High-frequency vibrational energy relaxation in liquids: The foundations of instantaneous-pair theory and some generalizations

Journal of Chemical Physics

Volumn 117, Issue 23, 2002, Pages 10752-10767

  Deng, Yuqing ^a   Ladanyi, Branka M ^b   Stratt, Richard M ^a  

^a BROWN UNIVERSITY   (United States)

^b Veterinary Dentistry and Oral Surgery   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMS; CORRELATION METHODS; FRICTION; FUNCTIONS; INTEGRATION; LIQUIDS; MOLECULAR DYNAMICS; MULTIPHOTON PROCESSES; RELAXATION PROCESSES; SOLVENTS;

HIGH FREQUENCY VIBRATIONAL ENERGY RELAXATION; INSTANTANEOUS NORMAL MODE; INSTANTANEOUS PAIR THEORY; POLYATOMIC SOLUTES;

MOLECULAR VIBRATIONS;

EID: 0037115899     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1517300     Document Type: Article

References (90)

1. L. K. Iwaki, J. C. Deak, S. T. Rhea, and D. D. Dlott, in Ultrafast Infrared and Raman Spectroscopy, edited by M. D. Fayer (Marcel Dekker, New York, 2001).
2. J. C. Deak, L. K. Iwaki, S. T. Rhea, and D. D. Dlott, J. Raman Spectrosc. 31, 263 (2000).
3. D. D. Dlott, Chem. Phys. 266, 149 (2001).
4. G. Käb, C. Schröder, and D. Schwarzer, Phys. Chem. Chem. Phys. 4, 271 (2002).
5. R. M. Stratt, in Ultrafast Infrared and Raman Spectroscopy, edited by M. D. Fayer (Marcel Dekker, New York, 2001).
6. D. Rostkier-Edelstein, P. Graf, and A. Nitzan, J. Chem. Phys. 107, 10470 (1997).
7. D. Rostkier-Edelstein, P. Graf, and A. Nitzan, J. Chem. Phys. 108, 9598(E) (1998).
8. D. Schwarzer and M. Teubner, J. Chem. Phys. 116, 5680 (2002).
9. M. Teubner, Phys. Rev. E 65, 031204 (2002).
10. R. E. Larsen and R. M. Stratt, J. Chem. Phys. 110, 1036 (1999).
11. J. Jang and R. M. Stratt, J. Chem. Phys. 113, 5901 (2000).
12. The basic ideas of IBC theory are reviewed by J. Chesnoy and G. M. Gale Adv. Chem. Phys. 70, (part 2), 297 (1988).
13. C. B. Harris, D. E. Smith, and D. J. Russell, Chem. Rev. 90, 481 (1990).
14. Some of the better known critical statistical mechanical analyses of IBC theory include (a) M. Fixman, J. Chem. Phys. 34, 369 (1961)
15. (b) R. Swanzig, ibid. 34, 1931 (1961)
16. R. Zwanzig, J. Chem. Phys. 36, 227 (1962)
17. (c) P. K. Davis and I. Oppenheim, ibid. 57, 505 (1972)
18. (d) D. Oxtoby, Mol. Phys. 34, 987 (1977)
19. (e) P. S. Dardi and R. I. Cukier, J. Chem. Phys. 89, 4145 (1988)
20. P. S. Dardi and R. I. Cukier, J. Chem. Phys. 95, 98 (1991).
21. The implications for IBC theory of some of the more recent studies are discussed in (a) V. Vikhrenko, D. Schwarzer, and J. Schroeder, Phys. Chem. Chem. Phys. 3, 1000 (2001)
22. (b) T. Yamaguchi, Y. Kimura, and N. Hirota, J. Chem. Phys. 111, 4169 (1999)
23. T. Yamaguchi, Y. Kimura, and N. Hirota, J. Chem. Phys. 113, 4340 (2000)
24. (c) J. Benzler, S. Linkersdörfer, and K. Luther, ibid. 106, 4992 (1997)
25. (d) D. Schawrzer, J. Troe, M. Votsmeier, and M. Zerezke, ibid. 105, 3121 (1996)
26. D. Schwarzer, J. Troe, and M. Zerezke, ibid. 107, 8380 (1997)
27. D. Schwarzer, J. Troe, and M. Zerezke, J. Phys. Chem. A 102, 4207 (1998).
28. R. M. Stratt, Acc. Chem. Res. 28, 201 (1995).
29. T. Keyes, J. Phys. Chem. A 101, 2921 (1997).
30. G. Goodyear, R. E. Larsen, and R. M. Stratt, Phys. Rev. Lett. 76, 243 (1996).
31. G. Goodyear and R. M. Stratt, J. Chem. Phys. 105, 10050 (1996).
32. G. Goodyear and R. M. Stratt, J. Chem. Phys. 107, 3098 (1997).
33. R. E. Larsen, E. F. David, G. Goodyear, and R. M. Stratt, J. Chem. Phys. 107, 524 (1997).
34. B. M. Ladanyi and R. M. Stratt, J. Phys. Chem. A 102, 1068 (1998).
35. Y. Deng and R. M. Stratt, J. Chem. Phys. 117, 1735 (2002).
36. A. Nitzan, S. Mukamel, and J. Jortner, J. Chem. Phys. 60, 3929 (1974)
37. A. Nitzan, S. Mukamel, and J. Jortner, J. Chem. Phys. 63, 200 (1975)
38. J. Jortner, Mol. Phys. 32, 379 (1976).
39. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 103, 1533 (1995)
40. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 105, 10153 (1995)
41. S. A. Egorov and J. L. Skinner, J. Chem. Phys. 106, 1034 (1997).
42. B. J. Cherayil, J. Chem. Phys. 115, 5536 (2001).
43. V. Hizhnyakov and H. Kaasik, J. Chem. Phys. 114, 3127 (2001).
44. V. M. Kenkre, A. Tokmakoff, and M. D. Fayer, J. Chem. Phys. 101, 10618 (1994).
45. P. Moore, A. Tokmakoff, T. Keyes, and M. D. Fayer, J. Chem. Phys. 103, 3325 (1995).
46. T. Mikami, M. Shiga, and S. Okazaki, J. Chem. Phys. 115, 9797 (2001)
47. S. Okazaki, Adv. Chem. Phys. 118, 191 (2001).
48. E. F. David and R. M. Stratt, J. Chem. Phys. 109, 1375 (1998).
49. A. Ma and R. M. Stratt, J. Chem. Phys. 116, 4972 (2002).
50. R. M. Whitnell, K. R. Wilson, and J. T. Hynes, J. Phys. Chem. 94, 8625 (1990)
51. R. M. Whitnell, K. R. Wilson, and J. T. Hynes, J. Phys. Chem. 96, 5354 (1992).
52. M. Tuckerman and B. Berne, J. Chem. Phys. 98, 7301 (1993).
53. Since a major goal of this paper is to test different versions and generalizations of instantaneous-pair theory against exact liquid dynamics, both the theory and the calculations we present here will be completely classical. See Refs. 20, 23, and 27 (and references therein) regarding the magnitudes and applicability of relevant quantum correction factors.
54. R. E. Larsen and R. M. Stratt, Chem. Phys. Lett. 297, 211 (1998).
55. Assuming the force being driven is instantaneously exponential is the analog of the basic (harmonic) INM assumption that the force doing the driving is instantaneously linear. Both are exact at short times.
56. H. C. Andersen, J. Comput. Phys. 52, 24 (1983).
57. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1989), pp. 78-82.
58. 2/ε has the value 2.239 ps for Ar.
59. -1).
60. J. T. Hynes and R. Rey, in Ultrafast Infrared and Raman Spectroscopy, edited by M. D. Fayer (Marcel Dekker, New York, 2001). These authors note that there are some examples involving hydrogen-bonded solvents in which electrostatic forces would, in fact, dominate.
61. S. Gnanakaran and R. M. Hochstrasser, J. Chem. Phys. 105, 3486 (1996)
62. S. Gnanakaran, M. Lim, N. Pugliano, M. Volk, and R. M. Hochstrasser, J. Phys.: Condens. Matter 8, 9201 (1966).
63. 0, Eq. (2.27), would diverge.
64. The vibrational friction for a homonuclear diatomic is identical in form to that of the symmetric stretch of a symmetric triatomic.
65. D. M. F. Edwards, P. A. Madden, and I. R. McDonald, Mol. Phys. 51, 1141 (1984).
66. B. M. Ladanyi and R. M. Stratt, J. Phys. Chem. 99, 2502 (1995).
67. D. Fincham, Mol. Simul. 11, 79 (1993).
68. In Ref. 36, Chap. 5.
69. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, 1973). The transform here was evaluated using the Numerical Algorithms Group Fortran library routine c06faf.
70. K. Singer, A. Taylor, and J. V. L. Singer, Mol. Phys. 33, 1757 (1977)
71. Ref. 36, pp. 90-91.
72. This result is in accord with the observation by M. Teubner (Ref. 7) that the higher the relevant frequency, the smaller the relevant angular momentum is for a colliding pair of molecules.
73. A similar mathematical structure can be seen in studies of the effects of allowing for rotational excitation in gas-phase atom-molecule scattering. A. Miklavc and S. F. Fischer, J. Chem. Phys. 69, 281 (1978).
74. P. J. Prince and J. R. Dormand, J. Comput. Appl. Math. 7, 67 (1981).
75. The potential for computational difficulties in computing high-frequency responses from simulations has been pointed out repeatedly. Schwarzer and Tuebner (Ref. 7) and Rostkier-Edelstein et al. (Ref. 6). The specific deficiencies of the Verlet algorithm will be illustrated in Sec. V (Fig. 11).
76. -2 σ. We take advantage of this feature in our numerical sampling to avoid undersampling infrequent solute-solvent close encounters.
77. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd Ed. (Cambridge University Press, New York, 1992), pp. 108-109.
78. M. Buchner, B. M. Ladanyi, and R. M. Stratt, J. Chem. Phys. 97, 8522 (1992).
79. In the solid state context it is frequently suggested that such combination bands contribute relatively little to high-frequency relaxation. See Refs. 21 and 22. However the issues here are first, whether the same phenomenology should apply to liquids, and second, what happens as the frequency decreases.
80. B. Bagchi, G. Srinivas, and K. Miyazaki, J. Chem. Phys. 115, 4195 (2001)
81. R. Biswas, S. Bhattacharya, and B. Bagchi, ibid. 108, 4963 (1998).
82. Diagonalization was accomplished using Householder tridiagonalization followed by Cuppen's divide-and-conquer algorithms as implemented in LAPACK. E. Anderson, Z. Bai, C. Bischof, et al., LAPACK Users' Guide, 3rd ed. (Society for Industrial and Applied Mathematics, Philadelphia, 1999) (also available as http:///www.netlib.org/lapack/lug/lapack_lug.html). The small contributions made by the imaginary modes were ignored.
83. 4 liquid configurations.
84. Using a conventional definition of the first solvation shell would palce most of the shell to be outside the range of mnn distances (Ref. 53) and therefore outside the (presumably most interesting) repulsive-force region of the solute-solvent interaction. Moreover, as with the polar solvent example (Ref. 41), such solvents would produce divergences in the nonlinear INM formalism. For the purposes of nonlinear INM theory, then, we define the first solvation shell as those solvents closer to the end site of the solute than σ (roughly the maximum of the solute-site/solvent radial distribution function). This definition leads to an average of 1.46 solvents in the first shell under our conditions.
85. The basic issue is that quantum mechanics automatically delocalizes intermolecular positions whereas INM theories are valid only locally. There is therefore no a priori reason to expect that the same instantaneous harmonic potentials that govern the short-time classical dynamics should have any relevance to quantum mechanical bound states in a liquid. Some interesting quantum mechanical generalizations of INM ideas have, nevertheless, been explored by J. Cao and G. Voth, J. Chem. Phys. 101, 6184 (1994)
86. S. A. Corcelli and J. D. Doll, Chem. Phys. Lett. 263, 671 (1996)
87. T. Keyes, J. Chem. Phys. 106, 46 (1997)
88. C. Chakravarty and R. Ramaswamy, ibid. 106, 5564 (1997).
89. -1 into 4-8 literal liquid "phonon" modes. L. K. Iwaki, J. C. Deak, S. T. Rhea, and D. D. Dlott, Chem. Phys. Lett. 303, 176 (1999). Given the results in this paper, the idea that such a multiphonon description could go over the liquids essentially unchanged may not be all that implausible.
90. M. Cho, G. R. Fleming, S. Saito, I. Ohmine, and R. M. Stratt, J. Chem. Phys. 100, 6672 (1994).