, J. Chem. Phys. 60, 3929 (1974).
10. A. Nitzan, S. Mukamel, and J. Jortner, J. Chem. Phys. 63, 200 (1975).
11. J. Jortner, Mol. Phys. 32, 379 (1976).
12. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 103, 1533 (1995).
13. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 105, 10153 (1996).
14. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 106, 1034 (1997).
15. 1. See Ref. 1.
16. D. Rostkier-Edelstein, P. Graf, and A. Nitzan, J. Chem. Phys. 107, 10470 (1997); 108, 9598(E) (1998).
17. D. Rostkier-Edelstein, P. Graf, and A. Nitzan, J. Chem. Phys. 107, 10470 (1997); 108, 9598(E) (1998).
18. M. Teubner and D. Schwarzer, J. Chem. Phys. 119, 2171 (2003); D. Schwarzer and M. Teubner, ibid. 116, 5680 (2002); M. Teubner, Phys. Rev. E 65, 031204 (2002).
19. M. Teubner and D. Schwarzer, J. Chem. Phys. 119, 2171 (2003); D. Schwarzer and M. Teubner, ibid. 116, 5680 (2002); M. Teubner, Phys. Rev. E 65, 031204 (2002).
20. M. Teubner and D. Schwarzer, J. Chem. Phys. 119, 2171 (2003); D. Schwarzer and M. Teubner, ibid. 116, 5680 (2002); M. Teubner, Phys. Rev. E 65, 031204 (2002).
21. Note the distinction from the more commonplace literature models that use a sum over the full set of intermolecular modes to compute the dynamics of a single collective coordinate. The model employed here computes the dynamics from a single mode, calculates the correlation function, and then averages the results over the possible mode frequencies. In the language of disordered systems, the conventional models carry out an annealed average whereas the present model performs a quenched average.
22. Handbook of Mathematical Functions, edited by M. Abramowitz and I. Stegun (National Bureau of Standards, Washington, 1972), Chap. 9.
23. R. Englman and J. Jortner, Mol. Phys. 18, 145 (1970); K. Freed and J. Jortner, J. Chem. Phys. 52, 6272 (1970); S. Fischer. ibid. 53, 3195 (1970).
24. R. Englman and J. Jortner, Mol. Phys. 18, 145 (1970); K. Freed and J. Jortner, J. Chem. Phys. 52, 6272 (1970); S. Fischer. ibid. 53, 3195 (1970).
25. R. Englman and J. Jortner, Mol. Phys. 18, 145 (1970); K. Freed and J. Jortner, J. Chem. Phys. 52, 6272 (1970); S. Fischer. ibid. 53, 3195 (1970).
26. A similar approach was taken by Jortner in Ref. 11. In some sense, this asymptotic formula plays the same role for us as a steepest-descent approximation does in other literature studies of multiphonon behavior. However using this large-n formula (which also works nicely for moderate n) allows us to avoid making indiscriminate asymptotic claims about the combined dynamical and density-of-states factors.
27. Another way to estimate the width of the subbands would be to look at the first subband that competes with neighboring subbands throughout its entire width, that is, the first subband that falls entirely to right of the peak of the density of states, ω̄. By construction, the left edge of this subband is likely to be close to ω̄. Imposing the condition that it lies identically at ω̄, though, provides enough of a constraint to fix the value of the subband width. The values obtained in this fashion are similar, but not identical, to those provided in the text.
28. Y. Deng and R. M. Stratt, J. Chem. Phys. 117, 1735 (2002).
29. -1 of 0.204 Å. Note that the latter value is not a fit; it is derived from the logarithmic deriviative of a Lennard-Jones intermolecular force assuming an Ar-like Lennard-Jones σ=3.504 Å (see footnote 79 in Ref. 3).
30. The constant subband width results plotted in Fig. 4 actually use a value for the width intermediate between the one predicted by Eq. (2.18) and the one predicted by the method described in footnote 22, but the small difference between the resulting curves is not likely to be visible on the scale shown in the figure.
31. 1 in supercritical fluids is given by D. J. Myers, M. Shigeiwa, M. D. Fayer, and B. J. Cherayil, in Ultrafast Infrared and Ra man Spectroxopy, edited by M. D. Fayer (Marcel Dekker, New York, 2001); J. L. Skinner, K. F. Everitt, and S. A. Egorov, ibid.
32. 1 in supercritical fluids is given by D. J. Myers, M. Shigeiwa, M. D. Fayer, and B. J. Cherayil, in Ultrafast Infrared and Ra man Spectroxopy, edited by M. D. Fayer (Marcel Dekker, New York, 2001); J. L. Skinner, K. F. Everitt, and S. A. Egorov, ibid.
33. 1 in supercritical fluids is given by D. J. Myers, M. Shigeiwa, M. D. Fayer, and B. J. Cherayil, in Ultrafast Infrared and Ra man Spectroxopy, edited by M. D. Fayer (Marcel Dekker, New York, 2001); J. L. Skinner, K. F. Everitt, and S. A. Egorov, ibid.
34. A conceptually similar "cluster-in-a-liquid" approach to quantum mechanical vibrational relaxation was employed by Q. Shi and E. Geva, J. Phys. Chem. A 107, 9070 (2003).