Free-ion S and P Terms in Crystal Fields

An S term, like an s orbital, is non-degenerate. Therefore, while the effect of a crystal field (of any symmetry) will be to shift its energy, there can be no question of its splitting. The ground term for the configuration is S. In an octahedral crystal field, this is relabelled Aig, in tetrahedral symmetry, lacking a centre of inversion, it is labelled M]. 

The three p orbitals are directed along the three cartesian axes and so, in an octahedral crystal field, suffer equal repulsion from point charges sited on those axes. The energies of the three p orbitals, therefore, remain degenerate. Similarly, a free-ion P term remains unsplit in octahedral or tetrahedral crystal fields and is labelled Tig or Ti respectively. 

The only spin-triplets arising from the configuration are (ground) and P. The effects of an octahedral or tetrahedral field upon these two terms are summarized in Fig. 3-16. 

We note that three spin-allowed electronic transitions should be observed in the d-d spectrum in each case. We have, thus, arrived at the same point established in Section 3.5. This time, however, we have used the so-called weak-field approach. Recall that the adjectives strong-field and weak-field refer to the magnitude of the crystal-field effect compared with the interelectron repulsion energies represented by the Coulomb term in the crystal-field Hamiltonian, 

A complete description of the effects of a crystal field upon a d ion would include similar analysis of the behavours of all terms arising for that d configuration. Box 3-7 summarizes the case for d, and in Box 3-8, we illustrate a method of using Fig. 3-19 to determine Dq and B values from real spectra. 

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