Correlation Table for O_h

This table shows how all of the irreducible representations in the point group O_h transform upon going to lower symmetry.  For example,  the irreducible represenation T_2g in O_h, becomes A₁+ B₁+ B₂ in C_2v.  This is used to predict how decreasing the symmetry of a molecule or ion causes its electronic states to split.  For the d⁹ Cu²⁺ ion the excited state is ²T_2g in O_h, but when this ion undergoes a Jahn-Teller distortion to D_4h symmetry (axial elongation) the ²T_2g state splits into ²B_2g and ²E_g states.   Note that group theory only tells us that the ²T_2g must split, but doesn't tell us which of the new states is lowest in energy; we need ligand field or crystal field theory for that.  Also note that lowering the symmetry did not affect the spin. Click here to obtain this file in PDF format (suitable for printing).