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Principles of ESR

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Principles and Applications of ESR Spectroscopy

Abstract

The ESR (electron spin resonance) method is employed for studies of paramagnetic substances most commonly in liquids and solids. A spectrum is obtained in continuous wave (CW) ESR by sweeping the magnetic field. The substances are characterized by measurements of the g-factor at the centre of the spectrum and of line splittings due to hyperfine structure from nuclei with spin I ≠ 0. Zero-field splitting (or fine structure) characteristic of transition metal ion complexes and other substances with two or more unpaired electrons (S ≥ 1) can be observed in solid samples. Concentration measurements with the CW-ESR method are common in other applications. High field and multi-resonance (e.g. ENDOR) methods employed in modern applications improve the resolution of the g-factor and of the hyperfine couplings, respectively. Pulse microwave techniques are used for measurements of dynamic properties like magnetic relaxation but also for structural studies.

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Author information

Authors and Affiliations

  1. Department of Physics, Chemistry and Biology, IFM, Linkoping University, The Emeritus Academy, Linkoping University, SE-581 83, Linkoping, Sweden

    Prof. Anders Lund

  2. Graduate School of Engineering, Hiroshima University, 4-26-8 Takamigaoka, Takaya, Higashi-Hiroshima, 739-2115, Japan

    Prof. Masaru Shiotani

  3. Graduate School of Engineering, Nagoya Institute of Technology, 44-66 Midorigaoka, Midori-Machi, Owari-Asahi, 488-0822, Japan

    Prof. Shigetaka Shimada

Authors
  1. Prof. Anders Lund
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  2. Prof. Masaru Shiotani
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  3. Prof. Shigetaka Shimada
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Corresponding author

Correspondence to Anders Lund .

Exercises

Exercises

  1. E1.1

    Naturally occurring chemical substances are in general diamagnetic. (a) Which of the substances CO, NO, CO2, and NO2 might be paramagnetic? (NO is a special case, see Chapter 6.) (b) Can any of the hydrocarbon species shown below be paramagnetic? Can ions of the species be paramagnetic?

  2. E1.2

    Ions of organic compounds have been extensively studied by ESR as discussed in Chapter 5.

    1. (a)

      The spin density is equally distributed over the carbon atoms of the cyclo-octatetraene anion radical. What is the expected hyperfine pattern (number and intensities of hyperfine lines due to hydrogen)?

    2. (b)

      Hyperfine couplings due to three groups of protons were observed from the radical cation produced by the treatment of anthracene with SbCl5 in liquid solution. The coupling constants were 6.44, 3.08 and 1.38 G, respectively [L.C. Lewis, L.S. Singer: J. Chem. Phys. 43, 2712 (1965)]. Assign the couplings to specific positions using the Hückel spin densities given below.

  3. E1.3

    The anisotropic hyperfine coupling of the NO3 radical trapped in a nitrate salt was found to be axially symmetric, A || = a + 2b, A ⊥ = a–b, with a = 0.7 G, b = 0.7 G [21]. The radical is assumed to be planar.

    1. (a)

      Estimate the spin density in the nitrogen 2pz orbital with its axis (z) perpendicular to the plane, the spin density at the nitrogen nucleus, and the total spin density on nitrogen by a procedure analogous to that in Section 1.5.3.

    2. (b)

      Estimate the spin density on the oxygen atoms by assuming that they are equivalent and that ρ(N) + 3· ρ(C) = 1.

  4. E1.4

    Consider the influence of the microwave frequency on the spectrum in Fig. 1.7 showing fine structure or zero-field splitting (zfs).

    1. (a)

      Would it be possible to directly measure the zero-field splitting with a microwave frequency that is 1/3 of that in the figure, for instance by measuring at S- rather than at X-band?

    2. (b)

      Do“first order”conditions strictly apply for the spectrum in Fig. 1.7? (The spectrum is first order when 2·D << hν in energy units or 2·D << B g in field units. The zfs can then be directly measured as shown in the figure.) Suggest an experimental method to satisfy this condition. (A theoretical procedure was applied to obtain the zfs of excited naphthalene in the S = 1 triplet state at an early stage, [H. van der Waals, M.S. de Groot: Mol. Phys. 2, 333 (1959)].

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Lund, A., Shiotani, M., Shimada, S. (2011). Principles of ESR. In: Principles and Applications of ESR Spectroscopy. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5344-3_1

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