Not-so-simple example

Systems with more than one unpaired electron are not only subject to the electronic Zeeman interaction but also to the magnetic-field independent interelectronic zero-field interaction, and the spin Hamiltonian then becomes 

However, we have previously seen in Chapter 5 that the number of elements in the zero-field tensor can be reduced to two (Equation 5.25) by making D traceless, and so the spin Hamiltonian can be written as 

The expression contains squared spin operators, which means that they have to be applied twice to the basic set of spin functions, and, for example, operator Sx2 connects I ms) states that differ by two units. The original set for S = 3/2 is 

It is informative to look at this matrix in zero field (B = 0)  

For axial symmetry (i.e., / = 0) this is a diagonal matrix with only two eigenvalues D and -D and a zero-field splitting AE = D —D = 2D as we have previously noted in 

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