High spins spin Hamiltonian parameters

Once a hyperfine pattern has been recognized, the line position information can be summarized by the spin Hamiltonian parameters, g and at. These parameters can be extracted from spectra by a linear least-squares fit of experimental line positions to eqn (2.3). However, for high-spin nuclei and/or large couplings, one soon finds that the lines are not evenly spaced as predicted by eqn (2.3) and second-order corrections must be made. Solving the spin Hamiltonian, eqn (2.1), to second order in perturbation theory, eqn (2.3) becomes 4... 

For relatively simple systems of high symmetry (or for systems assumed to be simple) the system spin Hamiltonian parameters are readily relatable to those of the individual centers, for example,... 

The zero-field spin Hamiltonian parameters, D and E, are assumed to be distributed according to a normal distribution with standard deviations oD and aE, which we will express as a percentage of the average values (D) and (E). -Strain itself is not expected to be of significance, because the shape of high-spin spectra in the weak-field limit is dominated by the zero-field interaction. 

In strong crystalline fields or highly distorted fields a doublet S= state becomes lowest in energy. In this situation there are generally no nearby states, so that g factors are close to 2.0023 and the ESR is observed at higher temperatures. The ESR results can be fitted to Eq. (171) and observed values for the spin Hamiltonian parameters are given in Table XVI. 

Spectroscopies are also used to experimentally probe transient species along a reaction coordinate, where often the sample has been rapidly freeze quenched to trap intermediates. An important theme in bioinorganic chemistry is that active sites often exhibit unique spectroscopic features, compared to small model complexes with the same metal ion.8 These unusual spectroscopic features reflect novel geometric and electronic structures available to the metal ion in the protein environment. These unique spectral features are low-energy intense absorption bands and unusual spin Hamiltonian parameters. We have shown that these reflect highly covalent sites (i.e., where the metal d-orbitals have significant ligand character) that can activate the metal site for reactivity.9... 

Figure 3. (a) Spectrum of N4 in irradiated KN3 for H 1 [100]. The arrows indicate satellite lines, due possibly to exchange-coupled pairs of N4 ions or to N3 ions, (b) Computer simulation of spectrum expected from an molecular ion with spin-Hamiltonian parameters of reference [34]. The simulation predicts lines (indicated by arrows) which agree in position but not intensity with satellite lines in (a). The simulated spectrum also predicts lines at the low- and high-field ends not observed experimentally. 

It should be apparent from the above that considerable information about the magnetic properties of triplet states can be obtained from a zf experiment. Table 6 summarizes the spin Hamiltonian parameters measured for 1-halonaphthalenes (IXN X = Cl, Br, I) in zero field additional parameters are known fi-om the high-field experiments (Kothandaraman et al., 1974b, 1975,1979) and are included for discussion purposes. We also list the parameters of the lowest triplet states of the parent molecule (Hutchison and Mangum, 1961) and its 1-fluoro derivative (Mispelter et al., 1971) for comparison. Measurements of many of the relevant optical properties of these species have been reported (Schwoerer and Sixl, 1969 Sixl and Schwoerer, 1970a Kothandaraman et al., 1975, 1979 Saigusa and Azumi, 1978) and some of these are listed in Table 7. 

The spin Hamiltonian parameters employed were ge = 2.00, D = 0.10 cm E D = 0.25, Ax =120.0, Ay = 120.0, and A = 240.0 x 10 cm . A narrow linewidth was chosen (30 MHz) in order to demonstrate the high efficiency of these schemes. The unit sphere has to be partitioned very finely in order to produce simulated spectra with high signal-to-noise ratios when there is large anisotropy and the spectral linewidths are narrow. 

EPR is used extensively to detect, identify and follow the fate of radicals involved in polymerization or polymer degradation processes. It is also used extensively to characterize polymeric materials in terms of their morphology, heterogeneity, structural transformations, chain dynamics, and so on [2-5]. For this purpose, one can take advantage of the stable paramagnetic centers present in material to be examined (e.g., residual post-polymerization radicals, or TMIs used as catalytic centers or stabilizers). In most cases, however, external spin probes are added, including spin-labeled macromolecules (see Sections 23.2.1.5 and 23.2.2.1) [6]. The sensitivity and high content of structural information contained in the spin Hamiltonian parameters allow to obtain valuable - and often unique - data on the studied systems [7]. 

The Mu spin Hamiltonian, with the exception of the nuclear terms, was first determined by Patterson et al. (1978). They found that a small muon hyperfine interaction axially symmetric about a (111) crystalline axis (see Table I for parameters) could explain both the field and orientation dependence of the precessional frequencies. Later /xSR measurements confirmed that the electron g-tensor is almost isotropic and close to that of a free electron (Blazey et al., 1986 Patterson, 1988). One of the difficulties in interpreting the early /xSR spectra on Mu had been that even in high field there can be up to eight frequencies, corresponding to the two possible values of Ms for each of the four inequivalent (111) axes. It is only when the external field is applied along a high symmetry direction that some of the centers are equivalent, thus reducing the number of frequencies. 

Fd n can be studied in two oxidation states. In the oxidized state the cluster has electronic spin S = H. This spin results fiom antiferromagnetic coupling of three high-spin ferric (Si = 2 = S3 = 5H) iron sites. The magnetic hyperfine parameters obtained from an analysis of the low tempo ture MSssbauer spectra have been analyzed (18) in the frmiework of the Heisenberg Hamiltonian. 

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