Multiphonon vibrational relaxation in liquids: An exploration of the idea and of the problems it causes for molecular dynamics algorithms

Journal of Chemical Physics

Volumn 119, Issue 13, 2003, Pages 6709-6718

  Ma, Ao ^a   Stratt, Richard M ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; MOLECULAR DYNAMICS; MOLECULAR VIBRATIONS; PHONONS; PROBABILITY DISTRIBUTIONS; RELAXATION PROCESSES; RESONANCE;

MULTIPHONON VIBRATIONAL RELAXATION;

FLUID DYNAMICS;

EID: 0142020895     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1605735     Document Type: Article

References (44)

1. J. C. Deàk, L. K. Iwaki, and D. D. Dlott, J. Phys. Chem. A 102, 8193 (1998).
2. L. K. Iwaki, J. C. Deàk, S. T. Rhea, and D. D. Dlott, Chem. Phys. Lett. 303, 176 (1999).
3. J. C. Deàk, L. K. Iwaki, S. T. Rhea, and D. D. Dlott, J. Raman Spectrosc. 31, 263 (2000).
4. L. K. Iwaki, J. C. Deàk, S. T. Rhea, and D. D. Dlott, in Ultrafast Infrared and Raman Spectroscopy, edited by M. D. Fayer (Marcel Dekker, New York, 2001).
5. V. M. Kenkre, A. Tokmakoff, and M. D. Fayer, J. Chem. Phys. 101, 10618 (1994); P. Moore, A. Tokmakoff, T. Keyes, and M. D. Fayer, ibid. 103, 3325 (1995).
6. V. M. Kenkre, A. Tokmakoff, and M. D. Fayer, J. Chem. Phys. 101, 10618 (1994); P. Moore, A. Tokmakoff, T. Keyes, and M. D. Fayer, ibid. 103, 3325 (1995).
7. A. Nitzan, S. Mukamel, and J. Jortner, J. Chem. Phys. 60, 3929 (1974); 63, 200 (1975); J. Jortner, Mol. Phys. 32, 379 (1976).
8. A. Nitzan, S. Mukamel, and J. Jortner, J. Chem. Phys. 60, 3929 (1974); 63, 200 (1975); J. Jortner, Mol. Phys. 32, 379 (1976).
9. A. Nitzan, S. Mukamel, and J. Jortner, J. Chem. Phys. 60, 3929 (1974); 63, 200 (1975); J. Jortner, Mol. Phys. 32, 379 (1976).
10. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 103, 1533 (1995); 105, 10153 (1995); 106, 1034 (1997).
11. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 103, 1533 (1995); 105, 10153 (1995); 106, 1034 (1997).
12. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 103, 1533 (1995); 105, 10153 (1995); 106, 1034 (1997).
13. R. E. Larsen and R. M. Stratt, J. Chem. Phys. 110, 1036 (1999).
14. Y. Deng, B. M. Ladanyi, and R. M. Stratt, J. Chem. Phys. 117, 10752 (2002).
15. D. Rostkier-Edelstein, P. Graf, and A. Nitzan, J. Chem. Phys. 107, 10470 (1997); 108, 9598(E) (1998).
16. D. Schwarzer and M. Teubner, J. Chem. Phys. 116, 5680 (2002); M. Teubner, Phys. Rev. E 65, 031204 (2002).
17. D. Schwarzer and M. Teubner, J. Chem. Phys. 116, 5680 (2002); M. Teubner, Phys. Rev. E 65, 031204 (2002).
18. A. Carati, L. Galgani, and B. Pozzi, Phys. Rev. Lett. 90, 010601 (2003).
19. R. M. Stratt, in Ultrafast Infrared and Raman Spectroscopy, edited by M. D. Fayer (Marcel Dekker, New York, 2001).
20. J. Chesnoy and G. M. Gale, Adv. Chem. Phys. 70 (part 2), 297 (1988); C. B. Harris, D. E. Smith, and D. J. Russell, Chem. Rev. (Washington, D.C.) 90, 481 (1990).
21. J. Chesnoy and G. M. Gale, Adv. Chem. Phys. 70 (part 2), 297 (1988); C. B. Harris, D. E. Smith, and D. J. Russell, Chem. Rev. (Washington, D.C.) 90, 481 (1990).
22. Unlike independent-binary-collision theory, instantaneous pair theory does not rely on the dynamical concept of a discrete collision, an arbitrary and rather poorly defined idea in the context of liquids. Instantaneous-pair theory looks instead for the equilibrium probability of the solute and a single solvent molecule to be sufficiently close that the dynamics becomes effectively pairlike. The subsequent dynamics can then be evaluated either by molecular dynamics or via instantaneous-normal-mode theory.
23. E. F. David and R. M. Stratt, J. Chem. Phys. 109, 1375 (1998); A. Ma and R. M. Stratt, ibid. 116, 4972 (2002).
24. E. F. David and R. M. Stratt, J. Chem. Phys. 109, 1375 (1998); A. Ma and R. M. Stratt, ibid. 116, 4972 (2002).
25. R. M. Whitnell, K. R. Wilson, and J. T. Hynes, J. Phys. Chem. 94, 8625 (1990); 96, 5354 (1992); M. Tuckerman and B. Berne, J. Chem. Phys. 98, 7301 (1993).
26. R. M. Whitnell, K. R. Wilson, and J. T. Hynes, J. Phys. Chem. 94, 8625 (1990); 96, 5354 (1992); M. Tuckerman and B. Berne, J. Chem. Phys. 98, 7301 (1993).
27. R. M. Whitnell, K. R. Wilson, and J. T. Hynes, J. Phys. Chem. 94, 8625 (1990); 96, 5354 (1992); M. Tuckerman and B. Berne, J. Chem. Phys. 98, 7301 (1993).
28. Y. Deng and R. M. Stratt, J. Chem. Phys. 117, 1735 (2002).
29. The "force" in this equation will, in general have factors of mass, See Ref. 18. Note also that we are implicitly presuming that a classical mechanical treatment suffices to explore the issues discussed in this paper. The idea in doing so is not to minimize the quantitative significance of quantum effects, but rather to focus on two specific questions; (1) the validity of a multiphonon representation of our previous classical theory; and (2) the errors introduced by using a particular algorithm to do classical molecular dynamics.
30. D. W. Miller and S. A. Adelman, Int. J. Radiat. Phys. Chem. 13, 359 (1994).
31. Handbook of Mathematical Functions, edited by M. Abramowitz and I.Stegun (National Bureau of Standards, Washington, D.C., 1972), Chap. 9.
32. R. M. Stratt, Acc. Chem. Res. 28, 201 (1995).
33. R. E. Larsen and R. M. Stratt, Chem. Phys. Lett. 297, 211 (1998).
34. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, Cambridge, 1986), Sees, (5.4), (6.4), and (6.5).
35. W. H. Press et al., in Ref. 24, Sec. (12.1).
36. 2/ε has the value of 2.239 ps for Ar.
37. R. D. Skeel, G. Zhang, and T. Schlick, SIAM J. Sci. Comput. (USA) 18, 203 (1997).
38. A. Friedman and S. P. Auerbach, J. Comput. Phys. 93, 171 (1991).
39. Indeed, one can see remnants of this kind of discreteness appearing in certain solid-state calculations. Note, for example, the oscillatory dependence of relaxation rates on frequency shown in the graphs of Ref. 7.
40. The origin and mathematical form of the band tails in the INM density of states are discussed by R. E. Larsen, E. F. David, G. Goodyear, and R. M. Stratt, J. Chem. Phys. 107, 524 (1997).
41. Obtaining the commonplace (nearly) single-exponential dependence of vibrational-energy relaxation rate on vibrational frequency involves more than just having a finite bandwidth of liquid modes. It apparently depends critically on the ability of the solute-mode/solvent coupling to compensate for the frequency dependence of the liquid's density of states. A. Ma and R. M. Stratt (in preparation).
42. A. Friedman and S. P. Auerbach, J. Comput. Phys. 93, 189 (1991).
43. M. E. Tuckerman and G. J. Martyna, J. Phys. Chem. B 104, 159 (2000).