Theory of two-dimensional ESR with nuclear modulation

A formalism for computing 2D ESR lineshapes with nuclear modulation is developed in a form which is useful for planning phase cycles for particular purposes. A simple method of processing spectra, utilizing quadrature detection, is shown to enhance the selectivity of the phase cycling techniques. Computed ESR-COSY, ESR-SECSY, and 2D ELDOR lineshapes are presented for several kinds of polycrystalline and single-crystal samples which exhibit nuclear modulation, due to one or several nuclei. The two-dimensional methods are found to give more detailed structural information than the corresponding ESEEM spectra. New phase cycles are found to eliminate completely all transverse and axial peaks in 2D ELDOR and in ESR-COSY, and at the same time eliminate all artifacts arising from incomplete image rejection. Other phase cycles are presented for selecting in those experiments only axial peaks, for measuring T1. It is also shown how selective phase cycles may help to distinguish between coherent and exchange cross peaks. In the special case of nitroxides in typical Zeeman fields, there are no significant nuclear modulation effects from the ¹⁴N nuclear spin interaction, but those from the protons (or deuterons) will, in general, be significant.