Question

When we have a molecule say (Co(NH₂)₆) hypothetically any octahedral molecule it has the point group of Oh and the character table shows the quadratic function such as (z2,2z2−x2−y2) (xy,xz,xy). These let you know about the breaking of degeneracy of orbitals. But for some groups likeC2vthere are functions likex2,y2which don't really correlate to any orbital. What is the significance of such functions?

Answer 1

The quadratic functions in symmetry point group character tables indicate how orbitals transform under symmetry operations, contributing to the symmetry properties of a molecule and instead of representing specific orbitals, they illustrate the influence of ligand fields on orbital energies.

Step-by-step explanation:

The functions like x2 or y2 in the character tables for point groups such as C2v serve to indicate how different types of orbitals or electronic functions transform under the symmetry operations of the point group. In molecular symmetry, the significance of these functions is to show how various orbitals, which may not directly correlate to any physical orbital alone, contribute to the overall symmetry properties of the molecule and interact with ligand fields. For example, in tetrahedral and square planar complexes, the splitting of degenerate d orbitals into sets such as eg and t2g orbitals is influenced by the geometric arrangement and can be analyzed using the character tables in crystal field theory.