Skip to main content
SpringerLink
Log in

The Dobryakov–Lebedev Relation Extended to Partially Resolved EPR Spectra

  • Original Paper
  • Published:
Applied Magnetic Resonance Aims and scope Submit manuscript

Abstract

The Dobryakov–Lebedev relation (Sov Phys Doklady 13:873, 1969), which relates the line width of the first-derivative of a Gaussian–Lorentzian convolution to the line widths of its Gaussian and Lorentzian components for an unresolved EPR line, is extended to resolved lines. Applying this extension to nitroxide-free radicals in solutions of low-viscosity solvents offers an opportunity to study interactions of the spins with the microwave field and spin–spin interactions previously inaccessible except by tedious numerical methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. A.S. AlOmar, Optik 225, 165533–165544 (2021)

    Article  ADS  Google Scholar 

  2. W. Voigt, Phys. Z. 14, 377 (1913)

    Google Scholar 

  3. B.H. Armstrong, J. Quant. Spect. Radiat. Transf. 7, 61–88 (1967)

    Article  ADS  Google Scholar 

  4. B.L. Bales, in Biological Magnetic Resonance, vol. 8, ed. by L.J. Berliner, J. Reuben (Plenum, New York, 1989), pp. 77–130

    Google Scholar 

  5. H.J. Halpern, M. Peric, C. Yu, B.L. Bales, J. Magn. Reson. 103, 13–22 (1993)

    Article  ADS  Google Scholar 

  6. G.K. Wertheim, M.A. Butler, K.W. West, D.N.E. Buchanan, Rev. Sci. 45, 1369–1371 (1974)

    Article  ADS  Google Scholar 

  7. S. Lee, A. Shetty, J. Chem. Phys. 83, 499–505 (1985)

    Article  ADS  Google Scholar 

  8. T.G. Castner Jr., Phys. Rev. 115, 1506–1515 (1959)

    Article  ADS  Google Scholar 

  9. J. Zimbrick, L. Kevan, J. Chem. Phys. 47, 2364–2371 (1967)

    Article  ADS  Google Scholar 

  10. L.J. Berliner, Spin labeling: the next millennium, in Biological magnetic resonance, vol. 14, ed. by L.J. Berliner (Kluwer Academic Publishers, New York, 2002), p. 444

    Chapter  Google Scholar 

  11. L.J. Berliner, Spin Labeling: Theory and Applications (Plenum Publishing Corporation, New York, 1989)

    Book  Google Scholar 

  12. L.J. Berliner, Spin Labeling II: Theory and Applications (Academic Press, New York, 1979)

    Google Scholar 

  13. D. Marsh, Spin-Label Electron Paramagnetic Resonance Spectroscopy (CRC Press. Taylor & Francis Group, Boca Raton, 2020)

    Google Scholar 

  14. C.P. Poole Jr., Electron Spin Resonance: A Comprehensive Treatise on Experimental Techniques, 2nd edn. (Dover, New York, 1996)

    Google Scholar 

  15. M.M. Bakirov, K.M. Salikhov, M. Peric, R.N. Schwartz, B.L. Bales, Appl. Magn. Reson. 50, 919–942 (2019)

    Article  Google Scholar 

  16. B.L. Bales, M.M. Bakirov, R.T. Galeev, I.A. Kirilyuk, A.I. Kokorin, K.M. Salikhov, Appl. Magn. Reson. 48, 1399–1445 (2017)

    Article  Google Scholar 

  17. B.L. Bales, M. Peric, M.T. Lamy-Freund, J. Magn. Reson. 132, 279–286 (1998)

    Article  ADS  Google Scholar 

  18. J.S. Hyde, M. Pasenkiewicz-Gierula, A. Jesmanowicz, W.E. Antholine, Appl. Magn. Reson. 1, 483–496 (1990)

    Article  Google Scholar 

  19. B.H. Robinson, C. Mailer, A.W. Reese, J. Magn. Reson. 138, 199–209 (1999)

    Article  ADS  Google Scholar 

  20. S.N. Dobryakov, Y.S. Lebedev, Sov. Phys. Doklady 13, 873 (1969)

    ADS  Google Scholar 

  21. K.M. Salikhov, Fundamentals of Spin Exchange. Story of a Paradigm Shift (Springer, Cham, 2019)

    Book  Google Scholar 

  22. P.L. Lee, Nucl. Instrum. Methods 144, 363–365 (1977)

    Article  ADS  Google Scholar 

  23. G. Poggi, C.S. Johnson Jr., J. Magn. Res. 3, 436–445 (1970)

    ADS  Google Scholar 

  24. C. Jolicoeur, H.L. Friedman, Ber. Bunsenges. Phys. Chem. 75, 248–257 (1971)

    Google Scholar 

  25. K.M. More, G.R. Eaton, S.S. Eaton, J. Magn. Reson. 60, 54–65 (1984)

    ADS  Google Scholar 

  26. M.F. Ottaviani, J. Phys. Chem. 91, 779–784 (1987)

    Article  Google Scholar 

  27. J.J. Windle, J. Magn. Reson. 45, 432–439 (1981)

    ADS  Google Scholar 

  28. P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969)

    Google Scholar 

  29. W.Z. Plachy, D.A. Windrem, J. Magn. Reson. 27, 237–239 (1977)

    ADS  Google Scholar 

  30. M.R. Kurban, M. Peric, B.L. Bales, J. Chem. Phys. 129, 064501-1-064501–10 (2008)

    Article  ADS  Google Scholar 

  31. M. Peric, B.L. Bales, M. Peric, J. Phys. Chem. A 116, 2855–2866 (2012)

    Article  Google Scholar 

  32. M.T. Jones, J. Chem. Phys. 38, 2892–2895 (1963)

    Article  ADS  Google Scholar 

  33. K.M. Salikhov, Appl. Magn. Reson. 723, 1074–1087 (2018)

    Google Scholar 

  34. https://pubchem.ncbi.nlm.nih.gov/compound/15600

  35. A.M. Portis, Phys. Rev. 91, 1071–1078 (1953)

    Article  ADS  Google Scholar 

  36. M.P. Eastman, R.G. Kooser, M.R. Das, J.H. Freed, J. Chem. Phys. 51, 2690 (1969)

    Article  ADS  Google Scholar 

  37. G.R. Eaton, S.S. Eaton, D.P. Barr, R.T. Weber, Quantitative EPR (Springer, New York, 2010)

    Book  Google Scholar 

  38. J.M. Backer, V.G. Budker, S.I. Eremenko, Y.N. Molin, Biochim. Biophys. Acta 460, 152–156 (1977)

    Article  Google Scholar 

  39. W.K. Subczynski, J.S. Hyde, Biophys. J. 41, 743–746 (1983)

    Article  Google Scholar 

  40. H.J. Halpern, C. Yu, M. Peric, E. Barth, D.J. Grdina, B.A. Teicher, Proc. Natl. Acad. Sci. 91, 13047–13051 (1994)

    Article  ADS  Google Scholar 

  41. R. Ahmad, P. Kuppusamy, Chem. Rev. 110, 3212–3236 (2010)

    Article  Google Scholar 

  42. B.L. Bales, F.L. Harris, M. Peric, M. Peric, J. Phys. Chem A 113, 9295–9303 (2009)

    Article  Google Scholar 

  43. B.L. Bales, M. Peric, I. Dragutan, J. Phys. Chem. A 107, 9086–9098 (2003)

    Article  Google Scholar 

  44. B.L. Bales, M. Peric, J. Phys. Chem. A 106, 4846–4854 (2002)

    Article  Google Scholar 

  45. B.L. Bales, M. Peric, J. Phys. Chem. B 101, 8707–8716 (1997)

    Article  Google Scholar 

  46. B.L. Bales, D. Mareno, F.L. Harris, J. Magn. Reson. A 104, 37–53 (1993)

    Article  ADS  Google Scholar 

  47. B.L. Bales, M. Meyer, S. Smith, M. Peric, J. Phys. Chem A 112, 2177–2181 (2008)

    Article  Google Scholar 

  48. D. Merunka, M. Peric, J. Chem. Phys. 152, 024502–024508 (2020)

    Article  Google Scholar 

  49. J. Labsky, J. Pilar, J. Lövy, J. Magn. Reson. 37, 515–522 (1980)

    ADS  Google Scholar 

  50. W. Plachy, D. Kivelson, J. Chem. Phys. 47, 3312 (1967)

    Article  ADS  Google Scholar 

  51. https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjq0qT71KPwAhXZQjABHZ3wDf8QFjAJegQIAxAD&url=https%3A%2F%2Fenterprisersproject.com%2Farticle%2F2020%2F9%2Fmoores-law-what-means-today&usg=AOvVaw1LpyMXWgEHsWWSUWqouCev. Moore’s Law

Download references

Acknowledgements

Support from NSF through NSF MRI (Grant No. 1626632—B.L.B. and M.P) and NSF RUI (Grant No. 1856746—M.P.) is acknowledged. This work was supported by the Grant for the fundamental research of the Presidium of the Russian Academy of Sciences 1.26 Π.

Author information

Authors and Affiliations

  1. Zavoisky Physical-Technical Institute, Russian Academy of Sciences, Sibirsky trakt 10/7, Kazan, 420029, Russian Federation

    M. M. Bakirov & I. T. Khairutdinov

  2. Electrical and Computer Engineering Department, University of California, Los Angeles, Los Angeles, CA, 90095, USA

    Robert N. Schwartz

  3. Department of Physics and Astronomy, The Center for Biological Physics, California State University at Northridge, Northridge, CA, 91330, USA

    Miroslav Peric & Barney L. Bales

Authors
  1. M. M. Bakirov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. T. Khairutdinov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert N. Schwartz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Miroslav Peric
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Barney L. Bales
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Barney L. Bales.

Additional information

Dedicated to Kev Salikhov and Klaus Möbius, the birthday brothers.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix: Criterion for Incipient Resolution

Appendix: Criterion for Incipient Resolution

The criterion for incipient resolution has always been subjective, defined as the value of \(\chi \) where a visual distortion of an IHB occurs. Before, we observed the peak of the line and decided if it was a normal smooth curve or not.

Figure 10 shows a series of simulated Tempol spectra at \(\chi \) = a 1.17, b 2.54, c 2.98, d 3.44, e 4.13, and f 5.29. The residuals are amplified as indicated; for example, in b, the residual has been amplified by a factor of 7.55. In our opinion, a practiced eye may discern incipient resolution in c at a glance, without any fitting. The insert shows the peak region in more detail. d with its insert shows a definite distortion that anyone may discern. This criterion is still subjective; however, once we decide, we may quantify it by specifying the ratio \({V}_{\mathrm{res}}/{V}_{\mathrm{pp}.}\) For c, \(\chi \) = 2.98, \({V}_{\mathrm{res}}/{V}_{\mathrm{pp}.}\) = 0.02. If it becomes important, one could subtract the broad resonances evident in Fig. 1c to be more precise because it is the narrow residual lines that yield the information.

Fig. 10
figure 10

A series of simulated Tempol spectra at \(\chi \) = a 1.17, b 2.54, c 2.98, d 3.44, e 4.13, and f 5.29. The residuals are amplified as indicated; for example, in b, the residual has been amplified by a factor of 7.55

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bakirov, M.M., Khairutdinov, I.T., Schwartz, R.N. et al. The Dobryakov–Lebedev Relation Extended to Partially Resolved EPR Spectra. Appl Magn Reson 53, 1151–1174 (2022). https://doi.org/10.1007/s00723-021-01433-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00723-021-01433-z

Search

Navigation