ESR powder spectra

ESR is applied for the analysis of anisotropies of g- hyperfine and (for S Vi) the zero-field splitting tensors of powder samples under the same conditions as for single crystals. 

The g-anisotropy of organic free radicals is small, often more pronounced for inorganic radicals, and significant in many transition metal ion complexes. Whether or not g-anisotropy is resolved in a powder spectrum depends on the difference between the -components, the linewidth, and the frequency band of the spectrometer. 

Axial symmetry The simplest case to analyse is that with an axially symmetric -tensor, which gives rise to a spectram of the type shown in Fig. 3.14. It has several characteristic features  

Approximate axial g-tensors are frequently observed for transition metal ion complexes. Inorganic radicals can also have appreciable axial g-anisotropy. This property is of value for the assignment of ESR powder spectra in applied studies. Carbon dioxide radical anions, CO2, and related species contribute for instance to the ESR signal used for geological dating [21] see Chapter 9. The ESR spectrum of this anion has also been employed as an indicator that a certain foodstuff has been irradiated, for dosimetric purposes in certain carboxylic acid salts, and as a component in tooth enamel samples used in retrospective dosimetry. 

The X-band spectrometers employed in those applications result in powder spectra that are usually not completely resolved, resulting in less accurate visual determination of the anisotropic g-factors. Spectra of the type in Fig. 3.15 are usully analysed by line shape simulations (see Section 3.4.1.7) when more accurate anisotropic g-values are of interest. The values obtained by this method in Fig. 3.15 are in the range typical for COJ radical anions, although also other species may contribute to the signal. 

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For (35 R = R = COjMe) the ESR powder spectra turned out to be very sensitive to the dihedral angle of the carbonyl oxygen with respect to the ring plane (cf. quantum chemical calculations Section 4.12.2). A very small discrepancy between the angles for both C=0 groups caused spin densities on both S atoms to diverge strongly and hence S lines in the spectrum to be considerably... 

For the Pd compound [46], since gPd is rhombic whereas gPer is isotropic, a rhombic g tensor is the result. The principal values of the averaged tensor are g, = gPer + x(g, - gPcr), where x is the fraction of interacting Pd spins in the sample and i = 1,2,3 refer to the principal values of isolated [Pd(mnt)2] species. The combined analysis of the ESR powder spectra (with each of the three g, values) and the static susceptibility made possible the separation of the contributions to Xper and Xpspin susceptibility Xper was considered to be the same. 

A COMPUTER ANALYSIS OF ESR POWDER SPECTRA OF SILVER AND SODIUM CLUSTERS IN MOLECULAR SIEVES... 

An iterative computer program for the optimization of ESR powder spectra is described. Its applicability to metal clusters is demonstrated. Spectra of silver and sodium clusters in zeolites are generally recognized to be composed of two isotropic signals metallic and ionic. An accurate iterative refinement requires introduction of a third underlying signal and dependence of the linewidth on the quantum number M,. 

The detained analysis of ESR powder spectra, as presented in this paper, has two advantages. (1) Reliable parameters of the paramagnetic species are obtained, which may be subjected to profound theoretical analysis. In that way a cluster-surface interaction may be established. (2) Quantitative measurements of overlapping signals are possible, as demonstrated for Na-clusters in this paper. This is important chemical information as only the metallic clusters are catalytically active [22],... 

Fig. 4.11 Simulated S = 2 ESR powder spectra at X- and W-bands for rfs parameters D = 0.200 cm and E = 0.0314 cm . Spectra are reproduced from [29] with permission from Springer...

Measurements at a higher frequency made it possible to obtain good resolution of the spectrum with respect to the g-anisotropy. Figure 7.27 shows the variation with temperature of the ESR powder spectra of peroxy radicals trapped in FIFE. The following principal values of the g-tensor were obtained at 77 K from the line shape of these spectra g3 = 2.038, g2 = 2.007 and gi = 2.002 gi was considered to correspond approximately to g//, while g2 and g3 represent gx. On the other hand, the spectrum measured at room temperature (Eig. 7.27(a)) was split into two components. The symmetric component (thin line) was attributed to the peroxy radical which had enough motional freedom to average out the entire anisotropy in g-tensor. 

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

It is important to note that even without hyperfine data, the powder spectra give valuable information about the carrier of the ESR spectrum. Both the molecular symmetry of the molecule and the effective distance between the unpaired electrons usually can be deduced from the spectra. 

B. Analysis of Experimental ESR Spectra Detailed accounts of interpretation and analysis of complex ESR spectra have been given by many authors (95,101,102) but there are certain aspects which are worth repeating here. We shall be concerned in this section with only isotropic and powder spectra since these are the most likely spectra a photochemist will... 

Fig. 4.9. Calculated powder pattern ESR absorption spectra for an axial defect such as the dangling bond, showing the effect of disorder broadening (increasing values of ga/Ag). The spectra are calculated using the g-values obtained from the crystalline Si-SiOj interface (Street and Biegelsen 1984).

We close this discussion by observing that Cu and Cu nuclei are usually not resolved in the ESR spectra of calcined Cu -zeoHtes. Both nuclei have spin 7= 2, have relative abundancies of respectively 69.2% and 30.8% and differ slightly in their nuclear Bohr magneton values and quadrupolar moment values. These values are respectively for Cu and Cu ] n( Cu)=3.743x10 J T" ]3n( =Cu)=4.005x 10-27 j. j-i. q(63cu)=-0.222 exlO cm and Q ( =Cu)=-0.195 ex 10 24 cm2.s iaU differences are often not resolved in the broad powder spectra. 

Paramagnetic species with g-factor and hyperfine coupling anisotropy were analysed by simulations at an early stage in frozen solutions of, for instance, copper enzymes [25]. In this section the powder spectra of two well-known species, the NO2 molecule and the isotope labelled COj anion radical are used to illustrate visual and simulation procedures for the analysis. The reader is referred to the classical textbook by Carrington and McLachlan [1] for an account of the electronic structures of these isoelectronic molecules (23 electron system) based on ESR data. 

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. 

Rgure 1 First-derivative powder and single crystal (at four orientations) X-band ESR spectra of copper(ll) in CaCd(CH3-COO)4 - 6H2O. The powder spectra show that parallel (II) features are absorption-like and they correspond to the 0 = 0° orientation in the crystal spectra. (Reproduced with permission from Pilbrow JR (1990) Transition Ion Electron Paramagnetic Resonance. Oxford Clarendon Press, Oxford University Press.)... 

In a macroscopically isotropic sample (all molecular orientations have the same probability), the spectrum consists of contributions from aU orientations when the rotational motion is frozen on the time scale of the experiment. As ESR lines are derivative absorption lines, negative and positive contributions from neighboring orientations cancel. Powder spectra are thus dominated by contributions at the minimum and maximum resonance fields, and by contributions at resonance fields that are common to many spins. The latter contribution provides the center line in the nitroxide powder spectrum (Fig. 3b). It corresponds mainly to molecules with nuclear magnetic quantum number rrii = 0 (center line of all triplets, only g-shift). The detailed shape of this powder spectrum can be simulated, but interpretation is not easy, mainly because hyperfine and g anisotropy are of similar magnitude. 

Fig. 4. Powder line shapes in continuous wave (CW) ESR (derivative absorption spectra) and echo-detected ESR (absorption spectra), (a) Rhombic g-tensor. (b) Axial g-tensor. (c) Axial hyperfine coupling tensor with dominating isotropic contribution.

SIMPOW6 A Software Package for the Simnlation of ESR Powder-Type Spectra... 

The position of an ESR line is usually determined as the point where the derivative spectrum crosses the zero level. For asymmetric lines in powder spectra the points of maximum and minimum derivative are also often determined. The precision of the measurements depends on the width of the line and the noise level. 

Solid-state, esr spectra of [Cu(Et2dtc)] and [Cu S2P(OPr )2 2] dissolved in coordinating and noncoordinating solvents have been compared with single-crystal and powdered samples diluted with the corresponding complexes of divalent nickel and zinc. With noncoordinating... 

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