General Analysis of 14N (l = 1) Electron Spin Echo Envelope Modulation

Hong In Lee, Peter E. Doan, Brian M. Hoffman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The analysis methods described to date for 14N electron spin echo envelope modulation (ESEEM) mostly deal with isotropic g- and 14N hyperfine coupling tensors. However, many cases of rhombic tensors are encountered. In the present report we present general equations for analyzing orientation-selective ESEEM and illustrate their use. (i) We present general equations for the nuclear interactions in an electron spin system where the EPR signal arises from an isolated Kramers doublet, then give the nuclear (electron-nuclear double resonance) frequencies for I = 1 associated with such a system, (ii) These are incorporated into equations for single-crystal ESEEM amplitudes, which in turn are incorporated into general equations for the orientation-selective ESEEM that arises when the EPR envelope of a frozen-solution (powder) sample is determined by g anisotropy. (iii) This development is first used in the simplest limit of an isotropic g-tensor and leads to a more general picture of the response of the I = 1 modulation amplitude to variations in the nuclear hyperfine and quadrupole coupling constants, relative to the nuclear Zeeman interaction, than had been presented previously. We find that strong modulation occurs not only in the well-known regime where the "exact/near cancellation" condition (A/2 ≃ νN) is satisfied, but also when the nuclear hyperfine interaction is much larger than the nuclear Zeeman interaction (A/νN > 3) with A/K = 4 ≃ 5. (iv) We then describe the orientation-selective 14N ESEEM frequency-domain patterns (g vs frequency) in the presence of anisotropic (rhombic) hyperfine and electron Zeeman interactions for both coaxial and noncoaxial cases. We derive analytical solutions when the g-, hyperfine, and nuclear quadrupole tensors are coaxial. (v) The method is applied to the ESEEM of the nitrogenase MoFe protein (A ν 1) to determine the full hyperfine and nuclear quadrupole tensors of 14N nuclei interacting with the S = 3/2 FeMo-cofactor (Fe7S8Mo: homocitrate).

Original languageEnglish (US)
Pages (from-to)91-107
Number of pages17
JournalJournal of Magnetic Resonance
Issue number1
StatePublished - Sep 1999


  • Electron spin echo envelope modulation
  • N
  • Orientation-selective
  • Pulsed EPR

ASJC Scopus subject areas

  • Biophysics
  • Biochemistry
  • Nuclear and High Energy Physics
  • Condensed Matter Physics


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