Ligand Field Theory

Pi Bonding in Coordination Compounds

Sigma bonding in coordination compounds involves the overlap of an occupied ligand-based orbital and one or more metal-based orbital in the region directly between the metal and the coordination site on the ligand. In the Cr-CO example, all atoms are located along the z axis and the σ bonding orbital has electron density concentrated on the z axis between the chromium and the carbon. The σ antibonding orbital has a nodal plane perpendicular to the z axis that separates the chromium and the carbon, thus depleting the electron density directly between the metal and ligand.

While all ligands participate in σ bonding interactions with the metal, some ligands are also capable of π bonding interactions. In a π bond, the line connecting the metal and the ligand coordination site lies in a nodal plane, and the electron density for the π bond is concentrated on either side of the nodal plane.

The σ bond always arises from donation of a pair of electrons from the ligand (a Lewis base) to the metal (a Lewis acid). By contrast, π bonds may involve donation of electrons from the ligand to the metal or from the metal to the ligand. The following exercises illustrate both cases.

Pi Bonding in Cr-CO

Once again, consider a single carbon monoxide ligand bound to chromium(0). Sigma bonding involves the highest occupied molecular orbital in CO, which is a nonbonding orbital with electron density concentrated on the carbon. Pi bonding requires an orbital on the carbon monoxide with electron density concentrated above and below the line of the σ bond, and that electron density must extend toward the chromium in order to provide significant overlap with one or more of the metal 3d orbitals. Examine the molecular orbitals for CO and determine which of the CO molecular orbitals might be suitable for forming a π bond with the chromium.

The CO π orbitals concentrate electron density above and below the line of the Cr-CO bond, but the electron density is also concentrated in the region between the carbon and oxygen. Thus there is no meaningful overlap between the CO π orbitals and any of the chromium 3d orbitals. In addition, the much lower energy of the CO π orbitals prevents meaningful mixing with the chromium 3d orbitals. On the other hand, the CO π* orbitals have a nodal plane separating the carbon and oxygen, and the electron density is greatest at the ends of the molecule, especially on the carbon end. These two CO π* orbitals are perfectly aligned for interaction with the chromium. (The * indicates that the orbital is an antibonding orbital.)

The energy diagram below shows the five chromium 3d orbitals and the two carbon monoxide π* orbitals. 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 the π interactions are shown. The σ interactions, which are shown in the previous exercise, are omitted to simplify the diagram.

  1. Examine the geometry of the CO π* orbitals. Then examine each of the five 3d orbitals of chromium. Which of the metal orbitals has compatible symmetry for a net interaction with the CO π* orbitals?
  2. When you have determined which 3d and CO π* orbitals have compatible symmetry, envision the geometries of the bonding and antibonding interactions. Click on the various molecular orbitals for the Cr-CO complex. Were your predictions correct?
  3. Note how the low energy orbitals are simultaneously π bonding with respect to the Cr-CO bond and π antibonding with respect to the C-O bond. Similary, note how the high energy orbitals are π antibonding with respect to both the Cr-CO and C-O bonds.
  4. Is the Cr-CO π orbital primarily metal based or carbon monoxide based?
  5. Is the Cr-CO π* orbital primarily metal based or carbon monoxide based?
  6. In the free (i.e., uncoordinated) ligand, are the CO π* orbitals occupied or unoccupied?
  7. What is the electron configuration for the Cr-CO complex? (For the purposes of this discussion, disregard σ bonding.) Which molecular orbitals are populated, which are empty?
  8. Does the coordination of carbon monoxide to chromium(0) strengthen or weaken the C-O bond? Or is there no effect on the C-O bond strength?
Molecular Orbital Diagram of Cr-CO

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All atoms lie along the z axis.

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Now that you have separately examined σ and π bonding in Cr-CO, let's put the pieces together. Both bonding interactions are depicted in the Cr-CO exercise.

Carbon monoxide is a π acceptor ligand, which means the ligand is capable of accepting a pair of electrons (through its CO π* orbital) to form a π bond with a metal. The fluoride ion is an example of a π donor ligand, which means the ligand is capable of donating a pair of electrons to form a π bond with a metal. Study the Cr(F)2+ exercise to see this type of π bonding.

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