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Notes: We present a theoretical investigation of the origin of the unusual 3-pulse electron spin echo envelope modulation (ESEEM) pattern obtained from 13C enriched polyacetylene, which exhibits modulation at multiple harmonics of the nuclear Larmor frequency ωn. ESEEM signals have been calculated for different models of the electron–nuclear spin coupling. It is shown that the local hyperfine tensors observed in electron nuclear double resonance (ENDOR) experiments on (13CH)x cannot account for the ESEEM results. These tensors have isotropic components which are too large to give narrow peaks at ωn, and there are too few nuclei to produce the large number of harmonics observed. Simulations for a point electron coupled to nuclei on a spherical shell, the spherical model, give insight into the conditions required to obtain narrow lines at multiple harmonics of ωn@B: The electron must be weakly coupled to a very large number of nuclei. Analytical results show that for the spherical model in the limit of small coupling, the intensity profile of the Fourier transform of the three-pulse ESEEM will be a Gaussian of width k¯ N, where k¯ is a function of the magnitude of the electron–nuclear coupling and N is the number of nuclei. Simulations assuming that the unpaired electron is delocalized in one dimension along the polyene chain and dipolar coupled to the 13C nuclei on neighboring chains give multiple harmonic patterns, at a reduced interchain distance. We conclude that the observed ESEEM pattern arises from nuclei on neighboring polyacetylene chains and is closely related to the matrix/distant ENDOR line observed for (13CH)x.

Notes: The magnetic couplings of 17O in H217O coordinated to high spin Mn2+ in a frozen aqueous solution were determined using the complementary magnetic resonance techniques of pulsed and continuous wave (cw) ENDOR (electron nuclear double resonance), ESEEM (electron spin echo envelope modulation), and PFSEPR [pulse field sweep electron paramagnetic resonance (EPR)]. Several complications arise from the high electron spin multiplicity of the d5, Mn2+ ion and the high nuclear spin multiplicity, I=5/2, of the 17O nucleus. At the applied magnetic field strengths in 9 GHz EPR studies, the zero-field splitting of the S=5/2 Mn2+ ion in aqueous frozen solution is small relative to the electron spin Zeeman interaction so that the MS=±1/2,±3/2,±5/2 electron spin states all contribute to the ENDOR spectrum.This results in a complex spectrum in which the 17O ENDOR powder pattern arising from the MS=±1/2 manifolds are separately resolved but the powder patterns from the MS=±3/2,±5/2 manifolds overlap the multiple 1H ENDOR lines arising from all six MS manifolds [X. Tan, M. Bernardo, H. Thomann, and C. P. Scholes, J. Chem. Phys. 98, 5147 (1993)]. Given this complexity, a combination of complementary spectroscopic techniques and numerical simulations are used to deconvolute the overlapping spectra and to assign the spectral lines. The ENDOR spectra provided an experimental description of H217O hyperfine couplings to high spin Mn2+ in a frozen solution. The ESEEM results are consistent with the first-order assignments of the ENDOR lines and demonstrate the feasibility of ESEEM measurements of 17O ligand hyperfine couplings to Mn2+. Simulations of the 17O ENDOR hyperfine patterns of aqueous frozen solutions of Mn2+, especially those near 20 MHz, indicated an A-tensor anisotropy of A⊥=−6.5±0.5 MHz and A(parallel)=−9.5±0.5 MHz, consistent with couplings observed by single crystal ENDOR of H217O ligated to Mn2+ doped in [LaMg(NO2)12⋅24(H2O)]. More detailed simulations of the ENDOR pattern below 10 MHz indicated the need for quadrupole couplings consistent with those measured by single crystal ENDOR and with those determined by gas phase measurements on H17OD. Simulations of the ENDOR spectra recorded by the cw and pulsed techniques have delineated important features of the techniques which must be taken into account for a quantitative analysis of the ENDOR amplitudes. It is expected that the general ENDOR conditions employed and the theory developed will be useful in frozen solution studies of 17O involved as a ligand to Mn2+ in enzymes. © 1995 American Institute of Physics.

Notes: For the water protons that coordinate to Mn2+, the frozen solution ENDOR (electron nuclear double resonance) spectra are made complex by the anisotropic electron–proton hyperfine interaction and by multiple contributions of the electron spin 5/2 manifold. A spin 5/2 Mn2+ ion having magnetic quantum numbers Ms=±1/2, ±3/2, ±5/2 and small zero-field splittings has overlapping electron spin EPR transitions. Proton hyperfine couplings to each of these electron spin states have yielded overlapping ENDOR patterns whose interpretation is nontrivial, even in so simple a system as Mn2+ ion having hexaaquo coordination. We have experimentally obtained and theoretically explained these proton ENDOR patterns and in so doing have laid the foundation for interpreting and sorting out frozen solution ENDOR patterns in more complex (enzyme) environments. Pulsed and cw ENDOR experiments showed features of metal-coordinated water protons occurring not only within a few MHz of the free proton frequency (as will happen for an electron spin 1/2 system) but extending over a range of up to 35 MHz. The EPR line of the Mn2+ S=5/2 manifold was broadened by zero-field splitting for hundreds of Gauss away from g=2.00, and the relative intensity of different ENDOR features reflected couplings to differing Ms spin states at varying fields across this EPR line.An expression was derived to show the dependence of proton ENDOR frequencies on the electron spin quantum number, Ms, upon the principal values of the intrinsic proton hyperfine tensor, upon the direction of the magnetic field, and upon the free proton frequency. This expression provided the starting point for powder simulations of the overall ENDOR pattern. These ENDOR powder pattern simulations were not elementary extensions of first-order theory as often applied to single-crystallike ENDOR spectra obtained at frozen solution EPR extrema. These simulations addressed the interpretation and the conditions for obtaining consistent hyperfine information from nuclei hyperfine coupled to Mn2+ where all Ms levels of the Mn2+ ion can furnish contributions to ENDOR and EPR. The aquo protons yielded an isotropic coupling As=0.8 MHz and a dipolar coupling Ad=3.4 MHz, where A(parallel)=2Ad+As (=7.6 MHz) and A⊥=As−Ad (=−2.6 MHz). Such couplings are in agreement with those obtained by proton ENDOR of [Mn(H2O)6]2+ in single crystals [R. DeBeer, W. DeBoer, C. A. Van't Hof, and D. Van Ormondt, Acta Cryst. B29, 1473 (1973)].