Subject Zeeman

Let us rewrite the resonance condition of an S = 1/2 system subject to the Zeeman interaction only as... 

Systems with more than one unpaired electron are not only subject to the electronic Zeeman interaction but also to the magnetic-field independent interelectronic zero-field interaction, and the spin Hamiltonian then becomes... 

For biomolecular S = 1/2 systems subject to central hyperfine interaction the intermediate-field situation (B S S I) is not likely to occur unless the micro-wave frequency is lowered to L-band values. When v = 1 GHz, the resonance field for g = 2 is at B = 357 gauss. Some Cu(II) sites in proteins have Az 200 gauss, and this would certainly define L-band EPR as a situation in which the electronic Zeeman interaction is comparable in strength to that of the copper hyperfine interaction. No relevant literature appears to be available on the subject. An early measurement of the Cun(H20)6 reference system (cf. Figure 3.4) in L-band, and its simulation using the axial form of Equation 5.18 indicated that for this system... 

An—at least, theoretically—simple example is the S = 1 system in weak-field subject to a dominant zero-field interaction and a weakly perturbing electronic Zeeman interaction (similar to the S = 2 case treated above). The initial basis set is... 

Note that the Zeeman interaction for a cubic system results in an isotropic g-value, but the combination with strain lowers the symmetry at least to axial (at least one of the 7 -, 0), and generally to rhombic. In other words, application of a general strain to a cubic system produces a symmetry identical to the one underlying a Zeeman interaction with three different g-values. In yet other words, a simple S = 1/2 system subject to a rhombic electronic Zeeman interaction only, can formally be described as a cubic system deformed by strain. 

Let us calculate the frequencies of transitions between Zeeman eigenstates s) and r), assuming that the nuclei are only subjected to an isotropic chemical shift and the first- and second-order quadrupolar interaction. As seen in Sect. 2.1, the Hamiltonian that governs the spin system in the frame of the Zeeman interaction (the rotating frame) is... 

While NMR has been a strong characterization tool for polymers for many years, it has increased in its usefulness because of continually improved instrumentation and techniques. When a nucleus is subjected to a magnetic field, two phenomena are observed Zeeman... 

Fig. 3. Energy level diagram for a spin f nucleus showing the effect of the first-order quadrupolar interaction on the Zeeman energy levels. Frequency of the central transition (shown in bold lines) is independent of the quadrupolar interaction to first order, but is subject to second-order quadrupolar effects (see text).

Tibben, M.M., Rademaker-Lakhai, J.M., Rice, J.R., Stewart, D.R., Schellens, J.H.M., Beijnen, J.H. Determination of total platinum in plasma and plasma ultrafiltrate, from subjects dosed with the platinum-containing N-(2-hydroxypropyl)methacrylamide copolymer AP5280, by use of graphite-furnace Zeeman atomic-absorption spectrometry. Anal. Bioanal. Chem. 373, 233-236 (2002)... 

Low-spin Fe(iii) porphyrins have been the subject of a number of studies. (638-650) The favourably short electronic spin-lattice relaxation time and appreciable anisotropic magnetic properties of low-spin Fe(iii) make it highly suited for NMR studies. Horrocks and Greenberg (638) have shown that both contact and dipolar shifts vary linearly with inverse temperature and have assessed the importance of second-order Zeeman (SOZ) effects and thermal population of excited states when evaluating the dipolar shifts in such systems. Estimation of dipolar shifts directly from g-tensor anisotropy without allowing for SOZ effects can lead to errors of up to 30% in either direction. Appreciable population of the excited orbital state(s) produces temperature dependent hyperfine splitting parameters. Such an explanation has been used to explain deviations between the measured and calculated shifts in bis-(l-methylimidazole) (641) and pyridine complexes (642) of ferriporphyrins. In the former complexes the contact shifts are considered to involve directly delocalized 7r-spin density... 

In order to use the Zeeman effect for background correction [306] several approaches can be applied (Fig. 87) [307]. A magnetic field around the primary source or around the atom reservoir can be provided, by which either the atomic emission lines or the absorption lines are subjected to Zeeman splitting. Use can be made of a constant transverse field and the absorption for the it- and the -components measured alternately with the aid of a polarizer and a rotating analyzer. However, an ac longitudinal field can be used and with the aid of a static polarizer only the cr-components are measured, once at zero and once at maximum field strength. 

In order to limit the size of the book, we have omitted from discussion such advanced topics as transformation theory and general quantum mechanics (aside from brief mention in the last chapter), the Dirac theory of the electron, quantization of the electromagnetic field, etc. We have also omitted several subjects which are ordinarily considered as part of elementary quantum mechanics, but which are of minor importance to the chemist, such as the Zeeman effect and magnetic interactions in general, the dispersion of light and allied phenomena, and most of the theory of aperiodic processes. 

The extent to which ring currents and local effects contribute to the anisotropy is a subject of discussion (see Pople,73 Davies,74 Dailey,78 Musher76). Recently Flygare el al.77 sa examined the rotational Zeeman... 

A very useful technique which has recently been developed for Fe work, although its application is more general, is the use of polarised radiation. It is convenient to discuss the subject here, but the reader is advised to refer to the appropriate sections in later chapters for more detailed discussion of the spectra of some of the materials mentioned. Polarisation of the emitted y-ray was first shown in 1960 [36], and can take place by the Stark and Zeeman effects already familiar in optical polarisation studies [37]. 

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