A GEOMETRIC REPRESENTATION OF NUCLEAR MODULATION EFFECTS - THE EFFECTS OF HIGH ELECTRON-SPIN MULTIPLICITY ON THE ELECTRON-SPIN ECHO ENVELOPE MODULATION SPECTRA OF MN-2+ COMPLEXES OF N-RAS P21

A theoretical treatment is presented for the analysis of ESEEM spectra of I = 1/2 nuclei coupled to an electron spin of high multiplicity, with specific attention to the case of S = 5/2. This treatment is shown to account for the observed spectral behavior of N-15 and P = 31 nuclei coupled to Mn2+ in a GDP complex with the protein N-ras p21. The treatment involves the decomposition of the multilevel electron spin system into a set of noninteracting two level systems, an approximation that is valid when the dispersed EPR spectral width is large compared to the microwave excitation bandwidth. The consequent spectral selectivity of the microwave excitation is accounted for, in ESEEM simulations, by attaching a weight to the ESEEM subspectra associated with each EPR transition, and calculating the total ESEEM spectrum as a weighted superposition of the subspectra. The simplest means of estimating the appropriate weight factors-identifying them with the cw EPR intensity of each transition, as deduced by simulation of the EPR spectra-leads to ESEEM simulations that account for the key features of the observed spectra, in particular, features that are peculiar to high multiplicity spin systems. In the studied Mn2+ system, no clear indication of orientation selective effects were found. A simple geometric representation is presented which enables the facile understanding of ESEEM spectra of nuclear spin I = 1/2 coupled to an electron spin of high spin multiplicity in orientationally disordered solids. Analytical expressions are derived for the ESEEM frequencies, frequency dispersions and amplitudes. It is shown that in these systems external field variation can lead to an array of spectral line-narrowing and amplitude resonance phenomena analogous to those observed in S = 1/2 systems.