So far, we have considered only the effects of sigma donation on the d orbital splitting diagram using the angular overlap model. When we looked at ligand field theory, we saw that pi-donor and pi-acceptor effects produced significant changes in these diagrams. We generally see these effects in any ligands that have orbitals that can accept electron density from the metal (back-bonding). The paradigm of a pi acceptor is carbon monoxide, of course. Similar effects can be found in related ligands in which the donor atoms participate in pi bonding with another atom in the ligand, thus making a pi* orbital available for back-bonding. In addition, back-bonding is a feature of phosphine ligands and some N-heterocyclic carbenes. We usually think about this interaction as illustrated below. The empty ligand orbital approaches so that it is perpendicular to the bond axis, allowing overlap with the filled metal d orbital. The interaction lowers the energy of the d electrons, which become bonding in nature, and raises the energy of the empty ligand orbital. We can use the same ligand positions for pi acceptors that we already used for sigma donors. The orbitals will be oriented differently than the sigma donor orbitals but they will approach from the same directions.. As before, we can use the results of calculations of the strengths of these interactions based on the amount of overlap; we don't need to know exactly how the numbers in the table below came about. This time, the maximum overlap occurs between a dxz orbital and a p orbital approaching in position 1, perpendicular to the bond axis. Several other combinations will be equally strong. This time, the stabilization is expressed in terms of eπ rather that eσ. The amount of energy in this case is somewhat smaller than in sigma donation because of a lesser degree of metal-ligand orbital overlap. Ligand Positions dz2 dx2-y2 dxy dxz dyz 1 0 0 0 1 1 2 0 0 1 1 0 3 0 0 1 0 1 4 0 0 1 1 0 5 0 0 1 0 1 6 0 0 0 1 1 7 2/3 2/3 2/9 2/9 2/9 8 2/3 2/3 2/9 2/9 2/9 9 2/3 2/3 2/9 2/9 2/9 10 2/3 2/3 2/9 2/9 2/9 11 0 3/4 1/4 1/4 3/4 12 0 3/4 1/4 1/4 3/4 These interactions modify the picture we built previously for simple sigma donors. In the new interaction diagram, a second set of ligand p orbitals is destabilized by the pi interaction. At the same time, some of the d orbitals are stabilized by the additional interaction. This modification is illustrated below for octahedral geometry. Problems 1. Use the table of pi interactions to calculate orbital energy stabilization or destabilization for the following geometries. a) trigonal planar ML3 b) square planar ML4 c) trigonal bipyramidal ML5 Solutions 1. a) Positions 2, 11, 12. dz2: 0 dx2-y2: - (0 + 3/4 + 3/4) eπ = 6/4 = - 3/2 eπ dxy: - (1 + 1/4 + 1/4) eσ = 6/4 = - 3/2 eπ dxz: - (1 + 1/4 + 1/4) eσ = 6/4 = - 3/2 eπ dyz: - (0 + 3/4 + 3/4) eσ = 6/4 = - 3/2 eπ Ligand in position 2: (0 + 0 + 0 + 1 + 1) eπ = 2eπ Ligand in position 11: (0 + 3/4 + 1/4 + 1/4 + 3/4) eπ = 2eπ Ligand in position 12: (0 + 3/4 + 1/4 + 1/4 + 3/4) eπ = 2eπ b) Positions 2, 3, 4, 5. dz2: 0 dx2-y2: 0 dxy: - (1 + 1 + 1 + 1) = -4 eπ dxz: - (1 + 0 + 1 + 0) = -2 eπ dyz: - (0 + 1 + 0 + 1) = -2 eπ Ligand in position 2: (0 + 0 + 1 + 1 + 0) eπ = 2 eπ Ligand in position 3: (0 + 0 + 1 + 0 + 1) eπ = 2 eπ Ligand in position 4: (0 + 0 + 1 + 1 + 0) eπ = 2 eπ Ligand in position 5: (0 + 0 + 1 + 0 + 1) eπ = 2 eπ c) Positions 1, 2, 6, 11, 12. dz2: 0 dx2-y2: - (0 + 0 + 0 + 3/4 + 3/4) eπ = -3/2 eπ dxy: - (0 + 1 + 0 + 1/4 + 1/4) eπ = -3/2 eπ dxz: - (1 + 1 + 1 + 1/4 + 1/4) eπ = -7/2 eπ dyz: - (1 + 0 + 1 + 3/4 + 4/4) eπ = -7/2 eπ Ligand in position 1: (0 + 0 + 0 + 1 + 1) eπ = 2 eπ Ligand in position 2: (0 + 0 + 1 + 1 + 0) eπ = 2 eπ Ligand in position 6: (0 + 0 + 0 + 1 + 1) eπ = 2 eπ Ligand in position 11: (0 + 3/4 + 1/4 + 1/4 + 3/4) eπ = 2 eπ Ligand in position 12: (0 + 3/4 + 1/4 + 1/4 + 3/4) eπ = 2 eπ