A magneto-theoretical hierarchy

We have seen that mononuclear complexes, with or without the first-order angular momentum, can be theoretically treated in different degrees of complexity. Thus we can speak of some magneto-theoretical hierarchy (Table 8.45). Depending on the basic postulate about the extent of the active space (a space of kets involved in the zero-order Hamiltonian), various levels of the theory can be distinguished. 

Level Description Active space Free parameters Magnetic parameters 

The second-order energy correction arising from the excited states (out of the active space) is given by the standard formula of perturbation theory 

In contrast, when the active space is restricted to the spin-only kets, the influence of all attainable excited states manifests itself in filling the magnetic parameters (tensors). In such a case the g-tensor deviates considerably from the free-electron value, the temperature-independent paramagnetism appears substantial and the spin-spin interaction tensor transforms to high values of the zero-field splitting parameters (D and E). 

A direct comparison of the magneto-chemical g-values with the spectral ESR readings may make a little sense. This can work only when the effective spin approach is of use, or for systems where a Kramers doublet is the only relevant active space (like Cu2+ and V4+ complexes). 

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