The theory of electron transfer
Review Paper
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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 slopesReferences
- 1.Thomson JJ (1897) On cathode rays. Phil Mag 44:293–316Google Scholar
- 2.Bohr NHD (1913) On the constitution of atoms and molecules, part I. Phil Mag 26:1–24Google Scholar
- 3.Schrödinger E (1926) Quantisierung als Eigenwertproblem. Ann Phys (Leipzig) 79:361–376Google Scholar
- 4.Heisenberg W (1927) Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z Physik 43:172–198CrossRefGoogle Scholar
- 5.Born M (1926) Zur Quantenmechanik der Stoßvorgänge. Z Physik 37:863–867CrossRefGoogle Scholar
- 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.Hund FH (1927) Zur Deutung der Molekelspektren I. Z Physik 40:742–764CrossRefGoogle Scholar
- 8.Hund FH (1927) Zur Deutung der Molekelspektren II. Z Physik 42:93–120CrossRefGoogle Scholar
- 9.Hund FH (1927) Zur Deutung der Molekelspektren III. Z Physik 43:805–826CrossRefGoogle Scholar
- 10.Fowler RH, Nordheim LW (1928) Electron emission in intense electric fields. Proc R Soc (Lond) 119:173–181CrossRefGoogle Scholar
- 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.Gurney RW, Condon EU (1928) Wave mechanics and radioactive disintegration. Nature 122:439–439CrossRefGoogle Scholar
- 13.Gurney RW, Condon EU (1929) Quantum mechanics and radioactive disintegration. Phys Rev 33:127–140CrossRefGoogle Scholar
- 14.Franck J, Dymond EG (1926) Elementary processes of photochemical reactions. Trans Faraday Soc 21:536–542CrossRefGoogle Scholar
- 15.Condon EU (1928) Nuclear motions associated with electron transitions in diatomic molecules. Phys Rev 32:858–872CrossRefGoogle Scholar
- 16.Dirac PAM (1927) The physical interpretation of the quantum dynamics. Proc R Soc (Lond) A113:621–641CrossRefGoogle Scholar
- 17.Gurney RW (1931) The quantum mechanics of electrolysis. Proc R Soc (Lond) A134:137–154CrossRefGoogle Scholar
- 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.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.Keenan JH (1951) Availability and irreversibility in thermodynamics. Brit J Appl Phys 2:183–192CrossRefGoogle Scholar
- 21.Rant Z (1956) Exergie, ein neues Wort für technische Arbeitsfähigkeit. Forsch Geb Ingenieurwesens 22:36–37Google Scholar
- 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.Marcelin R (1915) Contribution à l’Étude de la Cinétique Physico-Chimique. Ann Phys (Paris) 3:120–231Google Scholar
- 24.Eyring H (1935) The activated complex in chemical reactions. J Chem Phys 3:107–115CrossRefGoogle Scholar
- 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.Wigner E (1938) The transition state method. Trans Faraday Soc 34:29–41CrossRefGoogle Scholar
- 27.Debye P, Hückel E (1923) Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Physik Z 24:185–206Google Scholar
- 28.Debye P, Hückel E (1923) Zur Theorie der Elektrolyte. II. Das Grenzgesetz für die elektrische Leitfähigkeit. Physik Z 24:305–325Google Scholar
- 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.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.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.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.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.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.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.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.Taube H, Myers H (1954) Evidence for a bridged activated complex for electron transfer reactions. J Am Chem Soc 76:2103–2111CrossRefGoogle Scholar
- 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.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.Candlin JP, Halpern J (1965) Kinetics of the reduction of halopentaamminecobalt(III) complexes by chromium(II). Inorg Chem 4:766–767CrossRefGoogle Scholar
- 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.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.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.Creutz C, Taube H (1973) Binuclear complexes of ruthenium ammines. J Am Chem Soc 95:1086–1094CrossRefGoogle Scholar
- 45.Day P, Hush NS, Clark RJH (2008) Mixed valence: origins and developments. Phil Trans Roy Soc A366:5–14Google Scholar
- 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.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.George P, Hanania GIH, Irvine DH (1959) Potentiometric studies of some dipyridyl complexes. J Chem Soc 508:2548–2554CrossRefGoogle Scholar
- 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.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.Evans MG (1938) Thermodynamical treatment of transition state. Trans Faraday Soc 34:49–57CrossRefGoogle Scholar
- 52.Marcus RA (1956) On the theory of oxidation reduction reactions involving electron transfer. I. J Chem Phys 24:966–978CrossRefGoogle Scholar
- 53.Marcus RA (1956) Electrostatic free energy and other properties of states having nonequilibrium polarization (I). J Chem Phys 24:979–989CrossRefGoogle Scholar
- 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.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.George P, Griffith JS (1959) In: Boyer PD, Lardy H, Myrbäck N (eds) The enzymes, vol 1. New York, AcademicGoogle Scholar
- 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.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.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.Meyer TJ, Taube H (1968) Electron-transfer reactions of ruthenium ammines. Inorg Chem 7:2369–2379CrossRefGoogle Scholar
- 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.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.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.Habib HS, Hunt JP (1966) Electron-transfer reactions between aqueous cobaltous and cobaltic ions. J Am Chem Soc 88:1668–1671CrossRefGoogle Scholar
- 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.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.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.Kadhum AAH, Salmon GA (1982) General discussion. Faraday Disc Chem Soc Electron Proton Transfer R Soc Chem (Lond) 74:191–193Google Scholar
- 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.Kadhum AAH, Salmon GA (1986) Reactivity of solvated electrons in tetrahydrofuran. J Chem Soc Faraday Trans I 82:2521–2530CrossRefGoogle Scholar
- 71.Robertson HP (1929) The uncertainty principle. Phys Rev 34:163–164CrossRefGoogle Scholar
- 72.Dirac PAM (1930) The principles of quantum mechanics. Clarendon, OxfordGoogle Scholar
- 73.Slater JC (1930) Atomic shielding constants. Phys Rev 36:57–64CrossRefGoogle Scholar
- 74.Gütlich P, Garcia Y, Goodwin HA (2000) Spin crossover phenomena in Fe(II) complexes. Chem Soc Rev 29:419–427CrossRefGoogle Scholar
- 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.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.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.Dirac PAM (1927) The quantum theory of the emission and absorption of radiation. Proc R Soc (Lond) A114:243–265CrossRefGoogle Scholar
- 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.Levich VG, Dogonadze RR (1959) The theory of non-radiative electron transitions between ions in solution. Dokl Akad Nauk 124:123–126Google Scholar
- 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.Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284–304CrossRefGoogle Scholar
- 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.Erdey-Grúz T, Volmer M (1930) Zur Theorie der Wasserstoffüberspannung. Z Physik Chem A150:203–213Google Scholar
- 85.Parsons R (1951) General equations for the kinetics of electrode processes. Trans Faraday Soc 47:1332–1344CrossRefGoogle Scholar
- 86.Tafel J (1905) Über die Polarisation bei kathodischer Wasserstoffentwicklung. Z Physik Chem 50:641–712Google Scholar
- 87.Fletcher S (2009) Tafel slopes from first principles. J Solid State Electrochem 13:537–549CrossRefGoogle Scholar
- 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
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