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In octahedral complexes, the dz² and dx²−y² orbitals are increased in energy the most. We refer to the dz² and dx²−y² orbitals collectively as the eg d-orbitals. The images below illustrate the orbitals dz² (left) and dx²−y² (right) and their positioning within an octahedral complex. The central transition metal atom or ion is grey, the six ligands are red and the orbitals are yellow.
Let us continue to consider an octahedral complex. The remaining d orbitals, dxy, dxz and dyz see their energy increase to a lesser extent. We refer to the dxy, dxz and dyz orbitals collectively as the t2g d orbitals.
The images below illustrate these three orbitals in relation to the central metal atom and ligands in an octahedral complex. Compare these images of the t2g orbitals with those of the eg above. You may be able to see that the t2g orbitals are, on average, further away from the ligands than the eg orbitals. This is the reason for splitting.
Hybrid orbital theory can be used to describe how metals bond to ligands. When metals bond to ligands, magnetic data shows that some electrons are paired when there is no obvious reason for them to be paired. Molecular orbitals begin to account for this phenomenon by allowing wave functions to interfere in a constructive, low energy (bonding) or destructive, or high energy (antibonding) manner. Thus, the electrons can fill the lowest energy molecular orbitals available to them. However, the electron pairing may be different if the electrons were allowed to fill the lowest energy atomic orbitals available to them.
This diagram shows the field splitting of a metal with ligands in an octahedral configuration. The thick horizontal lines represent atomic orbitals of the metal (left) and ligands (right). The colors correspond to s (black), p (green) and d (red) orbitals. The middle column of horizontal lines represents molecular orbitals made of bonding (lower energy) and antibonding (higher energy) components.
If the ligands are oriented on the cartesian coordinate axes, the metal will still own 3 d orbitals, xy, xz, and xz, which do not intersect (and therefore do not interact) with the ligands. These are considered "nonbonding" orbitals, and are represented by dotted lines in the diagram.