Time-dependent fluorescence spectra of large molecules in polar solvents

Journal of Physical Chemistry A

Volumn 102, Issue 16, 1998, Pages 2658-2666

  Hsu, Chao Ping ^a   Georgievskii, Yuri ^a   Marcus, R A ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000445540     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp980255n     Document Type: Article

References (108)

1. Bakhshiev, B. G. Opt. Spectrosc. 1964, 16, 446.
2. Mazurenko, Y. T.; Bakshiev, B. G. Opt. Spectrosc. (USSR) 1970, 28, 490.
3. Mazurenko, Y. T.; Udaltsov, V. S. Opt. Spectrosc. (USSR) 1978, 44, 417.
4. Mazurenko, Y. T. Opt. Spectrosc. (USSR) 1980, 48, 388.
5. Nee, T.-W.; Zwanrig, R. J. Chem. Phys. 1970, 52, 6353, van der Zwan, G.; Hynes, J. T. J. Chem. Phys. 1982, 76, 2993.
6. Nee, T.-W.; Zwanrig, R. J. Chem. Phys. 1970, 52, 6353, van der Zwan, G.; Hynes, J. T. J. Chem. Phys. 1982, 76, 2993.
7. Ware, W. R.; Lee, S. K.; Brant, G. J.; Chow, P. P. J. Chem. Phys. 1971, 54, 4729. Okamura, T.; Sumitani, M.; Yoshihara, K. Chem. Phys. Lett. 1983, 94, 339. Su, S.-G.; Simon, J. D. J. Phys. Chem. 1987,91, 2693.
8. Ware, W. R.; Lee, S. K.; Brant, G. J.; Chow, P. P. J. Chem. Phys. 1971, 54, 4729. Okamura, T.; Sumitani, M.; Yoshihara, K. Chem. Phys. Lett. 1983, 94, 339. Su, S.-G.; Simon, J. D. J. Phys. Chem. 1987,91, 2693.
9. Ware, W. R.; Lee, S. K.; Brant, G. J.; Chow, P. P. J. Chem. Phys. 1971, 54, 4729. Okamura, T.; Sumitani, M.; Yoshihara, K. Chem. Phys. Lett. 1983, 94, 339. Su, S.-G.; Simon, J. D. J. Phys. Chem. 1987,91, 2693.
10. Jarzȩba, W.; Walker, G. C.; Johnson, A. E.; Kahlow, M. A.; Barbara, P. F. J. Phys. Chem. 1988, 92, 7039.
11. Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1987, 86, 6221.
12. Horng, M. L.; Gardecki, J. A.; Papazyan, A.; Maroncelli, M. J. Phys. Chem. 1995, 99, 17311.
13. Gardecki, J.; Horng, M. L.; Papazyan, A. Maroncelli, M. J. Mol. Liq. 1995, 65-6, 49.
14. Maroncelli, M. J. Phys. Chem. 1997, 106, 1545.
15. Kumar, P. V.; Maroncelli, M. J. Chem. Phys. 1995, 103, 3038.
16. Jimenez, R.; Fleming, G. R.; Kumar, P. V.; Maroncelli, M. Nature 1994, 369, 471.
17. Jarzeba, W.; Walker, G. C.; Johnson, A. E.; Barbara, P. F. Chem. Phys. 1991, 152, 57.
18. Castner, E. W., Jr.; Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1987, 86, 1090.
19. Maroncelli, M.; Castner, E. W., Jr.; Bagchi, B.; Fleming, G. R. Faraday Discuss. Chem. Soc. 1988, 85, 199.
20. Castner, E. W., Jr.; Fleming, G. R.; Bagchi, B. Chem. Phys. Lett. 1988, 143, 270.
21. Wolynes, P. G. J. Chem. Phys. 1987, 86, 5133. Rips, I.; Klafter, J.; Jortner, J. J. Chem. Phys. 1988, 88, 3246; Ibid. 1988, 89, 4288. Nichols III, A. L.; Calef, D. F. J. Chem. Phys. 1988, 89, 3783.
22. Wolynes, P. G. J. Chem. Phys. 1987, 86, 5133. Rips, I.; Klafter, J.; Jortner, J. J. Chem. Phys. 1988, 88, 3246; Ibid. 1988, 89, 4288. Nichols III, A. L.; Calef, D. F. J. Chem. Phys. 1988, 89, 3783.
23. Wolynes, P. G. J. Chem. Phys. 1987, 86, 5133. Rips, I.; Klafter, J.; Jortner, J. J. Chem. Phys. 1988, 88, 3246; Ibid. 1988, 89, 4288. Nichols III, A. L.; Calef, D. F. J. Chem. Phys. 1988, 89, 3783.
24. Wolynes, P. G. J. Chem. Phys. 1987, 86, 5133. Rips, I.; Klafter, J.; Jortner, J. J. Chem. Phys. 1988, 88, 3246; Ibid. 1988, 89, 4288. Nichols III, A. L.; Calef, D. F. J. Chem. Phys. 1988, 89, 3783.
25. Raineri, F. O.; Resat, H.; Perng, B.-C.; Hirata, F.; Friedman, H. L. J. Chem. Phys. 1994, 100, 1477. Zhou, Y.; Friedman, H. L.; Stell, G. J. Chem. Phys. 1989, 91, 4885. Fried, L. E.; Mukamel, S. J. Chem. Phys. 1990, 93, 932. Loring, R. F.; Mukamel, S. J. Chem. Phys. 1987, 8, 1272. Bagachi, B.; Chandra, A. J. Chem. Phys. 1989, 90, 7338.
26. Raineri, F. O.; Resat, H.; Perng, B.-C.; Hirata, F.; Friedman, H. L. J. Chem. Phys. 1994, 100, 1477. Zhou, Y.; Friedman, H. L.; Stell, G. J. Chem. Phys. 1989, 91, 4885. Fried, L. E.; Mukamel, S. J. Chem. Phys. 1990, 93, 932. Loring, R. F.; Mukamel, S. J. Chem. Phys. 1987, 8, 1272. Bagachi, B.; Chandra, A. J. Chem. Phys. 1989, 90, 7338.
27. Raineri, F. O.; Resat, H.; Perng, B.-C.; Hirata, F.; Friedman, H. L. J. Chem. Phys. 1994, 100, 1477. Zhou, Y.; Friedman, H. L.; Stell, G. J. Chem. Phys. 1989, 91, 4885. Fried, L. E.; Mukamel, S. J. Chem. Phys. 1990, 93, 932. Loring, R. F.; Mukamel, S. J. Chem. Phys. 1987, 8, 1272. Bagachi, B.; Chandra, A. J. Chem. Phys. 1989, 90, 7338.
28. Raineri, F. O.; Resat, H.; Perng, B.-C.; Hirata, F.; Friedman, H. L. J. Chem. Phys. 1994, 100, 1477. Zhou, Y.; Friedman, H. L.; Stell, G. J. Chem. Phys. 1989, 91, 4885. Fried, L. E.; Mukamel, S. J. Chem. Phys. 1990, 93, 932. Loring, R. F.; Mukamel, S. J. Chem. Phys. 1987, 8, 1272. Bagachi, B.; Chandra, A. J. Chem. Phys. 1989, 90, 7338.
29. Raineri, F. O.; Resat, H.; Perng, B.-C.; Hirata, F.; Friedman, H. L. J. Chem. Phys. 1994, 100, 1477. Zhou, Y.; Friedman, H. L.; Stell, G. J. Chem. Phys. 1989, 91, 4885. Fried, L. E.; Mukamel, S. J. Chem. Phys. 1990, 93, 932. Loring, R. F.; Mukamel, S. J. Chem. Phys. 1987, 8, 1272. Bagachi, B.; Chandra, A. J. Chem. Phys. 1989, 90, 7338.
30. Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1988, 89, 875.
31. Kahlow, M. A.; Jarzȩba, W.; Kang, T. J.; Barbara, P. F. J. Chem. Phys. 1989, 90, 151.
32. Bagchi, B.; Chandra, A. Adv. Chem. Phys. 1991, 80, 1. Bagchi, B. Annu. Rev. Phys. Chem. 1989, 40, 115.
33. Bagchi, B.; Chandra, A. Adv. Chem. Phys. 1991, 80, 1. Bagchi, B. Annu. Rev. Phys. Chem. 1989, 40, 115.
34. Roy, S.; Bagchi, B. J. Chem. Phys. 1993, 99, 9938.
35. Nandi, N.; Roy, S.; Bagchi, B. J. Chem. Phys. 1995, 102, 1390.
36. Biswas, R.; Nandi, N.; Bagchi, B. J. Phys. Chem. 1997, 101, 2968.
37. Roy, S.; Komath, S.; Bagchi, B. J. Chem. Phys. 1993, 99, 3139.
38. Gertner, B. J.; Whitnell, R. M.; Wilson, K. R.; Hynes, J. T. J. Am. Chem. Soc. 1991, 113, 74.
39. Ladanyi, B. M.; Stratt, R. M. J. Phys. Chem. 1995, 99, 2502; Ibid. 1996, 100, 1266.
40. Ladanyi, B. M.; Stratt, R. M. J. Phys. Chem. 1995, 99, 2502; Ibid. 1996, 100, 1266.
41. Maroncelli, M.; Fleming, G. R. J. Chem. Phys. 1988, 89, 5044.
42. Hsu, C.-P.; Song, X.; Marcus, R. A. J. Phys. Chem. B 1997, 101, 2546.
43. Carter, E. A.; Hynes, J. T. J. Chem. Phys. 1991, 94, 5961.
44. Rosenthal, S. J.; Jimenez, R.; Fleming, G. R.; Kumar, P. V.; Maroncelli, M. J. Mol. Liq. 1994, 60, 25.
45. Fonseca, T.; Ladanyi, B. M. J. Phys. Chem. 1991, 95, 2116.
46. Ando, K.; Kato, S. J. Chem. Phys. 1991, 95, 5966.
47. Zhu, J.; Cukier, R. I. J. Chem. Phys. 1993, 98, 5679.
48. Georgievskii, Y.; Hsu, C.-P.; Marcus, R. A. J. Chem. Phys., submitted.
49. Loring, R. F.; Yan, Y. J.; Mukamel S. J. Chem. 1987, 87, 5840.
50. Loring, R. F.; Yan, Y. Y.; Mukamel S. Chem. Phys. Lett. 1987, 135, 23.
51. Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford University Press: New York, 1995.
52. For example, Mahan, G. D. Many-particle Physics, 2nd ed.; Plenum Press: New York, 1990.
53. Fee, R. S.; Milsom, J. A.; Maroncelli, M. J. Phys. Chem. 1991, 95, 5170.
54. Fee, R. S.; Maroncelli, M. Chem. Phys. 1994, 183, 235.
55. For example: Passino, S. A.; Nagasawa, Y.; Joo, T.; Fleming, G. R. J. Phys. Chem. 1997, 101, 725. Bardeen, C. J.; Shank C. V. Chem. Phys. Lett. 1994, 226, 310.
56. For example: Passino, S. A.; Nagasawa, Y.; Joo, T.; Fleming, G. R. J. Phys. Chem. 1997, 101, 725. Bardeen, C. J.; Shank C. V. Chem. Phys. Lett. 1994, 226, 310.
57. Maroncelli, M., private communication.
58. Bagchi, B.; Oxtoby, D. W.; Fleming, G. R. Chem. Phys. 1984, 86, 257.
59. Kubo, R. J. Phys. Soc. Jpn. 1962, 17, 1100.
60. Kubo, R. In Fluctuation, Relaxation and Resonance in Magnetic Systems; ter Haar, D., Ed.; Oliver & Boyd: Edinburgh, 1962; p 23. Kubo, R. Adv. Chem. Phys. 1969, 15, 101.
61. Kubo, R. In Fluctuation, Relaxation and Resonance in Magnetic Systems; ter Haar, D., Ed.; Oliver & Boyd: Edinburgh, 1962; p 23. Kubo, R. Adv. Chem. Phys. 1969, 15, 101.
62. 2 term.
63. f replaces the reorganization energy λ in electron-transfer reactions.
64. 2 can be reasonable approximated as -∞ to ∞ and so can the limits for τ″ and u.
65. Lax, M. J. Chem. Phys. 1952, 20, 1752.
66. In ref 51 the absorption and emission spectra are shown to be the Fourier transformation of their time-dependent characteristic functions (eq 8.20). Expressions in eqs 23 and 24 are such characteristic functions (they correspond to eqs 8.13 and 8.11 of ref 51, respectively.).
67. f(0) U(t), where U(t) is the time-evolution operator which, when it operates on a wave function, propagates it forward for time t. The second equality makes use of the stationary property.
68. f(0)〉 is much smaller than its real part, at this high-temperature limit.
69. Ovchinnikov, A. A.; Ovchinnikova, M. Ya. Sov. Phys. JETP 1969, 29, 688.
70. Abrikosov, A. A.; Gorkov, L. P.; Dzyaloshinski, I. E. Methods of Quantum Field Theory in Statistical Physics; Dover Publications, Inc.: New York, 1963.
71. Caldeira, A. O.; Leggett, A. J. Ann. Phys. (N.Y.) 1983, 149, 374.
72. Mukamel, S. J. Phys. Chem. 1985, 89, 1077.
73. Georgievskii, Y.; Hsu, C.-P.; Marcus, R. A. Linear Response Theory Approach for Solvation Dynamics and Nonlinear Spectroscopy, in preparation.
74. For example: Chandler, D. In Liquids, freezing and glass transitions; Hansen, J. P., Levesque, D., Zinn-Justin, J., Eds.; Elsevier Science: North-Holland, 1991; p 201.
75. For example: Kubo, R.; Toda, M.; Hashitsume, N. Statistical Physics; Springer-Verlag: New York, 1983; Vol. II, Chapter 4.
76. Onsager, L. J. Am. Chem. Soc. 1936, 58, 1486.
77. Böttcher, C. J. F. Theory of Electric Polarization, Elsevier: Amsterdam, 1983; Vol. I.
78. van der Zwan, G.; Hynes, J. T. J. Phys. Chem. 1985, 89, 4181.
79. Mazurenko, Y. T. Opt. Spectrosc. (USSR) 1974, 36, 283.
80. 0dωJ(ω)/ω
81. Barhel, J.; Bachhuber, K.; Buchner, R.; Gill, J. B.; Kleebauer M. Chem. Phys. Lett. 1990, 167, 62.
82. Barthel, J.; Kleebauer, M.; Buchner, R. J. Solut. Chem. 1995, 24, 1.
83. Arnold, K. E.; Yarwood, J.; Price A. H. Mol. Phys. 1983, 48, 451.
84. Ikawa, S.; Ohba, T.; Tanaka, S.; Morimoto, S. Fukushi, K.; Kimura, M. Int. J. Infrared Millimeter Waves 1985, 6, 287.
85. Fujita, Y.; Ohba, T.; Ikawa S.-I. Can. J. Chem. 1991, 69, 1745.
86. Ohba, T.; Ikawa, S. Mol. Phys. 1991, 73, 985.
87. Firman, P.; Marchetti, M.; Xu, M.; Eyring, E. M.; Petrecci, S. J. Phys. Chem. 1991, 95, 7055.
88. Goplen, T. G.; Cameron, D. G.; Jones, R. N. Appl. Spectrosc. 1980, 34, 657.
89. Bertie, J. E. J. Phys. Chem. B 1997, 101, 4111.
90. 69 if the latter were scaled downward by 7%. That scaled profile, as shown in ref 70, is in good agreement with the results later reported in refs 71 and 72. Since only a few numerical data are available for those results, the overall spectrum in the present work is obtained from the curve in Figure 6 of ref 70 representing the scaled results of Arnold et al.
91. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes; Cambridge University Press: Cambridge, 1986.
92. -1.
93. For example: McQuarrie, D. A. Statistical Mechanics; Harper & Row: New York, 1976; pp 498-499.
94. Bertie, J. E.; Lan, Z. J. Chem. Phys. 1995, 108, 10152. The numbers in the row denoted as "Eq.(3)+" of Table IV are used.
95. -1.
96. 1(ω), the steady-state absorption and emission spectra in a nonpolar solvent (eq 2).)
97. s can be calculated using the expression discussed in footnote 66.
98. Barthel, J.; Bachhuber, K.; Buchner, R.; Hetzenauer, H. Chem. Phys. Lett. 1990, 165, 369.
99. Bertie, J. E.; Zhang, S. L.; Eysel, H. H.; Baluja, S.; Ahmed, M. K. Appl. Spectrosc. 1993, 47, 1100.
100. Kindt, J. T.; Schmuttenmaer, C. A. J. Phys. Chem. 1996, 100, 10373.
101. Kovalenko, S. A.; Ruthmann, J.; Ernsting, N. P. Chem. Phys. Lett. 1997, 271, 40.
102. Raineri, F. O.; Perng, B.-C.; Friedman, H. L. Electrochim. Acta 1997, 42, 2749.
103. For example, Weiner, A. M.; Desilvestri, S.; Ippen, E. P. J. Opt. Soc. B 1985, 2, 654. Bai, Y. S.; Fayer, M. D. Chem. Phys. 1988, 128, 135. Joo, T.; Albrecht, A. C. Chem. Phys. 1993, 176, 233. Meijers, H. C.; Wiersma, D. A. J. Chem. Phys. 1994, 101, 6927. Bardeen, C. J.; Shank, C. V. Chem. Phys. Lett. 1994, 226, 310.
104. For example, Weiner, A. M.; Desilvestri, S.; Ippen, E. P. J. Opt. Soc. B 1985, 2, 654. Bai, Y. S.; Fayer, M. D. Chem. Phys. 1988, 128, 135. Joo, T.; Albrecht, A. C. Chem. Phys. 1993, 176, 233. Meijers, H. C.; Wiersma, D. A. J. Chem. Phys. 1994, 101, 6927. Bardeen, C. J.; Shank, C. V. Chem. Phys. Lett. 1994, 226, 310.
105. For example, Weiner, A. M.; Desilvestri, S.; Ippen, E. P. J. Opt. Soc. B 1985, 2, 654. Bai, Y. S.; Fayer, M. D. Chem. Phys. 1988, 128, 135. Joo, T.; Albrecht, A. C. Chem. Phys. 1993, 176, 233. Meijers, H. C.; Wiersma, D. A. J. Chem. Phys. 1994, 101, 6927. Bardeen, C. J.; Shank, C. V. Chem. Phys. Lett. 1994, 226, 310.
106. For example, Weiner, A. M.; Desilvestri, S.; Ippen, E. P. J. Opt. Soc. B 1985, 2, 654. Bai, Y. S.; Fayer, M. D. Chem. Phys. 1988, 128, 135. Joo, T.; Albrecht, A. C. Chem. Phys. 1993, 176, 233. Meijers, H. C.; Wiersma, D. A. J. Chem. Phys. 1994, 101, 6927. Bardeen, C. J.; Shank, C. V. Chem. Phys. Lett. 1994, 226, 310.
107. For example, Weiner, A. M.; Desilvestri, S.; Ippen, E. P. J. Opt. Soc. B 1985, 2, 654. Bai, Y. S.; Fayer, M. D. Chem. Phys. 1988, 128, 135. Joo, T.; Albrecht, A. C. Chem. Phys. 1993, 176, 233. Meijers, H. C.; Wiersma, D. A. J. Chem. Phys. 1994, 101, 6927. Bardeen, C. J.; Shank, C. V. Chem. Phys. Lett. 1994, 226, 310.
108. Nishiyama, K.; Okada, T. J. Phys. Chem. A 1997, 101, 5729.