Skip to main content

Theory of Electron Transfer Reactions and Comparison with Experiments

  • Chapter

Part of the NATO ASI Series book series (ASIC,volume 376)

Abstract

In these lectures, reaction rate theory and the theory of electron transfer (ET) reactions are outlined. The topics discussed include the relation of the potential energy surfaces to free energy curves for ET reactions, classical ET theory for reactions in solution and at interfaces, quantum corrections, the inverted effect, relation to charge transfer spectra. the cross-relation, adiabatic and nonadiabatic ET reactions, electronic matrix elements, relation to other transfer reactions, predictions of and comparison with experiments, and miscellaneous questions.

Keywords

  • Electron Transfer
  • Potential Energy Surface
  • Separation Distance
  • Electron Transfer Reaction
  • Intersection Surface

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

From lectures given by RAM at the NATO Summer School at Aussois, 1991.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-94-011-2698-4_2
  • Chapter length: 40 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   59.99
Price excludes VAT (USA)
  • ISBN: 978-94-011-2698-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   79.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Marcus, R. A. and Sutin, N. (1985) Biochim. Biophys. Acta., 811, 265.

    CrossRef  CAS  Google Scholar 

  2. J. R. Bolton, N. Mataga and G. McLendon (eds.)(1991) Adv. Chem. Ser., 228, assorted articles.

    Google Scholar 

  3. Newton, M. D. and Sutin, N. (1984) Ann. Rev. Phys. Chem., 35, 437.

    CrossRef  CAS  Google Scholar 

  4. Sutin, N. (1983) Prog. Inorg. Chem., 30, 441.

    CrossRef  CAS  Google Scholar 

  5. Newton, M. D. (1991) Chem. Rev., 91, 767.

    CrossRef  CAS  Google Scholar 

  6. Cannon, R. D. (1980) Electron Transfer Reactions, Butterworths, London.

    Google Scholar 

  7. Eberson, L. (1987) Electron Transfer Reactions in Organic Chemistry, Springer, New York.

    CrossRef  Google Scholar 

  8. Fox, M. A. and Chanon, M. (eds.) (1988) Photoinduced Electron Transfer, Elsevier, New York. 4 vols.

    Google Scholar 

  9. Twigg, M. V. (ed.) (1991) Mechanisms ofInorganic and Organometallic Reactions, vol. 7, Chaps. 1 and 2, and earlier volumes.

    Google Scholar 

  10. Brunschwig, B. S., Logan, J., Newton, M. D. and Sutin, N. (1980) J. Am. Chem. Soc., 102, 5798.

    CrossRef  CAS  Google Scholar 

  11. Sutin, N. (1988) Pure & Appl. Chem., 60, 1817.

    CrossRef  CAS  Google Scholar 

  12. King, G. and Warshel, A. (1990) J. Chem. Phys., 93, 8682.

    CrossRef  CAS  Google Scholar 

  13. Marcus, R. A. (1960) Disc. Faraday Soc., 29, 21.

    CrossRef  Google Scholar 

  14. Marcus, R. A. (1956) J. Chem. Phys., 24, 966.

    CrossRef  CAS  Google Scholar 

  15. Marcus, R. A. (1965) J. Chem. Phys., 43, 679.

    CrossRef  CAS  Google Scholar 

  16. Kuharski, R. A., Bader, J. S., Chandler, D., Sprik, M., Klein, M. S. and Impey, R. W. (1988) J. Chem. Phys., 89, 3248; Hwang, J.-K. and Warshel, A. (1987) J. Am. Chem. Soc., 109, 715.

    CrossRef  CAS  Google Scholar 

  17. Landau, L. (1932) Phys. Z. Sowjetunion, 1, 88; 2, 46; Zener, C. (1932) Proc. Roy. Soc., 137 A, 696; 140A, 660. See also ref90 below.

    Google Scholar 

  18. Marcus, R. A. (1964) Ann. Rev. Phys. Chem., 16, 155.

    CrossRef  Google Scholar 

  19. Marcus, R. A. (1981) Int. J. Chem. Kinetics, 13, 865.

    CrossRef  CAS  Google Scholar 

  20. Since the value of ki will differ before and after the ET, it is often approximated as a particular average of the value for the reactants’ ith mode, kir and the value for the products’ ith mode, kip: ki= 2ki r ki p/(ki r + ki p ). This step has been called “symmetrizing” the PES. Calculations have been made showing that this approximation. Marcus, R. A. (1987) in A. E. Hansen, J. Avery and J. P. Dahl (eds), Understanding Molecular Properties, Reidel, Boston, p. 229.

    Google Scholar 

  21. Marcus, R. A. (1965) J. Chem. Phys., 43, 58.

    CrossRef  CAS  Google Scholar 

  22. Marcus, R. A. (1965) J. Chem. Phys., 43, 3477, Appendix I.

    CrossRef  CAS  Google Scholar 

  23. Marcus, R. A. (1965) J. Chem. Phys., 43, 1261.

    CrossRef  CAS  Google Scholar 

  24. Cannon, R. D. (1977) Chem. Phys. Lett., 49, 299.

    CrossRef  CAS  Google Scholar 

  25. Brunschwig, B. S., Ehrenson, S. and Sutin, N. (1986) J. Phys. Chem., 90, 3657.

    CrossRef  CAS  Google Scholar 

  26. Dogonadze, R. R. (1971) in Hush, N. S. (ed), Reactions of Molecules at Electrodes, Wiley, New York, Chap. 3, Eq. 201.

    Google Scholar 

  27. Surni, H. (1980) J. Phys. Soc. Jpn., 49, 1701; Surni, H. and Marcus, R. A. (1986) J. Chem. Phys., 84,4894.

    CrossRef  Google Scholar 

  28. Marcus, R. A. (1977) in P. A. Rock (ed.), Special Topics in Electrochemistry, Elsevier, New York, p. 161; Marcus, R. A. (1959) Can. J. Chem. 37, 155.

    Google Scholar 

  29. Levich, V. G. and Dogonadze, R. R. (1959) Dokl. Acad. Nauk SSSR, 124, 123; Dogonadze, R. R., Kuznetsov, A. M. and Vorotyntsev, M. A. (1972) Phys. Stat. Sol. B, 54,125,425; Levich, V. G. (1970) in Eyring, H. (ed.), Physical Chemistry, An Advanced Treatise, Academic, New York, Vol. 9, Chap. 12.

    Google Scholar 

  30. Marcus, R. A. (1963) J. Phys. Chem., 67, 853, 2889.

    CrossRef  CAS  Google Scholar 

  31. Marcus, R. A. (1965) J. Chem. Phys., 43, 2654; (1970) 52, 2803.

    CrossRef  CAS  Google Scholar 

  32. Wallace, W. L. and Bard, A. J. (1979) J. Phys. Chem., 83, 1350.

    CrossRef  CAS  Google Scholar 

  33. Kestner, N. R., Logan, J. and Jortner, J. (1974) J. Phys. Chem., 78, 2148; Ulstrup, J. and Jortner, J. (1975) J. Phys. Chem., 63, 4358; Efrirna, S. and Bixon, M. (1976) Chem. Phys., 13,447; Siders, P. and Marcus, R. A. (1981) J. Am. Chem. Soc. 103,741,748.

    CrossRef  CAS  Google Scholar 

  34. Marcus, R. A. and Siders, P. (1982) J. Phys. Chem., 86, 622.

    CrossRef  CAS  Google Scholar 

  35. Warshel, A. (1982) J. Phys. Chem., 86, 2218.

    CrossRef  CAS  Google Scholar 

  36. Marcus, R. A. (1984) J. Chem. Phys., 81, 4494.

    CrossRef  CAS  Google Scholar 

  37. Kober, E. M., Casper, J. V., Lumpkin, R. S. and Meyer, T. J. (1986) J. Phys. Chem. 90, 3722; Chen, P., Duesing, R., Graff, D. K. and Meyer, T. J. (1991) ibid. 95, 5850.

    CrossRef  CAS  Google Scholar 

  38. Engleman, R. and Jortner, J. (1970) Mol. Phys. 18, 145.

    CrossRef  Google Scholar 

  39. Liang, N., Miller, J. R. and Closs, G. L. (1990) J. Am. Chem. Soc. 112, 5353.

    CrossRef  CAS  Google Scholar 

  40. E.g., Landau, L. D. and Lifshitz (1958) Quantum Mechanics, Pergamon Press, New York, eq 51.6, and analogous arguments for the case where the slopes are of opposite sign in the tunneling region; Child, M. S. (1991) Semiclassical Mechanics With Molecular Application, Clarendon Press, New York, eq (5.120) with a=O there.

    Google Scholar 

  41. Li, T. T.-T. and Brubaker Jr., C. H. (1981) J. Organornet. Chem., 216, 223.

    CrossRef  CAS  Google Scholar 

  42. Powers, J. M. and Meyer, T. J. (1980) J. Am. Chem. Soc., 102, 1289; Callahan, R W. and Meyer, T. J. (1976) Chem. Phys. Lett., 39, 82.

    CrossRef  CAS  Google Scholar 

  43. Rehm, D. and Weller, A. (1970) Isr. J. Chem., 8, 259; Nagle, J. K., Dresick, W. J. and Meyer, T. J. (1975) J. Am. Chem. Soc., 97, 2909; Scandola, F. and Balzani, V. (1979) J. Am. Chem. Soc., 101, 6140.

    CAS  Google Scholar 

  44. Kikuchi, K., Takahashi, Y., Katagiri, T., Niwa, T. and Hoshi, M. (1991) Chem. Phys. Lett., 180,403; Kikuchi, K., Takahashi, Y., Hoshi, M., Niwa, T., Katagiri, T. and Miyashi, T. (1991) J. Phys. Chem. 95, 2378.

    Google Scholar 

  45. Miller, J. R, Closs, G. L. and Calcaterra, L. T. (1984), J. Am. Chem. Soc., 106, 3047.

    CrossRef  CAS  Google Scholar 

  46. Gould, I. R, Mueller, L. J. and Farid, S. (1991) Z. Phys. Chem., 170, 143; Gould, I. R, Ege, D., Moser, J. E. and Farid, S. (1990) J. Am. Chem. Soc., 112,4290, and references cited therein.

    CAS  Google Scholar 

  47. Asahi, T., Mataga, N., Takahashi, Y., Miyashi, T. (1990) Chem. Phys. Lett., 171, 309, and references cited therein.

    CrossRef  CAS  Google Scholar 

  48. Gaines, G. L., O’Neil, N. P., Svec, W. A., Niemczyk, M. P. and Wasielewski, M. R (1990) J. Am. Chem. Soc., 13, 719, and references cited therein.

    Google Scholar 

  49. Fox, L. S., Kozik, M., Winkler, J. R and Gray, H. B. (1990) Science 247, 1069.

    CrossRef  CAS  Google Scholar 

  50. Penner, R M., Heben, M. J., Longin, T. L. and Lewis, N. (1990) Science, 250, 1118; private communication.

    CrossRef  CAS  Google Scholar 

  51. Chidsey, G. E. (1991) Science, 251, 919.

    CrossRef  CAS  Google Scholar 

  52. Saveant, J. M. and Tessier, D. (1982) Faraday Disc. Chem. Soc., 74, 57; Weaver, M. J. and Hupp, J. T. (1982) Am. Chem. Soc. Syrnp. Series, 198, 181.

    CrossRef  Google Scholar 

  53. Iwasita, T., Schrnickler, W., and Schultze, J. W. (1985) Ber. Bunsenges. Phys. Chem., 89, 138.

    CrossRef  CAS  Google Scholar 

  54. Isied, S. S., Vassilian, A., Magnuson, R H. and Schwarz, H. A. (1985) J. Am. Chem. Soc., 107, 7432; Vassilian, A., Wishart, J. F., van Hernelyrck, B, Schwarz, H. and Isied, S. S. (1990) J. Am. Chem. Soc., 112, 7278..

    CrossRef  CAS  Google Scholar 

  55. Closs, G. L., Calcaterra, L. T., Green, N. J., Penfield, K. W. and Miller, J. R (1986) J. Phys. Chem., 90, 3673.

    CrossRef  CAS  Google Scholar 

  56. Penfield, K. W., Miller, J. R, Paddon-Row, M. N., Cotsaris, E., Oliver, A. M. and Hush, N. S. (1987) J. Am. Chem. Soc., 109, 5061.

    CrossRef  CAS  Google Scholar 

  57. Wasielewski, M. R, Niernczyk, M. P., Johnson, D. G., Svec, W. A. and Minsek, D. W. (1989) Tetrahedron, 45, 4785.

    CrossRef  CAS  Google Scholar 

  58. Beitz, J. V. and Miller, J. R (1979) J. Chem. Phys., 71, 4579.

    CrossRef  CAS  Google Scholar 

  59. Isied, S. S. (1984) Prog. Inorg. Chem., 32, 443.

    CrossRef  CAS  Google Scholar 

  60. Bowler, B. E., Raphael A. L. and Gray, H. B. (1990) Prog. Inorg. Chem., 38, 259.

    CrossRef  CAS  Google Scholar 

  61. Sykes, A. G. (1991) Adv. Inorg. Chem. 36, 377.

    CrossRef  CAS  Google Scholar 

  62. Hoffmann, B. M., Natan, M. J., Nocek, J. M. and Wallin, S. A. (1991) Struct. Bond., 75, 85.

    CrossRef  Google Scholar 

  63. Isied, S. S., Vassilian, A., Wishart, J. F., Creutz, C., Schwarz, H. A. and Sutin, N. (1988) J. Am. Chem. Soc., 110, 635.

    CrossRef  CAS  Google Scholar 

  64. Hush, N. S. (1967) Prog. Inorg. Chem., 8, 391.

    CrossRef  CAS  Google Scholar 

  65. Hopfield, J. J. (1977) Biophys. J., 18, 311.

    CrossRef  CAS  Google Scholar 

  66. Creutz, C. (1983) Prog. Inorg. Chem., 30, 1.

    CrossRef  CAS  Google Scholar 

  67. Stein, C. A., Lewis, N. A. and Seitz, G. J. (1982) J. Am. Chem. Soc., 104, 2596.

    CrossRef  CAS  Google Scholar 

  68. McConnell, H. M. (1961) J. Chem. Phys., 35, 508.

    CrossRef  CAS  Google Scholar 

  69. Larsson, S. (1981) J. Am. Chem. Soc., 103, 4034.

    CrossRef  CAS  Google Scholar 

  70. Siddarth, P. and Marcus, R. A. (1990) J. Phys. Chem., 94, 2985.

    CrossRef  CAS  Google Scholar 

  71. Axup, A. W., Albin, M., Mayo, S. J., Crutchley, R. J. and Gray, H. B. (1988) J. Am. Chem. Soc., 110, 435.

    CrossRef  CAS  Google Scholar 

  72. Siddarth, P. and Marcus, R. A. (1990) J. Phys. Chem., 94, 8430.

    CrossRef  CAS  Google Scholar 

  73. For a recent review, see Kartha, S. Das, R. and Norris, J. R. (1991), in H. Sigel (ed.), Metal Ions in Biological Systems, 27, 323.

    Google Scholar 

  74. Breton, J. and Vermeglio, A. (eds.) (1988) The PhotosyntheticBacterial Reaction Center—Structure and Dynamics, NATO ASI Series A: Life Sciences 149, Plenum, New York.

    Google Scholar 

  75. Michel-Beyerle, M. E. (ed.) (1985) Antennas and Rection Centers of Photosynthetic Bacteria, Springer, Berlin

    Google Scholar 

  76. Holzapfel, W., Finkele, U., Kaiser, W., Oesterhelt, D., Scheer, H., Stilz, H. U. and Zinth, W. (1990) Proc Natl. Acad. Sci. U.S.A., 87, 5168.

    CrossRef  CAS  Google Scholar 

  77. Kirmaier, C. and Holten, D. (1990) Proc. Natl. Acad. Sci. U.S.A., 87, 3552.

    CrossRef  CAS  Google Scholar 

  78. Plato, M., Mobius, K., Michel-Beyerle, M. E., Hixon, M. and Jortner, J. (1988) J. Am. Chem. Soc., 110, 7279.

    CrossRef  CAS  Google Scholar 

  79. Marcus, R. A. (1988) Isr. J. Chem. 28, 205.

    CAS  Google Scholar 

  80. Marcus, R. A. (1968) J. Phys. Chem. 72, 891.

    CrossRef  CAS  Google Scholar 

  81. Polik, W. F., Guyer, D. R. and Moore, C. B. (1990) J. Chem. Phys. 92, 3453.

    CrossRef  CAS  Google Scholar 

  82. Wigner, E. (1938) Trans. Faraday Soc. 34, 29.

    CrossRef  CAS  Google Scholar 

  83. Bergsma, J. P., Gertner, B. J., Wilson, K. R. and Hynes, J. T. (1987) J. Chem. Phys. 86, 1356.

    CrossRef  CAS  Google Scholar 

  84. Surni, H. and Marcus, R. A. (1986) J. Chem. Phys. 84, 4894; Nadler, W. and Marcus, R. A. (1987) ibid. 86, 3906.

    CrossRef  Google Scholar 

  85. Susman, L. D. (1980) Chem. Phys. 49, 295; Helman, A. B. (1982) ibid. 65,271; Calef, D. F. and Wolynes, P. G. (1983) J. Phys. Chem. 87, 3387; van der Zwan, G. and Hynes, J. J. (1985) ibid. 89, 4181.

    CrossRef  Google Scholar 

  86. Saveant, J.-M. (1987) J. Am. Chem. Soc. 109, 6788.

    CrossRef  CAS  Google Scholar 

  87. Marcus, R. A. (1990) J. Phys. Chem. 94, 4152, 7742; Marcus, R. A. (1991) J. Phys. Chem. 95, 2010; Geblewicz, G. and Schiffrin, D. J. (1988) J. Electroanal. Chem. 244,27.

    CrossRef  CAS  Google Scholar 

  88. Leidner, C. R. and Murray, R. W. (1984) J. Am. Chem. Soc. 1051606.

    Google Scholar 

  89. Leidner, C. R. and Murray, R. W. (1985) J. Am. Chem. Soc. 107, 551; Jernigan, J. C. and Murray, R. W. (1990) ibid., 112, 1034.

    CrossRef  CAS  Google Scholar 

  90. Kauzmann, W. (1957) Quantum Chemistry, Academic Press, New York, p. 539.

    Google Scholar 

  91. Bellman, R. (1960) Introduction to Matrix Analysis, McGraw Hill, New York, p. 96.

    Google Scholar 

  92. Marcus, R. A. (1989) J. Phys. Chem. 93, 3078.

    CrossRef  CAS  Google Scholar 

  93. Moser, C. C., Keske, J. M., Warncke, K., Farid, R. S. and Dutton, P. L. (1992) Nature 355, 796.

    CrossRef  CAS  Google Scholar 

  94. Johnson, M. D., Miller, J. R., Green, N. S. and Closs, G. L. (1989) J. Am. Chem. Soc. 111, 3751.

    CrossRef  Google Scholar 

  95. Siddarth, P. and Marcus, R. A. (1992) J. Phys. Chem. 96, 000.

    CrossRef  CAS  Google Scholar 

  96. McConnell, H. M. (1960) J. Chem. Phys. 33, 115.

    CrossRef  CAS  Google Scholar 

  97. An alternative discussion of the solvent reorganization in terms of charges and potentials instead of in terms of electric fields and polarization vectors is given in the first citation of ref. 28.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1992 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Marcus, R.A., Siddarth, P. (1992). Theory of Electron Transfer Reactions and Comparison with Experiments. In: Kochanski, E. (eds) Photoprocesses in Transition Metal Complexes, Biosystems and Other Molecules. Experiment and Theory. NATO ASI Series, vol 376. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2698-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2698-4_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5195-8

  • Online ISBN: 978-94-011-2698-4

  • eBook Packages: Springer Book Archive