Powder ESEEM

OPTESIM The OPTESIM toolbox enables automated numerical simulation of powder ESEEM for arbitrary number (N) and type (I, n) of coupled nuclei, and arbitrary mutual orientations of the hyperfine tensor principal axis systems. The toolbox is based on the Matlab environment, and includes the following features ... 

Simulation of powder ESEEM spectra is usually performed by a numerical integration over the magnetic field directions. Frequently used Equations [54, 57, 61, 82-85] are reproduced below. Angular selection can be taken into account in a manner analogous to that used in powder ENDOR simulations. 

None directly the MHQ technique yields a frozen powder, which can be analyzed by various types of low-temperature spectroscopy like X-, Q-band EPR, UV-Visible spectroscopy, resonance Raman and potentially or in the near future by MCD, Mossbauer, ESEEM, ENDOR, EXAFS, W-, D-band EPR, MAS-NMR and FTIR spectroscopy. 

Fig. 2.20 (a) 2-pulse ESEEM from CO2 radicals in an X-irradiated powder of lithium formate. The echo envelope shows modulations due to Li ions adjacent to the COf radicals. The smooth dashed curve shows an exponential decay with the phase memory time Tu (b) FT-tiansform of (a), (c) 2-pulse sequence employed in the experiment (Data provided by Dr. H. Gustafsson)... 

ENDOR and FT ESEEM spectra differ mainly in the intensities of the lines, which in ESEEM are given by a factor related to the ESR transition probabilities. A necessary prerequisite for modulations in the time domain spectrum is that the allowed Ami = 0 and forbidden Ami = 1 hyperfine lines have appreciable intensities in ESR. The zero ESEEM amplitude thus predicted with the field along the principal axes of the hyperfine coupling tensor is of relevance for the analysis of powder spectra. Analytical expressions describing the modulations have been obtained for nuclear spins I = V2 and / = 1 [54, 57] by quantum mechanical treatments that take into account the mixing of nuclear states under those conditions. Formulae are reproduced in Appendix A3.4. 

The following examples were selected to show the types of information that can be obtained by ENDOR and ESEEM studies of metal ions in randomly oriented (powder) samples. 

More advanced experiments, such as ENDOR, electron spin echo envelope modulation (ESEEM), or relaxation measurements by pulsed ESR rely on a selective excitation of spins close to the resonance field. Usually, the powder ESR spectrum is much broader than the excitation bandwidth of the pulses, which is in the range between 2 and 10 G. In cases where one anisotropic interaction dominates the spectrum, the experiments thus select contributions only from certain orientations of the molecule with respect to the external magnetic field. Such orientation selection is more efficient and easier to interpret at a field that is high enough for the g anisotropy to dominate. Finally, the size of mw resonators scales with wavelength and thus scales inversely with frequency. At higher frequency, spectra can thus be measured with much smaller sample volumes, yet the concentration does not need to be significantly increased. 

While ENDOR lines correspond fairly well to powder patterns and exhibit clear line shape singularities, this is not the case for ESEEM lines. The reason can be seen in Eq. 16 modulation depth depends on orientation and vanishes at the 9=90° singularity of a powder pattern as well as at the 0 = 0° outer edge (cf. Eig. 2a). Furthermore, ESEEM spectra usually cannot be properly phased and have to be displayed as magnitude spectra rather than absorption spectra. The combination of these problems makes line shapes in ID ESEEM spectra unreliable and hard to simulate. Line shape analysis in ID ESEEM spectra is therefore strongly discouraged. One-dimensional ESEEM spectra are useful for well-defined coordination environments in transition metal complexes, in particular, if single crystals are available. This situation is, however, unusual in polymer applications. 

Advanced EMR methods may be used to conduct quantitative measurements of nuclear hyperfine interaction energies, and these data, in turn, may be used as a tool in molecular design because of their direct relation to the frontier orbitals. The Zeeman field dependence of hyperfine spectra enables one to greatly improve the quantitative analysis of hyperfine interaction and assign numeric values to the parametric terms of the spin Hamiltonian. Graphical methods of analysis have been demonstrated that reduce the associated error that comes from a multi-parameter fit of simulations based on an assumed model. The narrow lines inherent to ENDOR and ESEEM enable precise measures of peak position and high-resolution hyperfine analyses on even powder sample materials. In particular, ESEEM can be used to obtain very narrow lines that are distributed at very nearly the zero-field NQI transition frequencies because of a quantum beating process that is associated with... 

Electron Spin Echo Envelope Modulation (ESEEM) and pulse Electron Nuclear Double Resonance (ENDOR) experiments are considered to be two cornerstones of pulse EPR spectroscopy. These techniques are typically used to obtain the static spin Hamiltonian parameters of powders, frozen solutions, and single crystals. The development of new methods based on these two effects is mainly driven by the need for higher resolution, and therefore, a more accurate estimation of the magnetic parameters. In this chapter, we describe the inner workings of ESEEM and pulse ENDOR experiments as well as the latest developments aimed at resolution and sensitivity enhancement. The advantages and limitations of these techniques are demonstrated through examples found in the literature, with an emphasis on systems of biological relevance. 

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