page_title: Electron paramagnetic resonance
section_title: Multiplicity
hierarchical_section_title: Electron paramagnetic resonance / Spectral parameters / Hyperfine coupling / Multiplicity
caption_attribution_description: Simulated EPR spectrum of CH3 radical
context_page_description: Electron paramagnetic resonance or electron spin resonance spectroscopy
  is a method for studying materials with unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance, but it is electron spins that are excited instead of the spins of atomic nuclei. EPR spectroscopy is particularly useful for studying metal complexes or organic radicals.
  EPR was first observed in Kazan State University by Soviet physicist Yevgeny Zavoisky in 1944, and was developed independently at the same time by Brebis Bleaney at the University of Oxford.
context_section_description: For a radical having M equivalent nuclei, each with a spin of I, the number of EPR lines expected is 2MI + 1. As an example, the methyl radical, CH₃, has three ¹H nuclei, each with I = 1/2, and so the number of lines expected is 2MI + 1 = 2(3)(1/2) + 1 = 4, which is as observed.
  For a radical having M₁ equivalent nuclei, each with a spin of I₁, and a group of M₂ equivalent nuclei, each with a spin of I₂, the number of lines expected is (2M₁I₁ + 1) (2M₂I₂ + 1). As an example, the methoxymethyl radical, H₂C(OCH₃), has two equivalent ¹H nuclei, each with I = 1/2 and three equivalent ¹H nuclei each with I = 1/2, and so the number of lines expected is (2M₁I₁ + 1) (2M₂I₂ + 1) = [2(2)(1/2) + 1] [2(3)(1/2) + 1] = 3×4 = 12, again as observed.
  The above can be extended to predict the number of lines for any number of nuclei.
  While it is easy to predict the number of lines, the reverse problem, unraveling a complex multi-line EPR spectrum and assigning the various spacings to specific nuclei, is more difficult.
  In the often encountered case of I = 1/2 nuclei (e.g., ¹H, ¹⁹F, ³¹P), the line intensities produced by a population of radicals, each possessing M equivalent nuclei, will follow Pascal's triangle. For example, the spectrum at the right shows that the three ¹H nuclei of the CH₃ radical give rise to 2MI + 1 = 2(3)(1/2) + 1 = 4 lines with a 1:3:3:1 ratio. The line spacing gives a hyperfine coupling constant of aH = 23 G for each of the three ¹H nuclei. Note again that the lines in this spectrum are first derivatives of absorptions.
  As a second example, the methoxymethyl radical, H₃COCH₂ the OCH₂ center will give an overall 1:2:1 EPR pattern, each component of which is further split by the three methoxy hydrogens into a 1:3:3:1 pattern to give a total of 3×4 = 12 lines, a triplet of quartets. A simulation of the observed EPR spectrum is shown at the right and agrees with the 12-line prediction and the expected line intensities. Note that the smaller coupling constant (smaller line spacing) is due to the three methoxy hydrogens, while the larger coupling constant (line spacing) is from the two hydrogens bonded directly to the carbon atom bearing the unpaired electron. It is often the case that coupling constants decrease in size with distance from a radical's unpaired electron, but there are some notable exceptions, such as the ethyl radical (CH₂CH₃).
caption: Simulated EPR spectrum of the CH3 radical
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