On the Calculations of the Exciton-Phonon Coupling Parameters in the Theory of Davydov Solitons

  • Victor A. Kuprievich
Part of the NATO ASI Series book series (NSSB, volume 243)


Davydov soliton (DS) theory2, 3 considers collective amide-1 vibrations (excitons) in the chains of the hydrogen-bonded peptide groups in the peptide α-helix and their coupling with longitudional deformations of the chains (acoustic phonons). The coupling leads to the H-bond length changes, thus resulting, under some conditions, in a self-trapping of the excitation. Due to the exciton-phonon coupling (EPC) the longitudional α-helix deformations affect the exciton Hamiltonian, changing the resonance parameters (which describe the hopping of the excitation between H-bonded peptide groups), and nonresonance (diagonal) parameters (which are the excitation energy of each peptide group). Accordingly, the EPC can be characterized by three parameters: the “resonance” parameter χres defined as the derivative of the hopping integral with the respect to the corresponding H-bond length and two “nonresonance” parameters, χ′ and χ″, which are the derivatives of the amide-1 excitation energy E in the peptide group with the respect to its distances to the “right” and “left” groups in the chain. In other words, χ′ and χ” present the extra forces with which some peptide group acts, when excited, upon its right and left neighbours in the chain.


Peptide Group Schroedinger Equation Davydov Soliton Reid Potential Hydrogen Bond theOry 
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  1. 1.
    A. S. Davydov, “Biology and quantum mechanics”, Pergamon Press, Oxford (1982).Google Scholar
  2. 2.
    A. S. Davydov, “Solitons in molecular systems”, Reidel Publishing Co., Dordrecht (1985).Google Scholar
  3. 3.
    J. M. Hyman, D. W. McLaughlin, and A. C. Scott, On Davydov’s alpha-helix solitons, Physica 3D:23 (1981).ADSGoogle Scholar
  4. 4.
    A. C. Scott, Dynamics of Davydov solitons, Phys. Rey. A 26:578 (1982).ADSCrossRefGoogle Scholar
  5. 5.
    L. MacNeil and A. C. Scott, Launching of Davydov soliton: II. Numerical studies, Phys. Scripta 29:284 (1984).ADSCrossRefGoogle Scholar
  6. 6.
    M. V. Volkenshtein, “Molecular biophysics” (Molekulyarnaya biofizika), Nauka, Moscow (1975).Google Scholar
  7. 7.
    V. A. Kuprievich and Z. G. Kudritskaya, Davydov solitons and deter mination of the exciton-phonon-interaction parameters in:“Modern problems of the solid state physics and biophysics” (Sovremennyje problemy fiziki twerdogo tela i biofiziki), V. G. Bar’yakhtar, ed., Naukova dumka, Kiev (1982).Google Scholar
  8. 8.
    B. M. Pierce, A. F. Lawrence, and D. B. Chang, A theoretical study of the interaction between amide-1 and hydrogen bond stretching vibrations in hydrogen-bonded polypeptides, in: “Spectroscopy of biological molecules”, A. J. P. Alix, L. Bernard, and M. Manfait, eds., Wiley, New York (1985).Google Scholar
  9. 9.
    N. Ostergard, “Ab initio calculations for hydrogen bonds in relation to biomolecualr dynamics” (thesis), The Technical University of Denmark, Lyngby (1988).Google Scholar
  10. 10.
    G. Careri, U. Buontempo, F. Galluzzi, A.C. Scott, E. Gratton, and E. Shyamsunder, Spectroscopic evidence for Davydov-like solitons in acetanilide, Phys. Rev. B 30:4689 (1984).ADSCrossRefGoogle Scholar
  11. 11.
    A. C. Scott, private communication (1989).Google Scholar
  12. 12.
    L. D. Landau and E. M. Liftshitz, “Quantum mechanics”, Pergamon, London and New York (1959) v. 1.Google Scholar
  13. 13.
    C. Reid, Semiempirical treatment of the hydrogen bond, J. Chem. Phys. 30:182 (1959).ADSCrossRefGoogle Scholar
  14. 14.
    N. D. Sokolov, Dynamics of a hydrogen bond in: “Hydrogen bond” (Wodorodnaya swyaz), Nauka, Moscow (1981).Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Victor A. Kuprievich
    • 1
  1. 1.Institute for Theoretical PhysicsAcademy of Sciences of the Ukrainian SSRKievUSSR

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