Analysis of electron spin echo modulation in randomly oriented solids: 15N modulation of radical cations of bacteriochlorophyll a and the primary donor of photosynthetic bacterium Rhodospirillum

The electron spin echo modulation spectrum of organic radicals in randomly oriented solids is analyzed in detail for axially symmetric hyperfine tensors. Numerical calculations of the modulation spectra are compared with experimental results from the radical cations of 15N labeled bacteriochlorophyll a and the primary donor of photosynthetic bacterium Rhodospirillum rubrum. Determination of hyperfine coupling constants from experimental spectra in the frequency domain is complicated by the anisotropy of modulation intensity, the effects of second and higher order hyperfine interactions, overlapping spectra from several nuclei, multiple quantum coherences among hyperfine levels, and the spectrometer deadtime. Nonlinear least-squares analysis of the time domain data [Tang et al., J. Chem. Phys. 83, 4197 (1985)] is the only reliable method for extracting coupling constants from randomly oriented organic radicals