The two orbitals of higher energy have their maximum electron density along the x, y, and z axes. These are the dx2-y2 and the dz2 orbitals. The other three degenerate orbitals have their maximum electron density concentrated between the axes, dxy, dxz, and dyz. As a ligand approaches along the x, y, or z axes a much greater interaction occurs between the electrostatic fields alined along the axes compared to those between the axes. The result is the higher energy of the dx2-y2 and the dz2 orbitals. The energy difference is known as crystal-field splitting.

Two types of complexes are known for cations of the transition metals: high-spin and low- spin. A high-spin complex has a large number of unpaired electrons. The electrons are arranged in the orbitals according to Hund's rule. Therefore, the electrons are distributed into all of the orbitals and the crystal-field splitting is small. If a small number of unpaired electrons exist, they will pair in the orbitals of lower energy. Electrons will not enter into the higher energy orbitals until those of lower energy are filled. The result is a greater energy difference between the two sets of orbitals.

Crystal field theory is employed to study the formation of many of the complexes observed with transition metals. This is a good model to conceptualize the orientations of the d orbitals and the basis behind the observed energy differences. However, the theory does also have weaknesses. The primary weakness is the original assumption to treat the complex as if the bonds are primarily electrostatic. This hinders the existence of molecules that are only slightly polar to exhibit behavior as ligands. A more extensive theory would have to be applied. Ligand- field theory is more sophisticated in that it accounts for covalent as well as ionic bonds and can better explain the behavior of complex ions.



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