Xylylene -Mn dmpe

Since we know that the hyperfine matrix major axis is not a g-matrix principal axis, we can immediately reject hybrids 1, 3, 4, 7, 8, and 10 for which the major axis is a common axis. Hybrids 2 and 6, 5 and 9, and 11 and 12 differ 

Straightforward application of eqns (4.24) yields a hyperfine matrix that can be diagonalized by rotation about the y-axis by the angle /  

The y-matrix can be written in relatively simple form if we assume that the only MOs close enough in energy to contribute significantly are the filled MOs, primarily dxz and dyz in character. With this assumption, we obtain a matrix which can be diagonalized by rotation about the y-axis by fl,  

For reasonable values of the hybridization ratio, b/a up to about 0.5, fj and fV can differ by only a few degrees and this kind of hybrid cannot explain the matrix axis non-coincidence. Following the same reasoning with x and y interchanged, exactly the same conclusions can be reached for hybrid 2. Flybrids 11 and 12 are  

Diagonalization requires rotation about the y-axis by the angle / ,  

---