Effective spin

It is relevant to note at this point that, because the metal ions are isoelcctronic, the spectra of low-spin Fe complexes might be expected to be similar to those of low-spin Co ". However, Fe" requires a much stronger crystal field to effect spin-pairing and the ligands which provide such a field also give rise to low-energy charge-transfer bands which almost always obscure the d-d bands. Nevertheless, the spectrum of the pale-yellow [Fe(CN)f,] shows a shoulder at... 

P/h can be interpreted as an effective spin density of this open shell system. Similarly to the electron binding exjvession there is no first order contribution in the correlation potential, that is, = 0, so that 5 is correct through second order. However, the second order correction in the electron correction for... 

If the electric quadrupole splitting of the 7 = 3/2 nuclear state of Fe is larger than the magnetic perturbation, as shown in Fig. 4.13, the nij = l/2) and 3/2) states can be treated as independent doublets and their Zeeman splitting can be described independently by effective nuclear g factors and two effective spins 7 = 1/2, one for each doublet [67]. The approach corresponds exactly to the spin-Hamiltonian concept for electronic spins (see Sect. 4.7.1). The nuclear spin Hamiltonian for each of the two Kramers doublets of the Fe nucleus is ... 

The effective spin Hamiltonian for energetically well isolated and orbitally nongene-rate ground states of transition metal ions with spin S is generally given by [1, 41, 103] ... 

Any set of energetically well-isolated levels can be described by an effective spin Hamiltonian operator by choosing S to match the corresponding number of levels. This can be just one isolated Kramers doublet of a high-spin multiplet if the... 

In the 5 d series however it is possible to derive additional information bearing upon the problem of the relative extent of central field and symmetry restricted covalency. For many 5 d complexes reasonable estimates of the effective spin-orbit coupling constant can be derived from the spectra, and thence the relativistic ratio, / (= complex/ gas). When both f) and / are known for a given system, Jorgensen (74) has suggested how estimates of both covalencv contributions may be made. 

We have not as yet however treated the charge-transfer data available for complexes of the 5 d series. For these latter species though the effective spin-orbit coupling constants are often of the order of 3 kK. or more, as compared with only about 1 kK. for Ad systems, and smaller values still for the 3d elements. Consequently, as for the d—d transitions it is often necessary explicitly to consider relativistic effects in the interpretation of charge-transfer spectra, and in particular to make allowance for the changes in spin-orbit contributions which may accompany a given di transition. In fact one of us has shown (18) that these changes are... 

Another approach to this problem is a search for the other more effective spin traps. Frejaville et al. [23] demonstrated that the half-life of spin-adduct of superoxide with 5-(diethoxyphosphoryl)-5-mcthyl-l -pyrrolinc-/V-oxide (DEMPO) is about tenfold longer than that of DMPO OOH. Despite a much more efficiency of this spin trap, its hydrophilic properties limit its use for superoxide detection in lipid membranes. Stolze et al. [24] studied the efficiency of some lipophilic derivatives of DEMPO in the reaction with superoxide. These authors demonstrated a higher stability of superoxide spin-adducts with 5-(di- -propoxypho-sphoryl)-5-methyl-1 -pyrrolinc-A -oxidc (DPPMPO) and 5-(di- -butoxyphosphoryl)-5-methyl-... 

Figure 8 In Kadanoff s construction the spin lattice (left), divided into blocks (centre), is equivalent to a new lattice of effective spins (right).

In Kadanoff s [130, 131] two-dimensional block-spin model four neighbouring spins are assumed to have identical spins, either up or down, near the critical point. The block of four then acts like a single effective spin. The lattice constant of the effective new lattice is double the original lattice constant. The coherence length measured in units of the new lattice constant will hence be at half of its original measure. Repetition of this procedure allows further reduction in by factors of two, until finally one has an effective theory with = 1. At each step it is convenient to define renormalized block spins such that their magnitude is 1 instead of 4. The energy of such blocked spins is... 

Nuclear Overhauser Effect, Spin-spin coupling and Chemical Shift... 

It is natural that the participation of N02 and NO+ in the one-electron oxidation puts forward the target of NO2 and NO determination. The direct determination of these gaseous products presents some problems. IR spectroscopy is a method (see, e.g., Todres et al. 1988), but this method is not always convenient or even available. The direct determination of NO2 and NO by ESR spectroscopy is not possible owing to the short relaxation time, which gives rise to broad absorption lines. Spin trapping of NO combined with ESR is recommended for this purpose (Norby et al. 1997). As an effective spin trap for NO2, poly(2-vinylpyridine) has been recently proposed (Davydov et al. 2006). 

The fonrth example in Scheme 3.64 puts forward the most stable cation-radical of hexaaza-octadecahydrocoronene (Miller et al. 1990). This cation-radical is characterized by effective spin delocalization with the participation of all its six nitrogen atoms. Interestingly, the parent neutral compound gives not only the cation-radical, but also the dication, tri(cation)-radical, and even tetracation. All of these cationic forms are stable and their crystal structures were described. 

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