Non-isotropic exchange in dinuclear systems

The isotropic exchange discussed so far represents only a portion of the total exchange interaction operating in binuclear and oligonuclear systems. 

The zero-field Hamiltonian appropriate for an exchange interaction in the dinuclear system adopts the form of 

In electron spin resonance also the hyperfine (superhyperfine) terms should be considered 

We have assumed that no angular momentum contribution assists. Then the basis set of spin functions consists of the uncoupled set Sa,Msa) Sb, Msb), or the coupled set SA,SB,S,Ms), its size is N = (2Sa + l)(2Ss + 1). Additionally, the orbital angular momentum can be added and then the basis set becomes a direct product of all orbital and spin functions. In a special case, spin delocalisation (double exchange) operates. 

There are two physical limiting cases according to which we should accommodate the computational strategy. 

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Isotropic exchange in heterospin dinuclear complexes differs from the homospin case in that the second-order van Vleck coefficients are also non-zero. The final formula for the magnetic susceptibility resembles the case of the narrow multiplets for mononuclear systems spin-orbit coupling can be formally substituted by spin-spin (exchange) coupling. However, the local atomic g-tensors should be properly combined into the molecular-state g-tensor. 

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