Question

in an octahedral field, the d-orbitals are split into two groups that have the symmetry labels t2g and eg. in a trigonal bipyramidal field, what would be the symmetry label associated with the dx2-y2 orbital?

Answer 1

In a trigonal bipyramidal field, the dx2-y2 orbital would adopt a different symmetry label that is specific to this environment and dependent on the positions of the ligands in relation to the orbitals.

Step-by-step explanation:

In a trigonal bipyramidal field, the dx2-y2 orbital would have a different symmetry label compared to what it has in an octahedral field.

In octahedral complexes, the t2g orbitals (dxy, dxz, and dyz) experience less repulsion as their lobes point between the ligands, whereas the eg orbitals (dx2-y2 and dz2) have lobes that point directly at the ligands, leading to greater repulsion and higher energy.

However, in a trigonal bipyramidal field, the geometry changes so the symmetry labels also change, and therefore, the dx2-y2 orbital does not fit into the eg or t2g labeling scheme.

Instead, it fits into a different symmetry label which is specific to the trigonal bipyramidal environment and needs to be determined based on the axis along which the orbitals orient in relation to the ligand positions.