Instantaneous perspectives on solute relaxation in fluids: The common origins of nonpolar solvation dynamics and vibrational population relaxation

Journal of Chemical Physics

Volumn 107, Issue 2, 1997, Pages 524-543

  Larsen, Ross E ^a   David, Edwin F ^a   Goodyear, Grant ^a,b   Stratt, Richard M ^a  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000456245     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.474413     Document Type: Article

References (119)

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12. P. G. Wolynes, J. Chem. Phys. 86, 5133 (1987); R. F. Loring and S. Mukamel, ibid. 87, 1272 (1987); B. Bagchi and A. Chandra, ibid. 90, 7338 (1989); M. S. Skaf, T. Fonseca, and B. M. Ladanyi, ibid. 98, 8929 (1993); A. Chandra, D. Wei, and G. N. Patey, ibid. 99, 4926 (1993); F. O. Raineri, B.-C. Perng, and H. L. Friedman, Chem. Phys. 183, 187 (1994); F. O. Raineri, H. Resat, B.-C. Perng, F. Hirata, and H. L. Friedman, J. Chem. Phys. 100, 1477 (1994).
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19. The validity, or lack thereof, of IBC models in the liquid state has been discussed extensively in the article by Harris et al. (Ref. 8) and the longer review by Oxtoby (Ref. 9). See also, M. J. Fixman, J. Chem. Phys. 34, 369 (1961); R. Zwanzig, ibid. 34, 1931 (1961); 36, 2227 (1962); P. S. Dardi and R. I. Cukier, ibid. 89, 41145 (1988); 95, 98 (1991).
20. The validity, or lack thereof, of IBC models in the liquid state has been discussed extensively in the article by Harris et al. (Ref. 8) and the longer review by Oxtoby (Ref. 9). See also, M. J. Fixman, J. Chem. Phys. 34, 369 (1961); R. Zwanzig, ibid. 34, 1931 (1961); 36, 2227 (1962); P. S. Dardi and R. I. Cukier, ibid. 89, 41145 (1988); 95, 98 (1991).
21. The validity, or lack thereof, of IBC models in the liquid state has been discussed extensively in the article by Harris et al. (Ref. 8) and the longer review by Oxtoby (Ref. 9). See also, M. J. Fixman, J. Chem. Phys. 34, 369 (1961); R. Zwanzig, ibid. 34, 1931 (1961); 36, 2227 (1962); P. S. Dardi and R. I. Cukier, ibid. 89, 41145 (1988); 95, 98 (1991).
22. The validity, or lack thereof, of IBC models in the liquid state has been discussed extensively in the article by Harris et al. (Ref. 8) and the longer review by Oxtoby (Ref. 9). See also, M. J. Fixman, J. Chem. Phys. 34, 369 (1961); R. Zwanzig, ibid. 34, 1931 (1961); 36, 2227 (1962); P. S. Dardi and R. I. Cukier, ibid. 89, 41145 (1988); 95, 98 (1991).
23. The validity, or lack thereof, of IBC models in the liquid state has been discussed extensively in the article by Harris et al. (Ref. 8) and the longer review by Oxtoby (Ref. 9). See also, M. J. Fixman, J. Chem. Phys. 34, 369 (1961); R. Zwanzig, ibid. 34, 1931 (1961); 36, 2227 (1962); P. S. Dardi and R. I. Cukier, ibid. 89, 41145 (1988); 95, 98 (1991).
24. R. M. Stratt and M. Maroncelli, J. Phys. Chem. 100, 12981 (1996).
25. R. M. Stratt, Acc. Chem. Res. 28, 201 (1995).
26. T. Keyes, J. Phys. Chem. A 101, 2921 (1997).
27. M. Buchner, B. M. Ladanyi, and R. M. Stratt, J. Chem. Phys. 97, 8522 (1992).
28. P. Moore and T. Keyes, J. Chem. Phys. 100, 6709 (1994); T. Keyes, ibid. 104, 9349 (1996); 106, 46 (1997).
29. P. Moore and T. Keyes, J. Chem. Phys. 100, 6709 (1994); T. Keyes, ibid. 104, 9349 (1996); 106, 46 (1997).
30. P. Moore and T. Keyes, J. Chem. Phys. 100, 6709 (1994); T. Keyes, ibid. 104, 9349 (1996); 106, 46 (1997).
31. M. Cho, G. Fleming, S. Saito, I. Ohmine, and R. M. Stratt, J. Chem. Phys. 100, 6672 (1994).
32. T. Keyes, J. Chem. Phys. 101, 5081 (1994).
33. R. M. Stratt and M. Cho, J. Chem. Phys. 100, 6700 (1994).
34. B. M. Ladanyi and R. M. Stratt, J. Phys. Chem. 99, 2502 (1995).
35. B. M. Ladanyi and R. M. Stratt, J. Phys. Chem. 100, 1266 (1996).
36. T. S. Kalbfleisch, L. D. Ziegler, and T. Keyes, J. Chem. Phys. 105, 7034 (1996).
37. G. Goodyear, R. E. Larsen, and R. M. Stratt, Phys. Rev. Lett. 76, 243 (1996).
38. S. J. Schvaneveldt and R. F. Loring, J. Chem. Phys. 102 2326 (1995); 104, 4736 (1996).
39. S. J. Schvaneveldt and R. F. Loring, J. Chem. Phys. 102 2326 (1995); 104, 4736 (1996).
40. G. Goodyear and R. M. Stratt, J. Chem. Phys. 105, 10050 (1996).
41. G. Goodyear and R. M. Stratt, J. Chem. Phys. (in press).
42. P. Moore, A. Tokmakoff, T. Keyes and M. D. Fayer, J. Chem. Phys. 103, 3325 (1995) suggested that INMs might someday be used to provide a fully quantum mechanical multiphonon treatment of intramolecular vibrational relaxation.
43. Our use of the terms homogeneous and inhomogeneous broadening differs somewhat from that commonly used in spectroscopic contexts, such as that in S. Palese, S. Mukamel, R. J. D. Miller, and W. T. Lotshaw, J. Phys. Chem. 100, 10380 (1996). Inhomogeneous broadening, in their terms, occurs whenever there are distinct peaks contributing to a spectrum, while homogeneous broadening results from dynamics. Although our instantaneous influence spectra are composed of many distinct spikes, we do not say that the instantaneous influence spectrum is inhomogeneously broadened - from our perspective the many peaks that occur for each configuration should be viewed as a signature of dynamical, and hence homogeneous, broadening.
44. J. Yu, T. J. Kang, and M. Berg, J. Chem. Phys. 94, 5787 (1991); J. T. Fourkas and M. Berg, ibid. 98, 7773 (1993); J. T. Fourkas, A. Benigno, and M. Berg, ibid. 99, 8552 (1993).
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46. J. Yu, T. J. Kang, and M. Berg, J. Chem. Phys. 94, 5787 (1991); J. T. Fourkas and M. Berg, ibid. 98, 7773 (1993); J. T. Fourkas, A. Benigno, and M. Berg, ibid. 99, 8552 (1993).
47. A clear discussion of the mathematical and physical principles underlying photon echo techniques has been given by I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1965). Infrared photon echo experiments on vibrational dynamics in liquids and glasses are discussed in the review article by A. Tokmakoff and M. D. Fayer, Acc. Chem. Res. 28, 437 (1995). The analogous Raman echo experiments are described by D. Vanden Bout and M. Berg, J. Raman Spectrosc. 26, 503 (1995).
48. A clear discussion of the mathematical and physical principles underlying photon echo techniques has been given by I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1965). Infrared photon echo experiments on vibrational dynamics in liquids and glasses are discussed in the review article by A. Tokmakoff and M. D. Fayer, Acc. Chem. Res. 28, 437 (1995). The analogous Raman echo experiments are described by D. Vanden Bout and M. Berg, J. Raman Spectrosc. 26, 503 (1995).
49. A clear discussion of the mathematical and physical principles underlying photon echo techniques has been given by I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Phys. Rev. 141, 391 (1965). Infrared photon echo experiments on vibrational dynamics in liquids and glasses are discussed in the review article by A. Tokmakoff and M. D. Fayer, Acc. Chem. Res. 28, 437 (1995). The analogous Raman echo experiments are described by D. Vanden Bout and M. Berg, J. Raman Spectrosc. 26, 503 (1995).
50. The importance to solute relaxation dynamics of repulsive interactions arising from nearby solvents has been emphasized recently by S. Gnanakaran and R. M. Hochstrasser, J. Chem. Phys. 105, 3486 (1996) and S. Gnanakaran, M. Lim, N. Pugliano, M. Volk, and R. M. Hochstrasser, J. Phys. Cond. Matt. 8, 9201 (1996).
51. The importance to solute relaxation dynamics of repulsive interactions arising from nearby solvents has been emphasized recently by S. Gnanakaran and R. M. Hochstrasser, J. Chem. Phys. 105, 3486 (1996) and S. Gnanakaran, M. Lim, N. Pugliano, M. Volk, and R. M. Hochstrasser, J. Phys. Cond. Matt. 8, 9201 (1996).
52. In numerical calculations, the three zero-frequency translational modes are neglected, since they do not contribute to the density of states in the thermodynamic limit.
53. D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University, Oxford, 1987), Chap. 8.
54. 2 is not exact in INM theory because INMs are not time-translation invariant. The origin and consequences of this property of the INMs are discussed in detail in Ref. 24.
55. H. Friedman, A Course in Statistical Mechanics (Prentice-Hall, Englewood Cliffs, 1985), pp. 285-293.
56. R. Kubo, M. Toda, and N. Hashitume, Statistical Physics II, 2nd ed. (Springer-Verlag, Berlin, 1991), Section 1.6.
57. α,jμ.
58. For comparison purposes, each of the spectra in Fig. 1 has been normalized to unit area.
59. The overlap between the normalized solvation and vibrational relaxation influence spectra is found to hold over a wide range of thermodynamic conditions and solute masses, as will be discussed in Sec. V.
60. Figure 11 of Ref. 20 shows that a purely dispersive solute/solvent interaction couples more weakly at high frequencies, and more strongly at low and imaginary frequencies than does the Lennard-Jones interaction.
61. A. M. Walsh and R. F. Loring, Chem. Phys. Lett. 186, 77 (1991).
62. J. G. Saven and J. L. Skinner, J. Chem. Phys. 99, 4391 (1993).
63. The LJ potential was truncated at 2.2σ in the solvation calculation, while the standard cutoff at half the box size was used in the vibrational relaxation calculations, except as noted. In test cases, it was found that removing the cutoff had no effect on the INMs.
64. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University, London, 1992), Chaps. 1 and 3.
65. For the vibrational relaxation and INM spectrum calculations, we used the Householder elimination routine, tred2, to generate a tridiagonal matrix, followed by the QL algorithm diagonalization routine, tqli, from W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, London, 1994). The solvation calculations used the IMSL routine, EIGRS, described in J. R. Rice, Numerical Methods, Software and Analysis: IMSL Reference Edition (McGraw-Hill, New York, 1983).
66. For the vibrational relaxation and INM spectrum calculations, we used the Householder elimination routine, tred2, to generate a tridiagonal matrix, followed by the QL algorithm diagonalization routine, tqli, from W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University Press, London, 1994). The solvation calculations used the IMSL routine, EIGRS, described in J. R. Rice, Numerical Methods, Software and Analysis: IMSL Reference Edition (McGraw-Hill, New York, 1983).
67. LJ = 2.16 ps.
68. P. B. Visscher and B. L. Holian, J. Chem. Phys. 89, 5128 (1988) avoided the averaging problem in their study of vibrational relaxation in a one-dimensional fluid of diatomics by characterizing interesting events - molecular collisions - before averaging.
69. A clear description of self-averaging and a discussion of its importance in the theory of disordered systems can be found in the review by K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986) and in M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1993), Chap. I.
70. A clear description of self-averaging and a discussion of its importance in the theory of disordered systems can be found in the review by K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986) and in M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1993), Chap. I.
71. -1.
72. M. Maroncelli, J. Chem. Phys. 94, 2084 (1991).
73. L. Perera, M. L. Berkowitz, J. Chem. Phys. 96, 3092 (1992); 97, 5253 (1992).
74. L. Perera, M. L. Berkowitz, J. Chem. Phys. 96, 3092 (1992); 97, 5253 (1992).
75. P. L. Muiño, P. R. Callis, J. Chem. Phys. 100, 4093 (1994).
76. α, we find that they account for 99.998% of the influence spectrum's area in the high-density supercritical solvent.
77. -4 for vibrational friction at the supercritical state point.
78. All of the graphic images were generated via the computer program Gl-man, described by D. Faken and H. Jonsson, Comput. Mat. Sci. 2, 279 (1994).
79. k}) is the importance measure of the single most important atom.
80. -1 modes, respectively.
81. The nearest neighbor to atom i, atom l, of course depends upon i.
82. Projections from the total INM density of states are discussed in Refs. 14 and 16. Projections similar in spirit have also been performed for a variety of solute relaxation problems, including partitions of the influence spectrum into components from first-solvation-shell/outer-shell solvents (Ref. 19) and from longitudinal/transverse (Ref. 22) and rotational/translational (Refs. 19 and 20) solvent motions.
83. γβ(a).
84. 2≤(a·a)(b·b), for any vectors a and b.
85. The distinction arises from the fact that there will be cases in which the nearest neighbor of an atom a is b, but the nearest neighbor of b is a different atom.
86. These rotational frequencies will not in general be zero; see J. E. Adams and R. M. Stratt, J. Chem. Phys. 93, 1632 (1990).
87. The first-order correction to the frequencies associated with the relational binary modes often turns out to be of the same order as the frequencies themselves in the dense LJ fluid, suggesting that the rotational binary modes may be poor representations of true INMs.
88. Both physical and mathematical considerations imply that the modes consisting of net translation by mnn pairs are unlikely to be realistic normal modes of the full dynamical matrix. For one thing, the three net translations by the system as a whole, which are exact normal modes, cannot be properly orthogonal to a translation by just a subset of atoms. More physically, translation against a frozen background is bound to carry a significant energy penalty in a dense fluid, so even if the eigenvector were correct, a zero eigenvalue could not be. We will therefore ignore these translational modes in our treatment.
89. Note that using an approximate form for the eigenvector in the projection operator could destroy the inequality in Eq. (5.2).
90. Methods for calculating nearest-neighbor distribution functions, distribution functions similar to the mutual-nearest-neighbor distributions needed here, are discussed in detail by S. Torquato, B. Lu, and J. Rubinstein, Phys. Rev. A 41, 2059 (1990), and by S. H. Simon, V. Dobrosavljevic, and R. M. Stratt, J. Chem. Phys. 93, 2640 (1990).
91. Methods for calculating nearest-neighbor distribution functions, distribution functions similar to the mutual-nearest-neighbor distributions needed here, are discussed in detail by S. Torquato, B. Lu, and J. Rubinstein, Phys. Rev. A 41, 2059 (1990), and by S. H. Simon, V. Dobrosavljevic, and R. M. Stratt, J. Chem. Phys. 93, 2640 (1990).
92. mnn is nonzero, lie far enough up the steeply repulsive wall of the potential that multiple roots are never seen.
93. Y. Wan and R. M. Stratt, J. Chem. Phys. 100, 5123 (1994).
94. T-M. Wu and R. F. Loring, J. Chem. Phys. 97, 8568 (1992); 99, 8936 (1993).
95. T-M. Wu and R. F. Loring, J. Chem. Phys. 97, 8568 (1992); 99, 8936 (1993).
96. rot|. This inconsistency in the mean-field theory supports the observation in Ref. 63 that the binary rotations by mutual-nearest-neighbors are unlikely to be accurate trial eigenvectors.
97. I. M. Lifshits, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988), Chap. 14.
98. Simon et al., Ref. 66, developed similar close-approach ideas in calculations for the local field distribution in a fluid. In much the same way that the dynamics of a member of a mutual-nearest-neighbor pair is dominated by its neighbor, the local field on an atom was found to be dominated by the field from the closest atom.
99. G. V. Vijayadamodar and A. Nitzan, J. Chem. Phys. 103, 2169 (1995); T.-M. Wu and S.-F. Tsay, ibid. 105, 9281 (1996). It has, however, been suggested that the form of the tail of the imaginary-mode branch of the density of states has some universal features. See U. Zurcher, T. Keyes, and B. B. Laird (preprint); T. Keyes, J. Chem. Phys. 101, 5081 (1994).
100. G. V. Vijayadamodar and A. Nitzan, J. Chem. Phys. 103, 2169 (1995); T.-M. Wu and S.-F. Tsay, ibid. 105, 9281 (1996). It has, however, been suggested that the form of the tail of the imaginary-mode branch of the density of states has some universal features. See U. Zurcher, T. Keyes, and B. B. Laird (preprint); T. Keyes, J. Chem. Phys. 101, 5081 (1994).
101. G. V. Vijayadamodar and A. Nitzan, J. Chem. Phys. 103, 2169 (1995); T.-M. Wu and S.-F. Tsay, ibid. 105, 9281 (1996). It has, however, been suggested that the form of the tail of the imaginary-mode branch of the density of states has some universal features. See U. Zurcher, T. Keyes, and B. B. Laird (preprint); T. Keyes, J. Chem. Phys. 101, 5081 (1994).
102. G. V. Vijayadamodar and A. Nitzan, J. Chem. Phys. 103, 2169 (1995); T.-M. Wu and S.-F. Tsay, ibid. 105, 9281 (1996). It has, however, been suggested that the form of the tail of the imaginary-mode branch of the density of states has some universal features. See U. Zurcher, T. Keyes, and B. B. Laird (preprint); T. Keyes, J. Chem. Phys. 101, 5081 (1994).
103. G. Seeley and T. Keyes, J. Chem. Phys. 91, 5581 (1989).
104. 2) rather than 3N modes] and require the use of the reduced mass rather than the atomic mass. If, on the other hand, one regarded the formula as assuming that each atom vibrates in a static background field created by the rest of the liquid (obviating the problems with normalization and effective mass), or for that matter, created by a spherical shell of near neighbors, then Eq. (5.9) would no longer be the desired expression for the frequency.
105. 3 = 0.01. The ideal gas result is suggestive but it does not fully explain the empirical result that just over half (2 × 0.273N) of the atoms in an atomic liquid are members of a mnn pair over quite a large density range.
106. A complication arises, however, if we study a molecular solute that is free to move: It is not clear that the desired mode should be thought of as a binary mode between a single atom in the solute and a single atom in the solvent. It is possible, however, to treat each normal mode of the molecule as a "solute" atom, using perturbation theory, and then construct binary "solute"-solvent modes, E. F. David and R. E. Larsen (unpublished). This method lets us treat solvent-induced V-V relaxation as well as the V-T relaxation discussed here, but we will not pursue this development here.
107. a - 1) in Eq. (5.19) increases the area under the binary-mode influence spectrum by approximately 18% in the high-density supercritical fluid, but by less than 1% in the liquid state. Interestingly, the increased area means that the two-body binary-mode spectrum fits the unprojected spectrum in the supercritical fluid more closely than does a more inclusive binary theory. For vibrational population relaxation by an infinitely massive diatomic, neglecting the interaction f between the binary-mode solvent atom b and the solute atom not associated with the binary mode introduces negligible error, changing the area under the spectrum by less than 4% for both the supercritical and the liquid state points.
108. The mutual-nearest-neighbor distribution function in Eq. (5.22) is in fact a solute/solvent distribution. For brevity, we have written the formula as if the solute/solvent distribution were identical to that for the neat solvent. We have also defined c(r) = f′(r)/ √μ and assumed isotropy.
109. solv≃0.1), however, we have found that the low-frequency part of the solvation spectrum does begin to change its shape [R. E. Larsen (unpublished results)].
110. solv≃0.1), however, we have found that the low-frequency part of the solvation spectrum does begin to change its shape [R. E. Larsen (unpublished results)].
111. solv≃0.1), however, we have found that the low-frequency part of the solvation spectrum does begin to change its shape [R. E. Larsen (unpublished results)].
112. solv≃0.1), however, we have found that the low-frequency part of the solvation spectrum does begin to change its shape [R. E. Larsen (unpublished results)].
113. solv≃0.1), however, we have found that the low-frequency part of the solvation spectrum does begin to change its shape [R. E. Larsen (unpublished results)].
114. solv≃0.1), however, we have found that the low-frequency part of the solvation spectrum does begin to change its shape [R. E. Larsen (unpublished results)].
115. B. M. Ladanyi and R. M. Stratt (unpublished).
116. P. V. Kumar and M. Maroncelli, J. Chem. Phys. 103, 3038 (1995).
117. An INM-based comparison of the electrostatic solvation influence spectrum and the spectrum describing the optical Kerr effect in acetonitrile has been made by B. M. Ladanyi and S. Klein, J. Chem. Phys. 105, 1552 (1996).
118. -1) part of ethanol's experimentally-measured optical-Kerr-effect spectrum and the simulated friction spectrum for dipolar HgI in ethanol.
119. A discussion of the extent to which fluctuations in the influence spectrum change vibrational relaxation dynamics may be found in Ref. 25.