Computer Synthesis of Electron Paramagnetic Resonance Spectra from a Parametric (Spin) Hamiltonian

  • John H. Mackey
  • Marcel Kopp
  • Edmund C. Tynan
  • Teh Fu Yen


A computer program has been developed for computing electron paramagnetic resonance (EPR) spectra from a spin Hamiltonian, ℋsp which is a linear combination of spin operators whose coefficients may be regarded as experimental parameters. The user supplies ℋsp, the spin number (orientation degeneracy) of each particle, and values of the parameters; output may be obtained in the form of the frequency spectrum for fixed applied magnetic-field strength, H 0, or the magnetic-field spectrum for fixed radiation frequency, v mr. In addition to the line positions, the program computes first-order transition intensities in a radiation field H 1 using eigenvectors generated by the calculation. Results have been obtained for (transition-metal) ions and free radicals in single crystals as a function of field orientation, and in powders and glasses (by summing over many orientations). The program can be adapted for calculation of NMR and NQR spectra of anisotropic systems, inclusion of line narrowing and broadening (relaxation) effects, and automatic adjustment of certain parameters to fit experimental spectra.


Electron Paramagnetic Resonance Electron Paramagnetic Resonance Spectrum Nuclear Quadrupole Resonance Field Orientation Powder Spectrum 
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.


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  1. 1.
    M. Kopp and J. H. Mackey, J. Computational Physics, 3, 539–543 (1969).CrossRefGoogle Scholar
  2. 2.
    Leonard I. Schiff, Quantum Mechanics (McGraw-Hill Book Co., New York, 1955), Chapters VI and VIII.Google Scholar
  3. 3.
    P. L. Corio, Structure of High Resolution NMR Spectra, ( Academic Press, New York, 1966 ).Google Scholar
  4. 4.
    J. D. Swalen and H. M. Gladney, IBM J. Res. Dev. 8, 515 (1964).CrossRefGoogle Scholar
  5. 5.
    A. Abragam and M. H. L. Pryce, Proc. Roy. Soc. (London) A205, 135, (1951); M. H. L. Pryce, Proc. Phys. Soc. 63, 25 (1950).Google Scholar
  6. 6.
    J. H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford University Press, Clarendon, 1965 ).Google Scholar
  7. 7.
    J. Greenstadt, in: Mathematical Methods for Digital Computers, A. Ralston and H. S. Wilf, eds. ( John Wiley and Sons, New York, 1965 ), Chapter 7.Google Scholar
  8. 8.
    A. A. Bothner-By and T. Castellano, J. Chem. Phys. 41, 3863–69 (1964).CrossRefGoogle Scholar
  9. 9.
    E. O. Schulz-du Bois, Bell Systems Tech. J. 38, 271–290 (1959).Google Scholar
  10. 10.
    D. G. Davis, Mellon Institute, unpublished data.Google Scholar
  11. 11.
    J. H. E. Griffiths, J. Owen, and I. M. Ward, Defects in Crystalline Solids, Reports of the Bristol Conference ( The Physical Society, London, 1955 ), p. 81.Google Scholar
  12. 12.
    M. C. M. O’Brien and M. H. L. Pryce, Defects in Crystalline Solids, Reports of the Bristol Conference (The Physical Society, London, 1955 ), p. 88.Google Scholar
  13. 13.
    M. C. M. O’Brien, Proc. Roy. Soc. (London), A23I, 404 (1955).Google Scholar
  14. 14.
    G. S. Smith and L. E. Alexander, Acta Cryst. 16, 462 (1963).CrossRefGoogle Scholar
  15. 15.
    B. Bleaney, in: Hyperfine Interactions, A. J. Freeman and R. B. Frankel, eds. ( Academic Press, New York, 1967 ), Appendix I.Google Scholar
  16. 16.
    E. M. Roberts, W. S. Koski, and W. S. Caughey, J. Chem. Phys. 34, 591 (1961).CrossRefGoogle Scholar
  17. 17.
    B. Bleaney, Phil. Mag. 42, 441 (1951).Google Scholar
  18. 18.
    L. J. Boucher, E. C. Tynan, and Teh Fu Yen, Paper No. 44 at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 4, 1968.Google Scholar
  19. 19.
    P. H. Kasai and E. B. Whipple, Mol. Phys. 9, 497 (1965).CrossRefGoogle Scholar
  20. 20.
    A. Horsfield, J. R. Morton, J. R. Rowlands, and D. H. Whiffen, Mol. Phys. 5, 241 (1962).CrossRefGoogle Scholar
  21. 21.
    A. R. Edmonds, Angular Momentum in Quantum Mechanics, (Princeton University Press, 1957 ), Chapter 3.Google Scholar
  22. 22.
    G. F. Koster and H. Statz, Phys. Rev. 113, 445 (1959); Phys. Rev. 115, 1568 (1959); T. Ray, Proc. Roy. Soc. (London) A277, 76 (1964); W. Hauser in: Paramagnetic Resonance, Vol. 1, W. Low, ed., ( Academic Press, New York, 1963 ), p. 297.Google Scholar
  23. 23.
    M. S. Itzkowitz, J. Chem. Phys. 46, 3048 (1967).CrossRefGoogle Scholar
  24. 24.
    A. G. Redfield, IBM J. Res. Dev. 1, 19 (1957); F. Bloch, Phys. Rev., 105, 1206 (1957); D. Kivelson, J. Chem. Phys., 33, 1094 (1960); J. H. Freed and G. K. Fraenkel, J. Chem. Phys., 39, 326 (1963).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1969

Authors and Affiliations

  • John H. Mackey
    • 1
  • Marcel Kopp
    • 1
  • Edmund C. Tynan
    • 1
  • Teh Fu Yen
    • 1
  1. 1.Mellon InstituteCarnegie-Mellon UniversityPittsburghUSA

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