Determination of hyperfine interaction matrix principal values and principal axis orientations in an orientationally disordered solid: A multifrequency electron spin echo envelope modulation study of nitrogen-15 in a copper(II)-¹⁵N-imidazole complex

A comprehensive experimental study of the magnetic field dependences of ESEEM (electron spin echo envelope modulation) for a spin one-half nucleus in an orientationally disordered solid is presented. Modulation effects from the remote (unligated) nitrogen of ¹⁵N-labeled imidazole in a Cu(II)-diethylenetriamine-¹⁵N-imidazole complex were registered at electron spin excitation frequencies in the 4.3 to 11.5 GHz range, which encompasses the "match range" of the Cu(II)-¹⁵N system under study. Field dependent trends in the ESEEM spectra - trends in spectral amplitudes, linewidths, and frequencies - are analyzed to obtain the magnitude and relative signs of the isotropic and axially symmetric hyperfine coupling constants (and to place an upper bound on the rhombic coupling). The relative utility of each of these trends for measuring hyperfine interactions in orientationally disordered solids is discussed. The orientation of the unique axis of the Cu(II)-¹⁵N hyperfine interaction matrix within the Cu(II) electron spin magnetic axis system is obtained from the field dependence of the ESEEM frequencies observed with orientationally selective excitation. The results of this study are compared to those previously obtained for relevant Cu(II)-¹⁵N systems by a variety of monofrequency ESEEM techniques.