M.O. Diagram of [Ni(CN)4]2- - Worked Example

The first thing to do is determine the point group of nickel tetracyanide. It is D4h.
Next we look at the group table for D4h, in particular the symmetry operations on the top line.

D4h E 2C4 C2 2C2' 2C2'' i 2S4 sh 2sv 2sd

We now look at the four ligands and work out what happens to them under each symmetry operation to generate the reducible representation.
Under the E operation, all ligands remain in the same place, so the entry is 4. Under the 2C4 and C2 operations, none remain in the same place. Under 2C2', (remember that this axis is along the ligand-metal-ligand bond) 2 ligands remain in the same place. Under 2C2'', i or 2S4 symmetry, none remain the same. All four remain unchanged upon sh reflection, two remain unchanged after each of the 2sv reflections, and none under 2sd.

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