Limit strong exchange

Consider now the limiting case of strong exchange coupling. When / > > A, R x J, and the 43 and 31 transitions are forbidden. The 42 and 21 transitions are at equal energy and so we have only ... 

Thus in the limit of strong exchange interaction, the resulting spectrum is identical to that which would be observed if one electron interacted with two equivalent nuclei with coupling constant A/2. 

Now consider a concrete example. Suppose we have a nitroxide biradical with aN = 13 G. In the strong exchange limit, we expect a five-line spectrum with a spacing of 6.5 G and the usual 1 2 3 2 1 intensity ratios for two equivalent spin-1 nuclei. In the weak exchange limit, we expect a three-line spectrum with a spacing of 13 G and intensity ratios 1 1 1. In intermediate cases, up to 15 lines are expected, as shown in Figure 6.1. 

Fig. 2. Magnetic-field dependence of the transmittance of the device shown in Fig. 1 for the limiting cases of a) weak and b) strong exchange coupling between dot and leads. The period AH and the width SH of the dips are given by Eqs. (21) and (20) for case a) and SH is given by Eq. (24) for the case b).

Fluoride Complexes. Fluoride is known to complex plutonium strongly, but quantitative data on these environmentally important complexes are limited. Cation exchange studies (17) yielded values of 4.5 X 10 at I = 1 M and 7.9 X 10 at I = 2 M for -the stability constant of the monofluoro complex of plutonium(IV), which are in satisfactory agreement with the value 1.2 X 10 obtained from... 

In the case of a strong exchange limit ( JAB is large) the classification of the field-dependent molecular states as slightly perturbed zero-field states 5, Ms) is fully justified. Consequently the replacement theorem holds true for S = S and the irreducible tensor operators containing the operator variable V can be substituted for those containing 5 as a variable. The spin Hamiltonian is somewhat different for each manifold of the spin 5, hence... 

The above formula for the matrix elements of the Zeeman operator has a general validity irrespective of strong or weak exchange limits. Of frequent interest is the case of the strong exchange limit when the total spin S becomes a proper quantum number. 

In the case of the strong exchange limit the spin Hamiltonian adopts the form of... 

In the limit of the strong exchange coupling the matrix elements of d- and e-type are neglected. The molecular-state ZMensors are composed with the help of Table 11.6, as follows ... 

The local magnetic parameters can be combined to yield the molecular-state parameters, particularly the -tensors and D -tensors. These are useful when one works in the limit of strong exchange coupling. 

Ea. corresponds to the stabilization energy. The exchange field is much stronger than the CEF effect. However, in a more advanced approach (see e.g. Stefahski and Kowalczyk 1991) additional CEF parameters 5°, 5°, etc., are involved in a definition of the phenomenological anisotropy constants. In the strong exchange limit valid for the ThMni2-type compounds the anisotropy constants are as follows ... 

Certainly the clearest conclusion from the examples of this chapter is the total absence of sharp features in the inelastic response function of anomalous lanthanide and metallic actinide materials. This contrasts strongly with the sharp dispersionless crystal-field excitations observed in most lanthanide compounds, in which the exchange interactions are weak (fig, 2), and with the sharp spin-wave excitations found in systems with strong exchange interactions. In many of the early studies with neutron inelastic scattering, for example of the heavy lanthanides or transition metals and their compounds, the width of the excitations was never an issue. It was almost always limited by the instrumental resolution, although it should be stressed that this resolution is relatively poor compared to that obtained by optical techniques. However, the situation is completely different in the materials discussed in this chapter. Now the dominant factor is often the width indeed in some materials the width of the over-damped response function is almost the only remaining parameter with which to characterize the response. 

Figure B2.4.5. Simulated lineshapes for an intennolecular exchange reaction in which the bond joining two strongly coupled nuclei breaks and re-fomis at a series of rates, given beside tlie lineshape. In slow exchange, the typical spectrum of an AB spin system is shown. In the limit of fast exchange, the spectrum consists of two lines at tlie two chemical shifts and all the coupling has disappeared.

Boron Removal. Boron [7440-42-8] is occasionaHy present in water suppHes at an unacceptable level. It cannot be removed with the standard anion-exchange resins unless the water is deionized. Selective removal is possible by using an anion exchanger functionalized with /V-methy1g1ucamine [6284-40-8]. This resin is in limited commercial supply. The borate form of conventional strong base anion exchangers is used in some nuclear reactors to adjust the concentration of boron in water used as a moderator. The resin releases boron as the water temperature rises. 

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