Spin Sublevels of dd States

We first discuss the dd states that are localized on the central metal ion. Since the electronic wavefimctions are localized on the central metal ion, the wavefunc-tions and energies may be obtained in a manner essentially identical to the atomic case. However, the following differences should be noted. First, because of the loss of the central symmetric nature, quantum numbers such as I and are no longer good quantum numbers. Therefore, characterization of states in terms of these quantum numbers is no longer possible. For example, in an atomic case, sublevels are very simply described in terms of the quantum number , and the energy separation is governed by the Lande interval rule [1] however, such a rule does not exist for meal-localized states of transition metal complexes. 

Second, due to the crystal field the five-fold degeneracy of the d atomic orbital is partially lifted, and fiiis symmetry breakdown results in a rather large effect in the splitting of the levels. 

Even though the quantum numbers I and lose their meaning in the case of the metal complex, symmetry properties based on group theory can be used to classify the states and to simplify the theory. Theoretical treatment of dd states may be slightly different depending on the symmetry and the number of d-elec-trons. In the following, we restrict ourselves to the symmetry of O. We will illustrate the theories for systems of one d-electron and of six d-electrons. 

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