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Ligand Field Theory

The mutual interaction between bonding electron pairs is the same for transition metal compounds as for compounds of main group elements.

All statements concerning molecular structure apply equally. However, non bonding valence electrons behave differently. For transition metal atoms these generally are d electrons that can be accommodated in five d orbitals.
The modified crystal field theory which admits that there is some covalent as well as electrostatic interaction between the ion and its neighbors, is called ligand field theory.
In what manner the electrons are distributed among these orbitals and in what way they become active stereo chemically can be judged with the aid of ligand field theory. The concept of ligand field theory is equivalent to that of the valence shell electron pair repulsion theory: it considers how the d electrons have to be distributed so that they attain a minimum repulsion with each other and with the bonding electron pairs.

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Ligand Field Theory Tetrahedral Complex

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An example of a tetrahedral metal complex is VCl4 which is shown in a convenient coordinate system. The 4s and 4p atomic orbitals of vanadium can be used to form sigma molecular orbitals. Although, the overlap patterns are rather complicated the 3dxz, 3dyz and 3dxy valence orbitals also are situated properly to form sigma molecular orbitals.

In terms of localized molecular orbitals both sd3 and sp3 hybrid orbitals are tetrahedrally oriented.

Tetrahedral Metal Complex

The ligand field splitting diagram for a tetrahedral complex such as VCl4 is shown below.

Ligand Field Splitting Diagram

  1. The anti bonding molecular orbitals derived from the 3d valence orbitals are divided into two sets.
  2. The orbitals formed from the 3dxz, 3dyz and 3dxy orbitals are of higher energy than those formed from the 3dz2and 3dx2-y2 orbitals.
  3. Thus, the change from octahedral to tetrahedral geometry exactly reverses the role and the energies of the d valence orbitals of the central metal ion.
  4. $\Delta _{t}$ is the energy difference between the t2 and e in tetrahedral complex.
  5. From ligand field theory we can predict that the t2 orbitals in a tetrahedral complex will not form as strong sigma bonds with ligand sigma orbitals as will the eg octahedral orbitals thereby resulting in a much less energetic t2 level and a relatively small value.
  6. Because of the small values all tetrahedral transition metal complexes have high spin ground state configurations.

Ligand Field Theory Square Planar Complex

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The d8 metal ions form square planar complexes. The example we will use here is [PtCl4]2-. The principle sigma bonding involves the overlap of 3p(sigma)Cl- orbitals with the 5dx2-y2, 6s, 6px and 6py metal valence orbitals. In the language of localized molecular orbital theory, the sigma bonding is summarized as dsp2 in a square planar complex.

Of principle interest the ligand field splitting of the anti bonding molecular orbitals derived from the metal d valence orbitals in a square planar complex.

Square Planar Complexes

The ligand field splitting diagram for a square planar complex such as [Pt(Cl)4]2- is shown below.Ligand Field Splitting Diagram

The ligand field splitting in a square planar complex is rather complicated because there are four different energy levels. For all square planar complexes it is reasonable to place the strongly anti bonding orbital at the highest energy level.

However regardless of the placement the most important characteristic of the ligand-field splitting in a square planar complex is that $d_{x^{2}-y^{2}}$ much higher energy than other four orbitals which are about the same energy.

Ligand Field Theory Pi Bonding

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Some metal ions and ligands also have the capability of forming pi bonds, pi bonding can be of two types. One is metal-to-ligand pi bonding in which the bonding electrons that form the pi bond come from the metal. The other type is ligand-to-metal bonding in which the electrons came from the ligand. Metal-to-ligand pi bonding occurs in complexes in which the metal ion is in a lower oxidation state.

Pi bonding also helps to explain the position of some ligands in the spectro-chemical series. These are explained as follows:
  1. Where the ligands act as pi acceptors by accepting electrons from the central metal. Examples include CO, CN-, NO+ and phosphines.
  2. Where the ligands act as pi donors and transfer charge from ligand to metal in pi interactions as well as sigma interactions. Pi bonding of this kind commonly occurs in oxo-ions of metals in high oxidation states.
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