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-RAS P21( COMPLEXES OF N)

A theoretical treatment is presented for the analysis of ESEEM spectra of I = 1/2 nuclei coupled to an electron spin of high multiplicity, w ith 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 nucl ei coupled to Mn2+ in a GDP complex with the protein N-ras p21. The tr eatment involves the decomposition of the multilevel electron spin sys tem into a set of noninteracting two level systems, an approximation t hat is valid when the dispersed EPR spectral width is large compared t o the microwave excitation bandwidth. The consequent spectral selectiv ity of the microwave excitation is accounted for, in ESEEM simulations , by attaching a weight to the ESEEM subspectra associated with each E PR 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 multiplici ty spin systems. In the studied Mn2+ system, no clear indication of or ientation selective effects were found. A simple geometric representat ion is presented which enables the facile understanding of ESEEM spect ra of nuclear spin I = 1/2 coupled to an electron spin of high spin mu ltiplicity in orientationally disordered solids. Analytical expression s are derived for the ESEEM frequencies, frequency dispersions and amp litudes. It is shown that in these systems external field variation ca n lead to an array of spectral line-narrowing and amplitude resonance phenomena analogous to those observed in S = 1/2 systems.