Question

Verify that the symmetry species of the antisymmetric Pd-Cl stretches of trans-[PdCl₂ (NH₃)₂] is B_2u.

Answer 1

by considering the effect of the various elements of the group on the displacement vectors of the Cl ligands.

The elements of D2h are E, C2 (x), C2 (y), C2 (z), i, (xy), (yz), and (zx). Of these, E, C2 (y), (xy), and (yz)

leave the displacement vectors unchanged and so have characters 1.

The remaining operations reverse the directions of the vectors, so giving characters of –1:

E C2 (x) C2 (y) C2 (z) i (xy) (yz) (zx)

1 -1 1 -1 -1 1 1 -1

this set of characters with the D2h character table and establish that the symmetry species is B2u.