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Sigma Bonding


Ligand Field Theory


While Crystal Field Theory provides valuable insights into the electronic structure of transition metals in crystal lattices, it has serious limitations. The most severe limitation is its inability to account for chemical bonding. Complexes may also be formed between neutral metal atoms and neutral or cationic (!) ligands. Crystal Field Theory is poorly suited to explain such interactions.

A more detailed description of bonding in coordination compounds is provided by Ligand Field Theory. In coordination chemistry, the ligand is a Lewis base, which means that the ligand is able to donate a pair of electrons to form a covalent bond. The metal is a Lewis acid, which means it has an empty orbital that can accept a pair of electrons from a Lewis base to form a covalent bond. This bond is sometimes called a coordinate covalent bond or a dative covalent bond to indicate that both electrons in the bond come from the ligand.

The principles of Ligand Field Theory are similar to those for Molecular Orbital Theory. Review the principles of Molecular Orbital Theory before exploring Ligand Field Theory.

The following list summarizes the key concepts of Ligand Field Theory.

  • One or more orbitals on the ligand overlap with one or more atomic orbitals on the metal.
  • If the metal- and ligand-based orbitals have similar energies and compatible symmetries, a net interaction exists.
  • The net interaction produces a new set of orbitals, one bonding and the other antibonding in nature. (An * indicates an orbital is antibonding.)
  • Where no net interaction exists, the original atomic and molecular orbitals are unaffected and are nonbonding in nature as regards the metal-ligand interaction.
  • Bonding and antibonding orbitals are of sigma (?) or pi (?) character, depending upon whether the bonding or antibonding interaction lies along the line connecting the metal and the ligand. (Delta (?) bonding is also possible, but it is unusual and is relatively weak.)


The ? bonding interactions always involve the ligand acting as a Lewis base and the metal as a Lewis acid, as described above. The ? bonding interactions may involve donation of electrons from the ligand to the metal or donation of electrons from the metal to the ligand. (The latter interaction is called ? back-bonding.)

The nature of ? bonding in coordination compounds is illustrated below by the binding of carbon monoxide to chromium(0).

Sigma Bonding in Cr-CO

An example of a coordination complex is hexacarbonylchromium(0), Cr(CO)6. We will begin our examination of Ligand Field Theory by examining the interaction of a single carbon monoxide ligand with a chromium atom to yield Cr-CO.

Bonding in coordination complexes usually involves a ligand orbital that is lower in energy than the metal d orbitals. Because a close match in energy is necessary for a strong bonding interaction, it is the highest occupied ligand orbital that is important in metal-ligand bonding. (Note that the metal d orbitals are typically the lowest unoccupied or partially occupied metal orbitals.) Examine the molecular orbital diagram for carbon monoxide to acquaint yourself with bonding in the free CO ligand.

The occupied carbon monoxide orbital that interacts with the metal to form a ? bond is the highest occupied molecular orbital (HOMO), which is a primarily nonbonding orbital formed by mixing of the carbon 2s and 2pz and oxygen 2pz orbitals. The electron density for this orbital resides primarily on the carbon. The large lobe on the carbon that extends away from the oxygen is in an ideal position to interact with the metal. Note that CO bonds with metals through the carbon, not the oxygen. This may seem counterintuitive, especially given the relative electronegativities of carbon and oxygen, but experimental crystal structures of carbonyl complexes confirm that it is the carbon that bonds with the metal. This behavior is consistent with the distribution of electron density in the carbon monoxide donor orbital.

The energy diagram below shows the five chromium 3d orbitals and the carbon monoxide nonbonding orbital. All atoms lie along the z axis, with the chromium at the origin. One may click on an orbital in the energy diagram and the 90% isosurface for that orbital will be shown in the virtual reality display at the right. Only ? bonding interactions are illustrated. There are also important ? bonding interactions, which will be illustrated in the next exercise. In this simplified scheme, only the chromium 3d orbitals are shown. In reality, the 4s and 4p orbitals are also available for bonding.

  1. Examine the geometry of the CO nonbonding orbital. Then examine each of the five 3d orbitals of chromium.
  2. Which of the metal orbitals has compatible symmetry for a net interaction with the CO donor orbital? Recall that there will be no net interaction if the electron density from the CO donor orbital approaches the metal orbital along a nodal surface. In this example, all atoms lie along the z axis.
  3. When you have determined which 3d orbital has compatible symmetry for bonding, envision the geometries of the bonding and antibonding interactions. Then click on the various molecular orbitals for the Cr-CO complex. Were your predictions correct?
  4. Which molecular orbital is the Cr-CO ? orbital? Is the Cr-CO ? orbital primarily metal based or carbon monoxide based?
  5. Which molecular orbital is the Cr-CO ?* orbital? Is the Cr-CO ?* orbital primarily metal based or carbon monoxide based?
  6. Which molecular orbital(s) is(are) nonbonding?
  7. What is the electron configuration for the Cr-CO complex? Which molecular orbitals are populated, which are empty?
  8. Why are molecular orbitals 4 and 5 higher in energy than molecular orbitals 2 and 3?
Molecular Orbital Diagram of Cr-CO

View Along
All atoms lie along the z axis.

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Last Modified
18:30, 1 Oct 2013

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