Magnetically coupled systems

At shorter distances occurring for instance in triplet state molecules a quantum mechanical averaging is necessary [35]. The opposite case with 7 -c D occurs for instance in distance measurements with pulsed ESR discussed in Chapter 2. 

The second interaction originates from the electrostatic Heisenberg exchange term in quantum mechanics. The magnitude of the interaction is conventionally denoted by the symbol J. The conventions for the sign of J differ between treatises [7]. In this work the sum of the zero-field and exchange interactions is expressed with a Hamiltonian of the type  

It is convenient to use a resultant effective spin when the S = V2 subunits are identical. It is then assumed that the complex can be treated as a species with S = 1 or 0. The mathematical procedure given in several text-books [20, 27, 35] to obtain the s under those conditions is technical and is not reproduced here. An expression for the exchange interaction can, however, easily be calculated using the relation for the addition of the spin angular moment vectors in quantum mechanics  

Spectrum is centred about the average g, while intermediate spectra with shapes different from the two extreme cases occur when AgixsB/J 1, allowing an estimate of the magnitude of the exchange term. 

The work by Fournel et al. [41] provides an instructional example of the use of multi-frequency ESR to obtain detailed data for a complex biochemical system (a bacterial enzyme), in particular the exchange interaction between a transition metal ion and a radical and the determination of the magnitude and sign of the zero-field coupling. Procedures are described for the less complex biradical systems in the following section. 

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In the case of magnetically coupled systems. Curie relaxation is simply additive as long as the magnetic susceptibility is the sum of the two components. When the magnetic susceptibility is not a simple sum of the components, the magnetic susceptibility contribution of each metal ion should be evaluated. 

There are no treatments for the pseudocontact term, since the orbital part has never been considered when dealing with magnetic coupled systems. However, Eqs. (6.7) and (6.10) hold for the hyperfine splitting in EPR spectra of both solids and solutions [1]. Therefore the same reasoning is likely to apply to the pseudocontact shift as well. The major complication arises from the point-dipolar nature of the pseudocontact shift treatment, which contrasts with the idea of a polymetallic center. 

A species of this type is probably best described as a [Fe - NO ] complex, with a resultant spin S = 3/2 characteristic of a shongly magnetically coupled complex. Magnetically coupled systems exhibiting the combined influence of and an electrostatic interaction termed Heisenberg exchange are discussed in Section 4.5. 

Fig. 5. Temperature dependence of the isotropic shift values calculated in a Fe(II)-Fe(III) magnetic coupled system, with a J coupling constant of 100 cm" (see text) b) Calculated dependence of the isotropic shift values in a Fe(II)-Fe(III) magnetic coupled system, and their ratio broken line) as a function of the J value. Temperature is 303 K...

We would like to stress that any analysis should start using the correct equations derived for the magnetically coupled system. This treatment is quite general and can be applied to both homo- and heterodimers. In the former class we can mention p-oxo diiron (III) porphyrins [4] and dinuclear copper(II) complexes... 

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