Notation crystal field theory

Tables of compatibility relations for the simple cubic structure have been given by Jones (1962, 1975), and similar tables can be compiled for other structures, as shown by the examples in Tables 17.2 and 17.5. Compatibility relations are extremely useful in assigning the symmetry of electronic states in band structures. Their use in correlation diagrams in crystal-field theory was emphasized in Chapters 7 and 8, although there it is not so common to use B SW notation, which was invented to help describe the symmetry of electronic states in energy bands in crystals (Bouckaert el al. (1936)).

The notation Dq has mathematical origins in crystal field theory. We prefer the use of Ao because of its experimentally determined origins (see Section 20.6). 

It is a merit of crystal field theory that, in principle at least, values of Aoct can be evaluated from electronic spectroscopic data (see Section 21.7). Consider the complex [Ti(OH2)6], for which the ground state is represented by diagram 21.2 or the notation t2g e. ... 

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