Subject Zeeman electronic

Now we can define the anisotropic resonance condition for an S = 1/2 system subject to the electronic 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. 

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 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. 

Subjects of recent publications on the spectroscopic properties and electronic structure of porphyrins include the photochemically induced dichroism of [(aetio)Zn]-,380 the absorption spectra of metallo-TPP compounds in SF , Ar, and n-octane matrices,361 the Zeeman effect in the absorption spectra of Pd-porphin in n-octane single crystals,362 the electronic spectra of Cu11- and Niu-corrin derivatives,363 m.c.d. studies on porphyrins,864 866 photoelectron spectra of porphyrins and pyrroles,366 and quantum mechanical calculations on porphyrins.367 368... 

The experimental spectrum of atomic H shows good agreement with this model, except when it is subjected to a magnetic field, which results in a splitting of the spectrum lines. This phenomenon, also known as the anomalous Zeeman effect, can be explained by assuming that, in addition to its orbital momentum, an electron possesses an intrinsic angular momentum, p, with value p = [s(s + l)y h, where s is the spin quantum... 

If an electron (or nuclear) spin S is subjected to a magnetic field Hq in the direction z then the Zeeman interaction... 

When a spectral line source is subject to a magnetic field, the spectral lines display hyperfine structure (Zeeman effect). In order to explain hyperfine structure it is postulated that the electron rotates on its axis with spin angular momentum S ... 

EMR spectra correspond to transitions among the electronic Zeeman levels, subject to selection rule Amg = 1, Amj = 0 (for all rtij of the system), and it follows that these comparatively large transition energies are difficult to correlate with weak molecular interactions or subtle changes in the nuclear hyperfine energies due to substituent effects. 

---