Symmetry and crystal field theory

In the present chapter the symbols Aig, A2g, Eg, Tig and T2g will be encountered with a spin state designated, for example, Eg ( doublet ee gee ) and Tig. The lower-case symbols used in Chapter 6 are also of frequent use, so, aig, g, tig 0. Thoso symbols may also have superscripts. We shall refer to ( tee two gee two ), for example when talking about two electrons in a set of t2g orbitals (other books may refer to this as (Gj/) )- Symbols such as tig or t2g) indicate that the set of three orbitals labelled t2g are occupied by three electrons. This usage follows the similar use of s, p and, very important for this chapter, d to indicate an orbital occupancy. One talks of sp( = s p ), d, d, d p and so on as configurations (appropriate to an isolated atom). In just the same way, symbols such as tig, tig, and tlgC refer to electron configurations in (for the examples given) octahedral (0 ) symmetry. 

It often happens that, for isolated atoms, one wishes to discuss all the electrons—or, certainly, the outermost ones—collectively rather than as individuals. One then refers to states or terms and uses uppercase symbols. 

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