Chapter 4, Problem 4.24P

For ${\text{D}}_{\text{4h}}$ symmetry use sketches to show that ${\text{d}}_{\text{xy}}$ orbitals have ${\text{B}}_{\text{2g}}$ symmetry and that $d_{x^2-y^2}$ orbitals have ${\text{B}}_{\text{1g}}$ symmetry. (Hint: you may find it useful to select a molecule that has ${\text{D}}_{\text{4h}}$ symmetry as a reference for the operations of the ${\text{D}}_{\text{4h}}$ point group. Observe how the signs on theorbital lobes change as the symmetry operations are applied)