Question

Irreducible representation for cH2cl2

Answer 1

The point group of CH2Cl2 is C2v so we must use the appropriate character table for the reducible representation of the sigma bonding, Γ σ. To determine Γ σ all we have to do is see how each symmetry operation affects the 4 σ bonds in the molecule – if the bond moves, it is given a value of 0, if it stays in the same place, the bond is given a value of 1. Put the sum of the 1’s and 0’s into the box corresponding to the symmetry operation. The E operation leaves everything where it is so all four bonds stay in the same place and the character is 4 (1+1+1+1). The C 2 operation moves all four bonds so the character is 0. Each σ v operation leaves two bonds where they were and moves two bonds so the character is 2 (1+1). Overall, the reducible representation is thus:

C2v	E	C2	σ v (XY)	σ’ v (YZ)
Γ σ	4	0	2	2