2.7: Solutions to Ligand Field Theory Problems
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Problem 1.
The three orbitals shown above interact a little more strongly with the ligands. The three orbitals shown below interact a little more weakly.
The reason for the difference in the interaction has to do with how close the nearest lobe of a d orbital comes to a ligand. There are really two possible positions: the face of a cube or the edge of a cube. If the ligands are at alternating corners of the cube, then the orbitals pointing at the edges are a little closer than those pointing at the faces of the cube.
Problem 2.
The ligands do not overlap with the d orbitals as well in tetrahedral complexes as they do in octahedral complexes. Thus, there is a weaker bonding interaction in the tetrahedral case. That means the antibonding orbital involving the d electrons is not raised as high in energy, so the splitting between the two d levels is smaller.
Problem 3.
Because the d orbital splitting is much smaller in the tetrahedral case, it is likely that the energy required to pair two electrons in the same orbital will be grester than the energy requied to promote an electron to the next energy level. In most cases, the complex will be high spin.
Problem 4.
The orbitals are shown in order of energy.
