Coupling exchange

This term, which has the form shown in eqn (6.1) introduces considerable complication into the shape and interpretation of ESR spectra. 

Further complicating the situation is the fact that the same term can arise from two quite different physical effects electron-electron dipolar interaction and spin-orbit coupling. 

In this section we consider the spin Hamiltonian appropriate to a biradical with weak dipolar coupling and see how ESR spectra of such species should appear. Obviously, it is possible to find triradicals, tetraradicals, etc. treatment of such species is similar, though of course somewhat more complicated. 

The spin Hamiltonian for a biradical consists of terms representing the electron Zeeman interaction, the exchange coupling of the two electron spins, and hyperfine interaction of each electron with the nuclear spins. We assume that there are two equivalent nuclei, each strongly coupled to one electron and essentially uncoupled to the other. The spin Hamiltonian is  

The singlet function corresponds to zero total electron spin angular momentum, S = 0 the triplet functions correspond to S = 1. Operating on these functions with the spin Hamiltonian, we get  

For a binuclear complex with two interacting paramagnetic metals, the Hamiltonian should firstly be defined, which can be written as  

This is a special case of the expression for homonuclear dimers up to S = 5/2 on each centre. 

For S = 5/2, the entire expression (Equation 3.20) is used, but for 5 = 2, the last exponential terms in the numerator and denominator are discarded. For 5 = 3/2, the last two terms are discarded, and so on. Details of the derivation can be found in Kahn.  

Examples of other polynuclear clusters that have more metals, dissimilar metals and/or higher spin metals will be of greater complexity than the simple example above, as they will have a larger number of energy levels to consider and it may be more laborious to specify the correct Van Vleck coefficients for each. The resulting expressions may then involve multiple g values, many exponential terms in the denominator and numerator and appear superficially complex however, the principles for the derivation of such equations are the same as those presented here. Those interested in the methods required to treat the general case are referred to the literature.  

The occurrence of intermolecular interactions and resulting bulk ordering in magnetic materials was discussed in Section 3.2.2. However, it is important to consider the mechanisms by which such interactions occur as such understanding will enable the design and control of new 

To see how triplet-triplet energy transfer can occur, we need to expand Eq. (7.14) to include spin wavefunctions. Let s refine the notation used there so that f) a and cpv, now explicitly denote spatial wavefunctions of molecule 1, 2a and (j)2b denote spatial wavefunctions of molecule 2, and and ff2b denote 

The term which is the one that the Forster theory considers, is called 

Equation (7.34b) indicates that can be appreciable rally if there is a 

In addition to and H12 can include other higher-order terms 

---

Forbes M D E, Closs G L, Calle P and Gautam P 1993 The temperature dependence of the exchange coupling in polymethylene biradicals. Conclusions regarding the mechanism of the coupling J. Phys. Chem. 97 3384-9... 

Forbes M D E 1993 The effect of localized unsaturation on the scalar exchange coupling in flexible biradicals J. Phys. Chem. 97 3390-5... 

In this case, a spin A that was coupled to the a orientation of the B spin may end up, after the exchange, coupled to either a or (3. Because of the Boltzmann distribution, the amounts of a and P orientation are each... 

Figure 10 presents the Curie temperature (T ) vs the TM-content (x) for Co- and Fe-based biaary alloys. Alloying rare-earth elements with small amounts of transition metals (x < 0.2) leads to a decrease ia Curie temperature. This is particularly obvious ia the Gd—Co system where it corresponds to a nonmagnetic dilution similar to that of Cu (41,42). This iadicates that TM atoms experience no exchange coupling unless they are surrounded by a minimum number j of other TM atoms. The critical number is j = 5 for Fe and j = 7 for Co. The steep iacrease of for Co-based alloys with x about 0.7 is based on this effect. 

Finally, carpet plots of efficiency against specific work are shown in Fig. 3.16, for all these plants. The increase in efficiency due to the introduction of heat exchange, coupled with reheating and intercooling, is clear. Further the substantial increases in specific work associated with reheating and intercooling are also evident. 

Singly and doubly excited states of exchange-coupled dimers. H. U. Gudel, Comments Inorg. Chem., 1984, 3,189-204 (28). 

Drillon M, Darriet J (1992) Progress in Polymetallic Exchange-Coupled Systems, some Examples in Inorganic Chemistry. 79 55-100 Duffy JA (1977) Optical Electronegativity and Nephelauxetic Effect in Oxide Systems. 32 147-166... 

It is well known that Hund s rule is applicable to atoms, but hardly so to the exchange coupling between two singly occupied molecular orbitals (SOMOs) of a diradical with small overlap integrals. Several MO-based approaches were then developed. Diradicals were featured by a pair of non-bonding molecular orbitals (NBMOs), which are occupied by two electrons [65-67]. Within the framework of Hiickel MO approximation, the relationship between the number of NBMOs,... 

Stevens, K. W. H. In Magneto-Structural Correlations in Exchange Coupled Systems Willett, R. D., Gatteschi, D. Kahn, O. Eds. Reidel, Dordrecht, 1985, 105. 

Desulforubidin was found in strains of the Desulfomicrobium genus and has been described as the sulfite reductase of this genus. The subunit composition and molecular mass are similar to what was observed for desulfoviridin. However, in desulforubidin all sirohydrochlorins are metalated as proved by Mossbauer spectroscopy (152). The as-isolated protein contains four [4Fe-4S] clusters two of them are exchange-coupled to two paramagnetic sirohemes. 

Bencini, A. Gatteschi, D. EPR of Exchange Coupled Systems Springer Berlin, 1990. 

The two spins 5a and 5b are assumed to be local, associated with the two sites a and b, respectively. The parameter J is the so-called exchange-coupling constant, which expresses the strength of the (super)exchange interaction between the... 

Finally, it is noteworthy that in addition to the isotropic part of spin coupling as treated above, there may also be an anisotropic contribution due to the presence of anisotropic exchange [114] or dipole interaction [106]. In this case, the exchange coupling constant is replaced by a tensor... 

---