A failure of continuum theory: Temperature dependence of the solvent reorganization energy of electron transfer in highly polar solvents

Journal of Physical Chemistry B

Volumn 103, Issue 43, 1999, Pages 9130-9140

  Vath, Peter ^a   Zimmt, Matthew B ^a   Matyushov, Dmitry V ^b   Voth, Gregory A ^b  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000760120     PISSN: 15206106     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp990494q     Document Type: Article

References (84)

1. (a) Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984, 35, 437.
2. (b) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265.
3. (c) Barbara, P. F.; Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100, 13148.
4. (a) Marcus, R. A. J. Chem. Phys. 1965, 43, 1261.
5. (b) Marcus, R. A. Ann. Rev. Phys. Chem. 1964, 15, 155.
6. (c) Marcus, R. A. Rev. Mod. Phys. 1993, 65, 599.
7. Kim, H. J.; Hynes, J. T. J. Am. Chem. Soc. 1992, 114, 10508;
8. J. Am. Chem. Soc. 1992, 114, 10528.
9. Kumar, K.; Kurnikiov, I. V.; Beratan, D. N.; Waldeck, D. H.; Zimmt, M. B. J. Phys. Chem. A 1998, 102, 5529.
10. (a) Walker, G. C.; Åkesson, E.; Johnson, A. E.; Levinger, N. E.; Barbara, P. F. J. Phys. Chem. 1992, 96, 3728.
11. (b) Cortés, J.; Heitele, H.; Jortner, J. J. Phys. Chem. 1994, 98, 2527.
12. (c) Morais, J.; Zimmt, M. B. J. Phys. Chem. 1995, 99, 8863.
13. (d) Kapturkiewicz, A.; Herbich, J.; Karpiuk, J.; Nowacki, J. J. Phys. Chem. A 1997, 101, 2332.
14. Marcus, R. A. J. Phys. Chem. 1989, 93, 3078.
15. Equations 1 and 2 are restricted to the conditions of linear solvent response and electronic state independent solute polarizability.
16. (a) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; CIareddon Press: Oxford, 1987.
17. (b) Sprik, M. In Computer Simulation in Chemical Physics; Allen, M. P., Tildesley, D. J., Eds.; Elsevier: Amsterdam, 1993; p 211.
18. (a) Monta, T.; Ladanyi, B. M.; Hynes, J. T. J. Phys. Chem. 1989, 93, 1386.
19. (b) Fonseca, T.; Ladanyi, B. M.; Hynes, J. T. J. Phys. Chem. 1992, 96, 4085.
20. (c) Chong, S.-H.; Miura, S.; Basu, G.; Hirata, F. J. Phys. Chem. 1995, 99, 10526.
21. (d) Perng, B.-C.; Newton, M. D.; Raineri, F. O.; Friedman, H. L. J. Chem. Phys. 1996, 104, 7153;
22. J. Chem. Phys. 1996, 104, 7177.
23. (e) Chong, S.-H.; Hirata, F. J. Chem. Phys. 1997, 106, 5225.
24. (a) Warshel, A. J. Phys. Chem. 1982, 86, 2218.
25. (b) Warshel, A.; Hwang, J.-K. J. Chem. Phys. 1986, 84, 4938.
26. (c) King, G.; Warshel, A. J. Chem. Phys. 1990, 93, 8682.
27. (a) Bader, J. S.; Berne, B. J. J. Chem. Phys. 1996, 104, 1293.
28. (b) Hummer, G.; Szabo, A. J. Chem. Phys. 1996, 105, 2004.
29. (c) Yelle, R. B.; Ichiye, T. J. Phys. Chem. B 1997, 101, 4127.
30. (d) Bader, J. S.; Cortis, C. M.; Berne, B. J. J. Chem. Phys. 1997, 100, 2372.
31. (e) Marchi, M.; Gehlen, J. N.; Chandler, D.; Newton, M. D. J. Am. Chem. Soc. 1993, 115, 4178.
32. (a) Matyushov, D. V. Mol. Phys. 1993, 79, 795.
33. (b) Matyushov, D. V. Chem. Phys. 1993, 174, 199.
34. (c) Matyushov, D. V. Chem. Phys. 1996, 211, 47.
35. (d) Matyushov, D. V.; Schmid, R.; Ladanyi, B. M. J. Phys. Chem. 1997, 101, 1035.
36. i (see eq 11). We assume, however, that the solute polarizability does not change with the transition. This assumption excludes the dispersion components from optical and ET parameters.
37. Patey, G. N.; Valleau, J. P. J. Chem. Phys. 1976, 64, 170.
38. (a) Matyushov, D. V.; Schmid, R. Mol. Phys. 1995, 84, 533.
39. (b) Matyushov, D. V.; Schmid, R. J. Chem. Phys. 1995, 103, 2034.
40. Reynolds, L.; Gardecki, J. A.; Frankland, J. V.; Horng, M. L.; Maroncelli, M. J. Phys. Chem. 1996, 100, 10337.
41. Acetonitrile is a nonspherical molecule, but the effective HS diameter σ = 4.14 Å can be obtained by fitting the liquid compressibility to the generalized van der Waals equation assuming spherical molecular hard cores. Schmid, R.; Matyushov, D. V. J. Phys. Chem. 1995, 99, 2397.
42. 2 = (2/3)Q:Q can be used as a measure of molecular quadrupole, see: Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids. Volume 1: Fundamentals; Clarendon Press: Oxford, 1984.
43. Matyushov, D. V.; Voth, G. A. J. Chem. Phys. 1999. In press.
44. Lax, M. J. Chem. Phys. 1952, 20, 1752.
45. (a) Pekar, S. I. Research in Electronic Theory of Crystals; USAEC: Washington, DC, 1963.
46. (b) Kim, H. J.; Hynes, J. T. J. Chem. Phys. 1992, 86, 5088.
47. (c) Gehlen, J. N.; Chandler, D. Kim, H. J.; Hynes, J. T. J. Phys. Chem. 1992, 96, 1748.
48. (d) Kim, H. J. J. Chem. Phys. 1996, 105, 6618;
49. J. Chem. Phys. 1996, 105, 6833.
50. (e) Matyushov, D. V.; Ladanyi, B. M. J. Chem. Phys. 1998, 108, 6362.
51. (f) Matyushov, D. V.; Ladanyi, B. M. J. Phys. Chem. A 1998, 102, 5027.
52. i.
53. Loring, R. F. J. Phys. Chem. 1990, 94, 513.
54. 0 < 1 as long as the solute radius is fitted to the experimental Stokes shift at T = 300 K.
55. (a) Lippert, E. Z. Electrochemie 1957, 61, 963.
56. (b) Liptay, W. In Modern Quantum Chemistry, Part II; Sinanoǧlu, O., Ed.; Academic Press: New York, 1965.
57. A most adequate physical realization of the continuum model is a lattice of permanent point dipoles that can rotate but cannot translate. There is a very instructive recent discussion of these features by Papazyan and Warshel, Papazyan, A.; Warshel, A. J. Phys. Chem. B 1997, 101, 11254.
58. (a) Matyushov, D. V.; Schmid, R. J. Chem. Phys. 1996, 105, 4729.
59. (b) Matyushov, D. V.; Ladanyi, B. M. J. Chem. Phys. 1997, 107, 1362.
60. (c) Matyushov, D. V.; Ladanyi, B. M. J. Chem. Phys. 1999, 110, 994.
61. Wertheim, M. S. Mol. Phys. 1979, 37, 83.
62. (a) Venkatasubramanian, V.; Gubbins, K. E.; Gray, C. G.; Joslin, C. G. Mol. Phys. 1984, 52, 1411.
63. (b) Joslin, C. G.; Gray, C. G.; Gubbins, K. E. Mol. Phys. 1985, 54, 1117.
64. Ben-Amotz, D.; Willis, K. G. J. Phys. Chem. 1993, 97, 7736.
65. Pasman, P.; Rob, F.; Verhoeven, J. W. J. Am. Chem. Soc. 1982, 104, 5127.
66. 3.
67. s values determined by fitting the reduced emission band shape are about 0.07 eV larger than the value determined according to eq 1. This result is consistent with literature discussions of this point, see: Mertz, E. L. Chem. Phys. Lett. 1996, 262, 27.
68. The energy attending distortion of the equilibrated radical cation (anion) to the ground state geometry, 0.32 eV (0.12 eV) are nearly identical to the energies determined for distortion of the ground state. PM3 calculations also generate a 0.45 eV value.
69. Miller K. J. J. Am. Chem. Soc. 1990, 112, 8533.
70. s.
71. 38b As far as the equilbrium response is concerned, rotational and translation modes are fully decoupled in the perturbation formalism and in more exact approaches.
72. (a) Ladanyi, B. M.; Stratt, R. J. Phys. Chem. 1995, 99, 2502.
73. (b) Ladanyi, B. M.; Maroncelli, M. J. Chem. Phys. 1998, 109, 3204.
74. Elliott, C. M.; Derr, D. L.; Matyushov, D. V.; Newton, M. D. J. Am. Chem. Soc. 1998, 120, 11714.
75. Ma, J.; Bout, D. V.; Berg, M. J. Chem. Phys. 1995, 103, 9146.
76. Dong, Y.; Hupp, J. T. Inorg. Chem. 1992, 31, 3322.
77. (a) Chen, P.; Mecklenburg, S. L.; Duesing, R.; Meyer, T. J. J. Phys. Chem. 1993, 97, 6811.
78. (b) Pérez-Tejeda, P.; Sánchez-Burgos, F.; Galán, M. J. Mol. Struc. (Theochem) 1996, 371, 153.
79. s in acetonitrile has been determined for a thia-decalin analog of the thia-cyclohexane molecule investigated in the present study. The same donor and acceptor groups are present in both molecules but are separated by five bonds in the thia-decalin analog. The solvent reorganization energy is larger, but its temperature derivative is smaller, for the five-bond separation in comparison to the three-bond separation, Vath, P.; Zimmt, M. B. J. Phys. Chem. A 1999. Manuscript in preparation.
80. or are equal to 31.5 eV and -30.6 eV. Therefore, only 3% of each response term remains after their mutual cancellation in eq 50.
81. The energetic cost of solvent rotations arises only from dipolar and induction forces in the present model. The relative contribution of density reorganization may increase for significantly elongated solvent molecules due to restrictions on rotations imposed by the local solvent packing.
82. Tepper, R. J.; Zimmt, M. B. Chem. Phys. Lett. 1995, 241, 566.
83. 19 does not modify the qualitative features of the dependences shown in Figure 4.
84. Roux, B.; Yu, H.-A.; Karplus, M. J. Phys. Chem. 1990, 94, 4683.