Journal of Experimental and Theoretical Physics

, Volume 91, Issue 3, pp 597–609 | Cite as

Multiple-quantum dynamics of one-dimensional nuclear spin systems in solids

  • S. I. Doronin
  • I. I. Maksimov
  • E. B. Fel’dman
Solids Electronic Properties


Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences.


External Magnetic Field Spin System Nuclear Spin Linear Chain Total Spin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. Cho and J. P. Yesinowski, J. Phys. Chem. 100, 15716 (1996).Google Scholar
  2. 2.
    J. Baum, M. Munowitz, A. N. Garroway, and A. Pines, J. Chem. Phys. 83, 2015 (1985).CrossRefADSGoogle Scholar
  3. 3.
    J. Baum and A. Pines, J. Am. Chem. Soc. 108, 7447 (1986).Google Scholar
  4. 4.
    B. E. Scruggs and K. K. Gleason, Macromolecules 25, 1864 (1992).CrossRefGoogle Scholar
  5. 5.
    D. H. Levy and K. K. Gleason, J. Phys. Chem. 96, 8125 (1992).CrossRefGoogle Scholar
  6. 6.
    M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1973).Google Scholar
  7. 7.
    D. P. Weitekamp, Adv. Magn. Reson. 11, 111 (1983).Google Scholar
  8. 8.
    S. Lacelle, S. J. Hwang, and B. G. Gerstein, J. Chem. Phys. 99, 8407 (1993).CrossRefADSGoogle Scholar
  9. 9.
    M. Tomaselli, S. Hediger, D. Suter, and R. R. Ernst, J. Chem. Phys. 105, 10672 (1996).Google Scholar
  10. 10.
    M. Munowitz, A. Pines, and M. Mehring, J. Chem. Phys. 86, 3172 (1987).ADSGoogle Scholar
  11. 11.
    M. Munowitz and M. Mehring, Solid State Commun. 64, 605 (1987).CrossRefGoogle Scholar
  12. 12.
    C. S. Johnson, J. Chem. Phys. 41, 3277 (1964).Google Scholar
  13. 13.
    M. Munowitz, Mol. Phys. 71, 959 (1990).Google Scholar
  14. 14.
    B. E. Scruggs and K. K. Gleason, Chem. Phys. 166, 367 (1992).CrossRefGoogle Scholar
  15. 15.
    G. Cho and J. P. Yesinowski, Chem. Phys. Lett. 205, 1 (1993).CrossRefGoogle Scholar
  16. 16.
    E. B. Fel’dman and S. Lacelle, Chem. Phys. Lett. 253, 27 (1996).Google Scholar
  17. 17.
    E. B. Fel’dman and S. Lacelle, J. Chem. Phys. 107, 7067 (1997).ADSGoogle Scholar
  18. 18.
    E. B. Fel’dman and S. Lacelle, J. Chem. Phys. 106, 6768 (1997).ADSGoogle Scholar
  19. 19.
    M. Gaudin, La fonction d’onde de Bethe (Masson, Paris, 1983; Mir, Moscow, 1984).Google Scholar
  20. 20.
    A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961; Inostrannaya Literatura, Moscow, 1963).Google Scholar
  21. 21.
    E. B. Fel’dman and M. G. Rudavets, Chem. Phys. Lett. 311, 453 (1999).Google Scholar
  22. 22.
    E. B. Fel’dman, R. Bruschweiler, and R. R. Ernst, Chem. Phys. Lett. 294, 297 (1999).Google Scholar
  23. 23.
    M. Goldman, Spin Temperature and Nuclear Magnetic Resonance in Solids (Clarendon Press, Oxford, 1970; Mir, Moscow, 1972).Google Scholar
  24. 24.
    D. Suter, S. B. Liu, J. Baum, and A. Pines, Chem. Phys. 114, 103 (1987).CrossRefGoogle Scholar
  25. 25.
    D. Shykind, J. Baum, S. B. Liu, et al., J. Magn. Reson. 60, 205 (1984).Google Scholar
  26. 26.
    H. Schneider and H. Schmiedel, Phys. Lett. A 30, 298 (1969).CrossRefADSGoogle Scholar
  27. 27.
    W.-K. Rhim, A. Pines, and J. S. Waugh, Phys. Rev. Lett. 25, 218 (1970).CrossRefADSGoogle Scholar
  28. 28.
    A. K. Roy and K. K. Gleason, J. Magn. Reson. A 120, 139 (1996).CrossRefGoogle Scholar
  29. 29.
    L. D. Landau and E. M. Lifshitz, Statistical Physics (Nauka, Moscow, 1976; Pergamon, Oxford, 1980), Part 2.Google Scholar
  30. 30.
    D. A. Lathrop, E. S. Handy, and K. K. Gleason, J. Magn. Reson. A 111, 161 (1994).CrossRefGoogle Scholar
  31. 31.
    E. H. Lieb, T. Schultz, and D. C. Mattis, Ann. Phys. 16, 407 (1961).MathSciNetGoogle Scholar
  32. 32.
    A. K. Khitrin and B. M. Fung, J. Chem. Phys. 111, 7480 (1999).ADSGoogle Scholar
  33. 33.
    S. Zhang, B. H. Meier, and R. R. Ernst, Phys. Rev. Lett. 69, 2149 (1992).ADSGoogle Scholar
  34. 34.
    Z. L. Madi, B. Brutscher, T. Schulte-Herbruggen, et al., Chem. Phys. Lett. 268, 300 (1997).CrossRefGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2000

Authors and Affiliations

  • S. I. Doronin
    • 1
  • I. I. Maksimov
    • 1
  • E. B. Fel’dman
    • 1
  1. 1.Institute of Chemical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia

Personalised recommendations