, Volume 59, Issue 2, pp 189–198 | Cite as

Two-dimensional model of a double-well potential: Proton transfer upon hydrogen bond deformation

Molecular Biophysics


Proton tunneling in a hydrogen bond can only take place if the potential energy surface has two minima; this is known as a double-well potential. The aim of this work was (i) to present a simple enough 2D model of H-bond double-well potential in harmonic approximation and (ii) to assess how proton transfer therein is affected by H-bond deformations (shifts and turns such as result from conformational motion of molecular structures carrying the donor and the acceptor). It is shown that even small stretching of the H-bond and reorientation of its covalent part (‘bending’) increase the characteristic time of proton tunneling by orders of magnitude. On the other hand, the model, being two-dimensional, demonstrates that different types of deformation not only can aggravate each other but in some cases can be mutually compensatory in terms of proton transfer efficiency. The properties of the model and some implications of the results are discussed.


H-bond deformation proton tunneling double-minimum potential 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. C. Pimentel and A. L. McClellan, The Hydrogen Bond (San Francisco: W. H. Freeman, 1960).Google Scholar
  2. 2.
    R. P. Bell, The Proton in Chemistry, 2nd ed. (Chapman and Hall, London, 1973).CrossRefGoogle Scholar
  3. 3.
    D. Eisenberg and W. Kauzmann, The Structure and Properties of Water (Oxford University Press, New York, 1969).Google Scholar
  4. 4.
    R. P. Bell, The Tunnel Effect in Chemistry (Chapman and Hall, London, 1980).CrossRefGoogle Scholar
  5. 5.
    Y. Cha, C. J. Murrat, and J. P. Klinman, Science 243, 1325 (1989).CrossRefADSGoogle Scholar
  6. 6.
    R. Schiott, B. B. Iversen, G. K. H. Madsen, et al., Proc. Natl. Acad. Sci. USA 95, 12799 (1998).CrossRefADSGoogle Scholar
  7. 7.
    N. S. Scrutton, J. Basran, and M. J. Sutcliffe, Eur. J. Biochem. 264, 666 (1999).CrossRefGoogle Scholar
  8. 8.
    M. J. Sutcliffe and N. S. Scrutton, Eur. J. Biochem. 269, 3096 (2002).CrossRefGoogle Scholar
  9. 9.
    A. Chernyshev, R. Pomes, and S. Cukiermann, Biophys. Chem. 103, 179 (2003).CrossRefGoogle Scholar
  10. 10.
    J. Teissie, Nature 379, 305 (1996).CrossRefADSGoogle Scholar
  11. 11.
    S. Serowy, S. P. Saparov, Y. N. Antonenko, et al., Biophys. J. 84, 1031 (2003).CrossRefADSGoogle Scholar
  12. 12.
    E. C. Abresch, M. L. Paddock, M. H. B. Stowell, et al., Photosyn. Res. 55, 119 (1998).CrossRefGoogle Scholar
  13. 13.
    C. Tommos and G. T. Babcock, Biochim. Biophys. Acta 1458, 199 (2000).CrossRefGoogle Scholar
  14. 14.
    P. M. Krasilnikov, P. A. Mamonov, P. P. Knox, et al., Biochim. Biophys. Acta 1767, 541 (2007).CrossRefGoogle Scholar
  15. 15.
    P. M. Krasilnikov, P. P. Knox, and A. B. Rubin, Photochem. Photobiol. Sci. 8, 181 (2009).CrossRefGoogle Scholar
  16. 16.
    O. J. Riveros and D. J. Diestler, J. Am. Chem. Soc. 110, 7206 (1988).CrossRefGoogle Scholar
  17. 17.
    N. Agmon, Chem. Phys. Lett. 244, 456 (1995).CrossRefADSGoogle Scholar
  18. 18.
    S. Woutersen and H. J. Bakker, Phys. Rev. Lett. 96, 138305 (2006).CrossRefADSGoogle Scholar
  19. 19.
    J. A Sussmann, Phys. Kondens. Materie 2, 146 (1964).ADSGoogle Scholar
  20. 20.
    W. Siebrand, T. A. Wildman, and M. Z. Zgierski, J. Am. Chem. Soc. 106, 4083 (1984).CrossRefGoogle Scholar
  21. 21.
    S. Pnevmatikos, Phys. Rev. Lett. 60, 1534 (1980).CrossRefADSGoogle Scholar
  22. 22.
    D. C. Borgis, S. Lee, and J. T. Hynes, Chem. Phys. Lett. 162, 19 (1989).CrossRefADSGoogle Scholar
  23. 23.
    P. M. Kiefer, V. B. P. Leite, and R. M. Whitnell, Chem. Phys. 194, 33 (1995).CrossRefADSGoogle Scholar
  24. 24.
    N. I. Pavlenko, J. Chem. Phys. 112, 8637 (2000).CrossRefADSGoogle Scholar
  25. 25.
    I. V. Stasyuk, R. Ya. Stetsiv, and Yu. V. Sizonenko, Condens. Matt. Phys. 5, 685 (2002).CrossRefGoogle Scholar
  26. 26.
    R. I. Cukier, J. Phys. Chem. 99, 16101 (1995).CrossRefGoogle Scholar
  27. 27.
    A. Luzar and D. Chandler, Phys. Rev. Lett. 76, 928 (1996).CrossRefADSGoogle Scholar
  28. 28.
    K. Modig, B. G. Pfrommer, and B. Halle, Phys. Rev. Lett. 90, 075502 (2003).CrossRefADSGoogle Scholar
  29. 29.
    S. Ia. Ishenko, M. V. Vener, and V. M. Mamaev, Theor. Chim. Acta 68, 351 (1995).CrossRefGoogle Scholar
  30. 30.
    R. H. Luchsinger, P. F. Meier, and Y. Zhou, Phys. Rev. B 57, 4413 (1998).CrossRefADSGoogle Scholar
  31. 31.
    E. Arunan, G. R. Desiraju, R. A. Klein et al., Pure Appl. Chem. 83, 1619 (2011).Google Scholar
  32. 32.
    T. Steiner, Angew. Chem. Int. Ed. 41, 48 (2002).CrossRefGoogle Scholar
  33. 33.
    K. Giese, M. Petkovi H. Naundorf, and O. Kühn, Phys. Rep. 430, 211 (2006).CrossRefADSGoogle Scholar
  34. 34.
    T. K. Harris and A. S. Mildvan, Proteins 35, 275 (1999).CrossRefGoogle Scholar
  35. 35.
    J. Emsley, Chem. Soc. Rev. 9, 91 (1980).CrossRefGoogle Scholar
  36. 36.
    P. M. Krasilnikov and P. A. Mamonov, Biophysics 51, 226 (2006).CrossRefGoogle Scholar
  37. 37.
    P. M. Krasilnikov, P. A. Mamonov, P. P. Knox, and A. B. Rubin, Biophysics 53, 207 (2008).CrossRefGoogle Scholar
  38. 38.
    G. R. Desiraju and T. Steiner, The Weak Hydrogen Bond: In Structural Chemistry and Biology (Oxford University Press, 2001).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2014

Authors and Affiliations

  1. 1.Biological FacultyMoscow State UniversityMoscowRussia

Personalised recommendations