Статья
2017

Adiabatic and non-adiabatic electrochemical electron transfer in terms of Green’s function theory


Wolfgang Schmickler Wolfgang Schmickler
Российский электрохимический журнал
https://doi.org/10.1134/S1023193517100123
Abstract / Full Text

We present a model Hamiltonian for electrochemical electron transfer, and use Green’s functions as the starting point for three different approaches to the calculation of rate constants: first order perturbation theory, which is equivalent to the Levich and Dogonadze theory, the calculation of adiabatic free energy surfaces, and propagation in time. We discuss the similarities and differences between these methods.

Author information
  • Institute of Theoretical Chemistry, Ulm University, D-89069, Ulm, Germany

    Wolfgang Schmickler

References
  1. Levich, V.G., Kinetics of reactions with charge transfer, in Physical Chemistry, an Advanced Treatise, Vol. Xb, Eyring, H., Henderson, D., and Jost, W., New York: Academic Press, Academic Press, 1970.
  2. Kuznetsov, A.M., Charge Transfer in Physics, Chemistry and Biology, Gordon & Breach, Reading, 1995.
  3. Schmickler, W., A Theory of adiabatic electron transfer reactions, J. Electroanal. Chem., 1986, vol. 204, p. 31.
  4. Anderson, P.W., Localized magnetic states in metals, Phys. Rev., 1961, vol. 124, p. 41.
  5. Newns, D.M., Self-consistent model of hydrogen chemisorption, Phys. Rev., 1969, vol. 178, p. 1123.
  6. Marcus, R.A., On the theory of oxidation-reduction reactions involving electron transfer, J. Chem. Phys., 1956, vol. 24, p. 966.
  7. Schmickler, W., A unified model for electrochemical electron and ion transfer reactions, Chem. Phys. Lett., 1995, vol. 237, p. 152.
  8. Economu, E.N., Green’s Functions in Quantum Physics, 3rd ed., Berlin: Springer, 2006.
  9. Davison, S.G. and Sulston, K.W., Green-Function Theory of Chemisorption, Berlin: Springer, 2006.
  10. Cohen-Tannoudji, C., Diu, B., and Laloë, F., Quantum Mechanics, New York: J. Wiley & Sons, 1977, vol. 2, App. II.
  11. Gerischer, H., Z. Phys. Chem. NF, 1960, vol. 26, p. 223
  12. Gerischer, H., Z. Phys. Chem. NF, 1961, vol. 7, p. 40, 48.
  13. Schmickler, W. and Santos, E., Interfacial Electrochemistry 2nd ed., Berlin: Springer Verlag, 2010.
  14. Santos, E. and Schmickler, W., d-band catalysis in electrochemistry, Chem. Phys. Chem., 2006, vol. 7, p. 2282.
  15. Santos, E., Quaino, P., and Schmickler, W., Theory of electrocatalysis: Hydrogen evolution and more, PCCP, 2012, vol. 14, p. 11224.
  16. Kravtsov, V.E. and Malshukov, A.G., Sov. Phys. JETF, 1978, vol. 48, p. 348.
  17. Hush, N.S., Adiabatic theory of outer sphere electrontransfer reactions in solution, Trans. Faraday Soc., 1961, vol. 57, p. 557.
  18. Kramers, H.A., Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, 1940, vol. 7, p. 284.
  19. Schmickler, W., Santos, E., Bronshtein, M., and Nazmutdinov, R., Adiabatic electron transfer reaction on semiconducting electrodes, Chem. Phys. Chem., 2017, vol. 18, p. 111.
  20. Mohr, J. and Schmickler, W., Exactly solvable quantum model for electrochemical electron-transfer reactions, Phys. Rev. Lett., 2000, vol. 84, p. 1051.
  21. Abramowitz, M. and Stegun, I., Handbook of Mathematical Function, Applied Mathematics series, Vol. 55, National Bureau of Standards, 1966, p. 297.
  22. Mohr, J. and Schmickler, W., The rate of electrochemical electron-transfer reactions, J. Chem. Phys., 2001, vol. 117, p. 2867.
  23. Iwasita, T., Schmickler, W., and Schultze, J.W., The influence of the metal on the kinetics of outer sphere redox reactions, Ber. Bunsenges. Phys. Chem., 1985, vol. 89, p. 138.