Journal of Solid State Electrochemistry

, Volume 14, Issue 5, pp 705–739 | Cite as

The theory of electron transfer

Review Paper

Abstract

This article provides an overview of the theory of electron transfer. Emphasis is placed on the history of key ideas and on the definition of difficult terms. Among the topics considered are the quantum formulation of electron transfer, the role of thermal fluctuations, the structures of transition states, and the physical models of rate constants. The special case of electron transfer from a metal electrode to a molecule in solution is described in detail.

Keywords

Electron transfer reactions Quantum theory Perturbation theory Marcus theory Rate constants Fluctuations Transition states Reorganization energy Inverted region Tafel slopes 

References

  1. 1.
    Thomson JJ (1897) On cathode rays. Phil Mag 44:293–316Google Scholar
  2. 2.
    Bohr NHD (1913) On the constitution of atoms and molecules, part I. Phil Mag 26:1–24Google Scholar
  3. 3.
    Schrödinger E (1926) Quantisierung als Eigenwertproblem. Ann Phys (Leipzig) 79:361–376Google Scholar
  4. 4.
    Heisenberg W (1927) Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z Physik 43:172–198CrossRefGoogle Scholar
  5. 5.
    Born M (1926) Zur Quantenmechanik der Stoßvorgänge. Z Physik 37:863–867CrossRefGoogle Scholar
  6. 6.
    Born M (1954) Die statistiche Deutung der Quantenmechanik (Nobel lecture delivered on 11 December 1954 at Stockholm). English translation: The Statistical Interpretation of Quantum Mechanics, in Nobel Lectures: Physics 1942–1962 (Nobel Foundation) Amsterdam–New York (1964)Google Scholar
  7. 7.
    Hund FH (1927) Zur Deutung der Molekelspektren I. Z Physik 40:742–764CrossRefGoogle Scholar
  8. 8.
    Hund FH (1927) Zur Deutung der Molekelspektren II. Z Physik 42:93–120CrossRefGoogle Scholar
  9. 9.
    Hund FH (1927) Zur Deutung der Molekelspektren III. Z Physik 43:805–826CrossRefGoogle Scholar
  10. 10.
    Fowler RH, Nordheim LW (1928) Electron emission in intense electric fields. Proc R Soc (Lond) 119:173–181CrossRefGoogle Scholar
  11. 11.
    Wood RW (1897) A new form of cathode discharge, and the production of X-rays, together with some notes on diffraction. Phys Rev (Ser I) 5:1–10CrossRefGoogle Scholar
  12. 12.
    Gurney RW, Condon EU (1928) Wave mechanics and radioactive disintegration. Nature 122:439–439CrossRefGoogle Scholar
  13. 13.
    Gurney RW, Condon EU (1929) Quantum mechanics and radioactive disintegration. Phys Rev 33:127–140CrossRefGoogle Scholar
  14. 14.
    Franck J, Dymond EG (1926) Elementary processes of photochemical reactions. Trans Faraday Soc 21:536–542CrossRefGoogle Scholar
  15. 15.
    Condon EU (1928) Nuclear motions associated with electron transitions in diatomic molecules. Phys Rev 32:858–872CrossRefGoogle Scholar
  16. 16.
    Dirac PAM (1927) The physical interpretation of the quantum dynamics. Proc R Soc (Lond) A113:621–641CrossRefGoogle Scholar
  17. 17.
    Gurney RW (1931) The quantum mechanics of electrolysis. Proc R Soc (Lond) A134:137–154CrossRefGoogle Scholar
  18. 18.
    Maxwell JC (1878) Tait’s thermodynamics. Nature 17:257–259, Reprinted in The Scientific Papers of James Clerk Maxwell. Dover, NY (1952)CrossRefGoogle Scholar
  19. 19.
    Waterston JJ (1892) On the physics of media that are composed of free and perfectly elastic molecules in a state of motion. Phil Trans Roy Soc (Lond) A183:1–79, Published posthumously with notes by Lord RayleighCrossRefGoogle Scholar
  20. 20.
    Keenan JH (1951) Availability and irreversibility in thermodynamics. Brit J Appl Phys 2:183–192CrossRefGoogle Scholar
  21. 21.
    Rant Z (1956) Exergie, ein neues Wort für technische Arbeitsfähigkeit. Forsch Geb Ingenieurwesens 22:36–37Google Scholar
  22. 22.
    Fletcher S (2007) A non-Marcus model for electrostatic fluctuations in long range electron transfer. J Solid State Electrochem 11:965–969CrossRefGoogle Scholar
  23. 23.
    Marcelin R (1915) Contribution à l’Étude de la Cinétique Physico-Chimique. Ann Phys (Paris) 3:120–231Google Scholar
  24. 24.
    Eyring H (1935) The activated complex in chemical reactions. J Chem Phys 3:107–115CrossRefGoogle Scholar
  25. 25.
    Evans MG, Polanyi M (1935) Some applications of the transition state method to the calculation of reaction velocities, especially in solution. Trans Faraday Soc 31:875–894CrossRefGoogle Scholar
  26. 26.
    Wigner E (1938) The transition state method. Trans Faraday Soc 34:29–41CrossRefGoogle Scholar
  27. 27.
    Debye P, Hückel E (1923) Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Physik Z 24:185–206Google Scholar
  28. 28.
    Debye P, Hückel E (1923) Zur Theorie der Elektrolyte. II. Das Grenzgesetz für die elektrische Leitfähigkeit. Physik Z 24:305–325Google Scholar
  29. 29.
    Tissandier MD, Cowen KA, Feng WY, Gundlach EG, Cohen MH, Earhart AD, Coe JV, Tuttle TR (1998) The proton’s absolute aqueous enthalpy and Gibbs free energy of solvation from cluster-ion solvation data. J Phys Chem A102:7787–7794Google Scholar
  30. 30.
    Marcus Y (1994) A simple empirical model describing the thermodynamics of hydration of ions of widely varying charges, sizes, and shapes. Biophys Chem 51:111–127CrossRefGoogle Scholar
  31. 31.
    Schmid R, Miah AM, Sapunov VN (2000) A new table of the thermodynamic quantities of ionic hydration: values and some applications (enthalpy–entropy compensation and Born radii). Phys Chem Chem Phys 2:97–102CrossRefGoogle Scholar
  32. 32.
    Wagman DD, Evans WH, Parker VB, Schumm RH, Halow I, Bailey SM, Churney KL, Nuttall RL (1982) The NBS tables of chemical and thermodynamic properties. Selected values for inorganic and C1 and C2 organic substances in SI units. J Phys Chem Ref Data (JPCRD) 11(Suppl No. 2):1–392Google Scholar
  33. 33.
    Randles JEB (1952) Kinetics of rapid electrode reactions. Part 2. Rate constants and activation energies of electrode reactions. Trans Faraday Soc 48:828–832CrossRefGoogle Scholar
  34. 34.
    Werner A (1913) On the constitution and configuration of higher-order compounds. Nobel Lecture, 11 December 1913. Reprinted in Nobel Lectures, Chemistry 1901–1921, Elsevier, Amsterdam, 1966Google Scholar
  35. 35.
    Lewis WB, Coryell CD, Irvine JW (1949) The electron transfer (exchange) between cobaltous and cobaltic amine complexes. J Chem Soc (Suppl Issue) 2:S386–S392Google Scholar
  36. 36.
    Taube H, Myers H, Rich RL (1953) Observations on the mechanism of electron transfer in solution. J Am Chem Soc 75:4118–4119CrossRefGoogle Scholar
  37. 37.
    Taube H, Myers H (1954) Evidence for a bridged activated complex for electron transfer reactions. J Am Chem Soc 76:2103–2111CrossRefGoogle Scholar
  38. 38.
    Taube H (1983) Electron transfer between metal complexes—retrospective. Nobel Lecture, 8 December 1983. Reprinted in Nobel Lectures, Chemistry 1981–1990, World Scientific Publishing Co., Singapore, 1992Google Scholar
  39. 39.
    Ball DL, King EL (1958) The exchange reactions of chromium(II) ion and certain chromium(III) complex ions. J Am Chem Soc 80:1091–1094CrossRefGoogle Scholar
  40. 40.
    Candlin JP, Halpern J (1965) Kinetics of the reduction of halopentaamminecobalt(III) complexes by chromium(II). Inorg Chem 4:766–767CrossRefGoogle Scholar
  41. 41.
    Przystas TJ, Sutin N (1973) Kinetic studies of anion-assisted outer-sphere electron transfer reactions. J Am Chem Soc 95:5545–5555CrossRefGoogle Scholar
  42. 42.
    Chou M, Creutz C, Sutin N (1977) Rate constants and activation parameters for outer-sphere electron-transfer reactions and comparisons with the predictions of Marcus theory. J Am Chem Soc 99:5615–5623CrossRefGoogle Scholar
  43. 43.
    Creutz C, Taube H (1969) A direct approach to measuring the Franck–Condon barrier to electron transfer between metal ions. J Am Chem Soc 91:3988–3989CrossRefGoogle Scholar
  44. 44.
    Creutz C, Taube H (1973) Binuclear complexes of ruthenium ammines. J Am Chem Soc 95:1086–1094CrossRefGoogle Scholar
  45. 45.
    Day P, Hush NS, Clark RJH (2008) Mixed valence: origins and developments. Phil Trans Roy Soc A366:5–14Google Scholar
  46. 46.
    Biner M, Buergi H-B, Ludi A, Roehr C (1992) Crystal and molecular structures of [Ru(bpy)3][PF6]3 and [Ru(bpy)3][PF6]2 at 105 K. J Am Chem Soc 114:5197–5203CrossRefGoogle Scholar
  47. 47.
    Young RC, Keene FR, Meyer TJ (1977) Measurement of rates of electron transfer between Ru(bpy)33+ and Fe(phen)32+ and between Ru(phen)33+ and Ru(bpy)32+ by differential excitation flash photolysis. J Am Chem Soc 99:2468–2473CrossRefGoogle Scholar
  48. 48.
    George P, Hanania GIH, Irvine DH (1959) Potentiometric studies of some dipyridyl complexes. J Chem Soc 508:2548–2554CrossRefGoogle Scholar
  49. 49.
    Yee EL, Cave RJ, Guyer KL, Tyma PD, Weaver MJ (1979) A survey of ligand effects upon the reaction entropies of some transition metal redox couples. J Am Chem Soc 101:1131–1137CrossRefGoogle Scholar
  50. 50.
    Bruhn H, Nigam S, Holzwarth JF (1982) Catalytic influence of the environment on outer-sphere electron-transfer reactions in aqueous solutions. Faraday Discuss Chem Soc 74:129–140CrossRefGoogle Scholar
  51. 51.
    Evans MG (1938) Thermodynamical treatment of transition state. Trans Faraday Soc 34:49–57CrossRefGoogle Scholar
  52. 52.
    Marcus RA (1956) On the theory of oxidation reduction reactions involving electron transfer. I. J Chem Phys 24:966–978CrossRefGoogle Scholar
  53. 53.
    Marcus RA (1956) Electrostatic free energy and other properties of states having nonequilibrium polarization (I). J Chem Phys 24:979–989CrossRefGoogle Scholar
  54. 54.
    Marcus RA (1992) Electron transfer reactions in chemistry: theory and experiment. Nobel Lecture, 8 December 1992. Reprinted in Nobel Lectures, Chemistry 1991–1995, World Scientific Publishing Co., Singapore (1997)Google Scholar
  55. 55.
    Marcus RA (1994) Free energy of non-equilibrium polarization systems. 4. A formalism based on the non-equilibrium dielectric displacement. J Phys Chem 98:7170–7174CrossRefGoogle Scholar
  56. 56.
    George P, Griffith JS (1959) In: Boyer PD, Lardy H, Myrbäck N (eds) The enzymes, vol 1. New York, AcademicGoogle Scholar
  57. 57.
    Kubo R, Toyozawa Y (1955) Application of the method of generating function to radiative and non-radiative transitions of a trapped electron in a crystal. Prog Theor Phys 13:160–182CrossRefGoogle Scholar
  58. 58.
    Fletcher S (2008) The new theory of electron transfer. Thermodynamic potential profiles in the inverted and superverted regions. J Solid State Electrochem 12:765–770CrossRefGoogle Scholar
  59. 59.
    Hoddenbagh JMA, Macartney DH (1990) Kinetics of electron-transfer reactions involving the Ru(CN)64–/3– couple in aqueous media. Inorg Chem 29:245–251CrossRefGoogle Scholar
  60. 60.
    Meyer TJ, Taube H (1968) Electron-transfer reactions of ruthenium ammines. Inorg Chem 7:2369–2379CrossRefGoogle Scholar
  61. 61.
    Bernhard P, Helm L, Ludi A, Merbach AE (1985) Direct measurement of a prominent outer-sphere electron self-exchange: kinetic parameters for the hexaaquaruthenium(II)/(III) couple determined by oxygen-17 and ruthenium-99 NMR. J Am Chem Soc 107:312–317CrossRefGoogle Scholar
  62. 62.
    Brunschwig BS, Creutz C, Macartney DH, Sham T-K, Sutin N (1982) The role of inner-sphere configuration changes in electron exchange reactions of metal complexes. Disc Faraday Soc 74:113–127CrossRefGoogle Scholar
  63. 63.
    Jolley WH, Stranks DR, Swaddle TW (1990) Pressure effect on the kinetics of the hexaaquairon(II/III) self-exchange reaction in aqueous perchloric acid. Inorg Chem 29:1948–1951CrossRefGoogle Scholar
  64. 64.
    Habib HS, Hunt JP (1966) Electron-transfer reactions between aqueous cobaltous and cobaltic ions. J Am Chem Soc 88:1668–1671CrossRefGoogle Scholar
  65. 65.
    Nielson RM, McManis GE, Safford LK, Weaver MJ (1989) Solvent and electrolyte effects on the kinetics of ferrocenium–ferrocene self-exchange. A re-evaluation. J Phys Chem 93:2152–2157CrossRefGoogle Scholar
  66. 66.
    Kirchner K, Dang SQ, Stebler M, Dodgen HW, Wherland S, Hunt JP (1989) Temperature, pressure, and electrolyte dependence of the ferrocene/ferrocenium electron self-exchange in acetonitrile-d3. Inorg Chem 28:3604–3606CrossRefGoogle Scholar
  67. 67.
    Marcus RA (1960) Exchange reactions and electron transfer reactions including isotopic exchange. Theory of oxidation–reduction reactions involving electron transfer. Part 4—a statistical–mechanical basis for treating contributions from solvent, ligands, and inert salt. Disc Faraday Soc 29:21–31CrossRefGoogle Scholar
  68. 68.
    Kadhum AAH, Salmon GA (1982) General discussion. Faraday Disc Chem Soc Electron Proton Transfer R Soc Chem (Lond) 74:191–193Google Scholar
  69. 69.
    Miller JR, Calcaterra LT, Closs GL (1984) Intramolecular long-distance electron transfer in radical anions. The effects of free energy and solvent on the reaction rates. J Am Chem Soc 106:3047–3049CrossRefGoogle Scholar
  70. 70.
    Kadhum AAH, Salmon GA (1986) Reactivity of solvated electrons in tetrahydrofuran. J Chem Soc Faraday Trans I 82:2521–2530CrossRefGoogle Scholar
  71. 71.
    Robertson HP (1929) The uncertainty principle. Phys Rev 34:163–164CrossRefGoogle Scholar
  72. 72.
    Dirac PAM (1930) The principles of quantum mechanics. Clarendon, OxfordGoogle Scholar
  73. 73.
    Slater JC (1930) Atomic shielding constants. Phys Rev 36:57–64CrossRefGoogle Scholar
  74. 74.
    Gütlich P, Garcia Y, Goodwin HA (2000) Spin crossover phenomena in Fe(II) complexes. Chem Soc Rev 29:419–427CrossRefGoogle Scholar
  75. 75.
    Doine H, Swaddle TW (1988) Pressure effects on the rate of electron transfer between tris(1, 10-phenanthroline)iron(II) and -(III) in aqueous solution and in acetonitrile. Can J Chem 66:2763–2767CrossRefGoogle Scholar
  76. 76.
    Warren RML, Lappin AG, Mehta BD, Neumann HM (1990) Electron-transfer reactions of optically active tris(phenanthroline) cobalt (3+/2+) and derivatives. Inorg Chem 29:4185–4189CrossRefGoogle Scholar
  77. 77.
    Orear J, Rosenfeld AH, Schluter RA (1950) Nuclear physics, a course given by Enrico Fermi at the University of Chicago. University of Chicago Press, ChicagoGoogle Scholar
  78. 78.
    Dirac PAM (1927) The quantum theory of the emission and absorption of radiation. Proc R Soc (Lond) A114:243–265CrossRefGoogle Scholar
  79. 79.
    Boltzmann L (1909) In: Hasenöhrl F (ed) Wissenschaftliche Abhandlungen, vol I–III. Barth, Leipzig, re-issued Chelsea Publishing Co., New York, 1968Google Scholar
  80. 80.
    Levich VG, Dogonadze RR (1959) The theory of non-radiative electron transitions between ions in solution. Dokl Akad Nauk 124:123–126Google Scholar
  81. 81.
    Dogonadze RR, Chizmadzhev YA (1962) Kinetics of some electrochemical oxidation–reduction reactions on metals (in Russian). Dokl Akad Nauk 145:848–851Google Scholar
  82. 82.
    Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284–304CrossRefGoogle Scholar
  83. 83.
    Butler JAV (1924) Studies in heterogeneous equilibria. Part II—the kinetic interpretation of the Nernst theory of electromotive force. Trans Faraday Soc 19:729–733CrossRefGoogle Scholar
  84. 84.
    Erdey-Grúz T, Volmer M (1930) Zur Theorie der Wasserstoffüberspannung. Z Physik Chem A150:203–213Google Scholar
  85. 85.
    Parsons R (1951) General equations for the kinetics of electrode processes. Trans Faraday Soc 47:1332–1344CrossRefGoogle Scholar
  86. 86.
    Tafel J (1905) Über die Polarisation bei kathodischer Wasserstoffentwicklung. Z Physik Chem 50:641–712Google Scholar
  87. 87.
    Fletcher S (2009) Tafel slopes from first principles. J Solid State Electrochem 13:537–549CrossRefGoogle Scholar
  88. 88.
    Zhang J, Kuznetsov AM, Medvedev IG, Chi Q, Albrecht T, Jensen PS, Ulstrup J (2008) Single-molecule electron transfer in electrochemical environments. Chem Rev 108:2737–2791CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of ChemistryLoughborough UniversityLoughboroughUK

Personalised recommendations