Dynamical hyperfine spectra

Figure Bl.4.9. Top rotation-tunnelling hyperfine structure in one of the flipping inodes of (020)3 near 3 THz. The small splittings seen in the Q-branch transitions are induced by the bound-free hydrogen atom tiiimelling by the water monomers. Bottom the low-frequency torsional mode structure of the water duner spectrum, includmg a detailed comparison of theoretical calculations of the dynamics with those observed experimentally [ ]. The symbols next to the arrows depict the parallel (A k= 0) versus perpendicular (A = 1) nature of the selection rules in the pseudorotation manifold.

As we will see in Chapter 4, g-matrices are often difficult to interpret reliably. The interpretation of isotropic g-values is even less useful and subject to misinterpretation. Thus isotropic ESR spectra should be used to characterize a radical by means of the hyperfine coupling pattern, to study its dynamical properties through line width effects, or to measure its concentration by integration of the spectrum and comparison with an appropriate standard but considerable caution should be exercised in interpreting the g-value or nuclear hyperfine coupling constants. 

A number of methods have been developed for assessing nitroxide dynamics based on the cw-EPR spectrum (see review by Sowa and Qin, 2008). In the semiquantitative approach, parameters measured directly from the EPR spectrum, such as the central fine-width (AHpp, Fig. 15.9A), the splitting of the resolved hyperfine extrema (2AeS, Fig. 15.9A), and the second moment (H2, characterizing how broad the spectrum is), are used to characterize nitroxide dynamics (Columbus and Hubbell, 2002, 2004 Mchaourab et al., 1996). These parameters report on the nitroxide mobility, which describes a combined effect of the rate and the amplitude of motion. For example, a broad center fine gives a small (AHpp) 1 value and indicates low mobility, which can result from low frequency but large amplitude motions, or small amplitude motions with fast rates. The line-shape parameters can be easily measured on a properly processed EPR spectrum, and... 

From the point of view of the solvent influenee, there are three features of an electron spin resonance (ESR) speetrum of interest for an organic radical measured in solution the gf-factor of the radical, the isotropie hyperfine splitting (HFS) constant a of any nucleus with nonzero spin in the moleeule, and the widths of the various lines in the spectrum [2, 183-186, 390]. The g -faetor determines the magnetic field at which the unpaired electron of the free radieal will resonate at the fixed frequency of the ESR spectrometer (usually 9.5 GHz). The isotropie HFS constants are related to the distribution of the Ti-electron spin density (also ealled spin population) of r-radicals. Line-width effects are correlated with temperature-dependent dynamic processes such as internal rotations and electron-transfer reaetions. Some reviews on organic radicals in solution are given in reference [390]. 

The e.s.r. and absorption (5-6 kK) spectra of Ir in octahedral sites of Y3Ga50 2 have been obtained, and it was concluded that the properties of the T2 ground state are affected by interaction with higher excited states. The e.s.r. spectrum of K2[Ir(N03)g] in K2[Pt(N03)g], expected to involve a 12-co-ordinated complex of Tj symmetry, has been recorded. An isotropic spectrum was observed at 77 K, so any Jahn-Teller effect of the ground term must be dynamic. The hyperfine constants indicated considerable Md - Lti delocalization. 

Fig. 4 Information from nitroxide CW EPR spectra, (a) Right principal axis system of electron-Zeeman and hyperfine tensors (collinear). Left the effect of rotational dynamics on the CW EPR spectra. Fast rotation (i.e., faster than a typical rotational correlation time of Tc 10 ps) leads to the averaged spectrum. The isotropic g-value gjgo determines the center of the central line and spacing between the lines that is dominated by a- a- In the intermediate motion regime 100 ns > tc > 1 ns and the rigid limit is reached at Tj, 1 ps [19]. (b) Influence of the chemical environment on CW EPR spectra. As both, hydrophilic and polar environments lead to an increased electron spin density at the nitroxide nucleus (see gray inset), and hence the line splitting in the spectra in hydrophilic and polar surroundings is larger than in non-polar and hydrophobic environments...

The interaction of nitric oxide (NO) with metal ions in zeolites has been one of the major subjects in catalysis and environmental science and the first topic was concerned with NO adsorbed on zeolites. NO is an odd-electron molecule with one unpaired electron and can be used here as a paramagnetic probe to characterize the catalytic activity. In the first topic focus was on a mono NO-Na" complex formed in a Na -LTA type zeolite. The experimental ESR spectrum was characterized by a large -tensor anisotropy. By means of multi-frequency ESR spectroscopies the g tensor components could be well resolved. The N and Na hyperfine tensor components were accurately evaluated by ENDOR spectroscopy. Based on these experimentally obtained ESR parameters the electronic and geometrical structures of the NO-Na complex were discussed. In addition to the mono NO-Na complex the triplet state (NO)2 bi-radical is formed in the zeolite and dominates the ESR spectrum at higher NO concentration. The structure of the bi-radicai was discussed based on the ESR parameters derived from the X- and Q-band spectra. Furthermore the dynamical ESR studies on nitrogen dioxides (NO2) on various zeolites were briefly presented. 

In some systems, when an anisotropic spectrum is detected at low temperatures, increasing the temperature leads to averaging of the principal components of the hyperfine and g tensors, and therefore to isotropic spectra. As an example, we show in Figure lb the ESR spectrum at 278 K of VO + in polyacrylamide networks swollen by a water/acetone mixture (80 20 v/v), which consists of eight equally spaced lines of equal intensity (22,23). The height of each line is different, because the dynamical process gives lines with different widths. The experimental spectrum is well reproduced (broken lines) using a theoretical expression for the... 

The dynamical processes described in the previous section take place when the Mossbauer atom physically moves during the lifetime of the Mossbauer nucleus. However, even when the temperature is moderately low in comparison with the melting point of the crystal and diffusive jumps are rather infrequent, there is another source of time-dependent effects which has a strong influence on the spectrum. These arise when the environment of the Mossbauer nucleus changes within its lifetime, thereby altering the frequency coq of the Mossbauer radiation. These processes are usually called relaxation and they occur when the hyperfine interactions, by which the Mossbauer nucleus senses its environment, undergo time-dependent fluctuations. 

The translational motions and spin dynamics of conduction electrons in metals produce fluctuating local magnetic hyperfine fields. These couple to the nuclear magnetic moments, inducing transitions between nuclear spin levels and causing nuclear spin relaxation. The translational motions of electrons occur on a very rapid time scale in metals (<10 s), so the frequency spectrum of hyperfine field fluctuations is spread over a wide range of w-values. Only a small fraction of the spectral intensity falls at the relatively low nuclear resonance frequency (ojq 10 s ). Nevertheless, the interaction is so strong that this process is usually the dominant mode of relaxation for nuclei in metallic systems, either solid or liquid. 

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