The Simple MO Description of Octahedral Complexes

We discuss the situation pertaining to a simple octahedral complex of a M transition metal ion [e.g., MF orMO ). The details have been given many times previously e.g., Refs. (77, 26, 30, 31). Bonding is assumed to place between the metal ion and the ligand ions. The relation of the MO formalism to the configuration interaction description has been discussed by Owen and Thornley (77). 

The filled bonding orbitals of mainly ligand character are  

Because the bonding orbitals are filled they do not directly contribute to the magnetic properties the magnetic interactions associated with transition metal ions reflect the properties of the unpaired electrons in the antibonding orbitals, which have mainly d character. Orthogonal to the bonding orbitals, they may be written  

we see that experiments such as magnetic neutron diffraction and spin resonance which measure X are sensitive to a combination of the covalency admixture parameter y and the overlap integral. However, it has become customary to treat as a measure of the covalency. Clearly this situation is not entirely satisfactory, but may be tolerated in interpretive situations given the other approximations of the model. 

The ligand field splitting A is shown in Fig. 3. From the simple MO model this is given by 

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