Degenerate & non-Degenerate d Orbitals (CIE A Level Chemistry)

• There are five d orbitals in an isolated transition element atom or ion
  • An isolated transition element is one that is not bonded to anything else
• These d orbitals are all at the same energy level (they are equal in energy) and are therefore said to be degenerate orbitals
• When ligands are attached, the transition element ion is not isolated anymore
• The dative bonding from the ligands causes the five d orbitals to split into two sets
• These two sets are not equal in energy and are described as being non-degenerate orbitals

Degenerate orbitals forming non-degenerate orbitals

Upon binding to ligands, the d orbitals of the transition element ion split into two non-degenerate sets of orbitals

• An isolated transition element has five degenerate 3d orbitals
• Upon dative covalently bonding to a ligand, these d orbitals are split into two sets of non-degenerate orbitals

Splitting in octahedral complexes

• In octahedral complexes, there are six ligands arranged around the central metal ion
• The lone pairs of the ligands repel the electrons in the x²-y² and z² orbitals of the metal ion more than they repel the electrons in the 3d_yz, 3d_xz, and 3d_xy orbitals
• This is because the 3d_x2-y2 and 3d_z2 orbitals line up with the dative bonds in the complex’s octahedral shape
• This is because the ligands are attached to or approaching the central metal ion along the x, y and z axes, and the 3d_x2-y2 and 3d_z2 orbitals have lobes along these axes
• The electrons in these two orbitals are closer to the bonding electrons, so there is more repulsion
• This means that when the d orbitals split, the 3d_x2-y2 and 3d_z2 orbitals are at a slightly higher energy level than the other three
• The difference in energy between the non-degenerate d orbitals is labelled as ΔE

Splitting of 3d orbitals in an octahedral complex

The 3d_x²-y² and 3d_z² non-degenerate orbitals are slightly higher in energy than the 3d_yz, 3d_xz and 3d_xy non-degenerate orbitals

Splitting in tetrahedral complexes

• In tetrahedral complexes, there are four ligands arranged around the central metal ion
• The bonding pair of electrons from the four ligands now line up with the 3d_yz, 3d_xz, and 3d_xy orbitals of the central metal ion
• Now, the 3d_x2-y2 and 3d_z2 orbitals lie between the metal-ligand bonds
• Therefore, there is less repulsion with the 3d_x2-y2 and 3d_z2 orbitals
• When the d orbitals split this time, the 3d_x2-y2 and 3d_z2 orbitals are at lower and more stable energy level than the other three

Splitting of 3d orbitals in a tetrahedral complex

The 3d_yz, 3d_xz and 3d_xy  non-degenerate orbitals are slightly higher in energy than the 3d_x²-y² and 3d_z² non-degenerate orbitals