Coordination Chemistry3 Ligand Field Theory

1. Coordination Chemistry(3)Ligand Field Theory We are going to use molecular orbital theory (the combination of atomic orbitals to form molecular orbitals) to understand the molecular orbitals that exist in coordination compounds. This will explain the �splitting of the d orbitals� in a much more proper manner than Crystal Field Theory and will allow us to understand why different ligands cause different amounts of spitting (large or small ?oct). The point of this slide is to remember that when atomic orbitals (AO) have the correct symmetry to interact to form a molecular orbital (MO), the AO that is closer in energy to the MO being formed will make a greater contribution to the MO, hence the coefficients. When AO�s interact, they form bonding and anti-bonding orbitals. The bonding MO�s have more character of the lower energy AO and the anti-bonding MO�s have more character of the higher energy AO�s, indicated by the coefficients. We will use this idea in forming the MO�s for our coordinate covalent complexes. We will use MO theory to create the s bonding forming the coordinate covalent bonds in the complexes and then look at the pi bonding which we have ignored thus far. We are going to use molecular orbital theory (the combination of atomic orbitals to form molecular orbitals) to understand the molecular orbitals that exist in coordination compounds. This will explain the �splitting of the d orbitals� in a much more proper manner than Crystal Field Theory and will allow us to understand why different ligands cause different amounts of spitting (large or small ?oct). The point of this slide is to remember that when atomic orbitals (AO) have the correct symmetry to interact to form a molecular orbital (MO), the AO that is closer in energy to the MO being formed will make a greater contribution to the MO, hence the coefficients. When AO�s interact, they form bonding and anti-bonding orbitals. The bonding MO�s have more character of the lower energy AO and the anti-bonding MO�s have more character of the higher energy AO�s, indicated by the coefficients. We will use this idea in forming the MO�s for our coordinate covalent complexes. We will use MO theory to create the s bonding forming the coordinate covalent bonds in the complexes and then look at the pi bonding which we have ignored thus far.

2. Molecular orbital theory applied to coordination compounds is called Ligand Field Theory. We will only consider octahedral complexes. Considering the ligands as coming along the six directions of the x, y, & z axes, the s-bonds are made from the overlap of the metal atom orbitals and the ligand orbitals that lie along these axes. For the first row of transition metals, these would be the 4s (which points in all directions equally), 4px, 4py, 4pz, 3dx2-y2, and 3dz2 orbitals. We will only consider the ligand orbital that is involved in the s bonding and ignore the rest. For ammonia, this would be the lone pair sp3 orbital. For Cl- or CN-, this would be the sp orbital that is pointed at the metal. (The p and pi orbitals on these ligands will not be involved in the sigma bonding, but will be involved in the pi bonding which we will consider later.) The dxy, dxz, dyz orbitals have the wrong symmetry to interact with ligand orbital involved in sigma bonding. Thus, they are unaffected by the sigma bonding and do not change energy. Molecular orbital theory applied to coordination compounds is called Ligand Field Theory. We will only consider octahedral complexes. Considering the ligands as coming along the six directions of the x, y, & z axes, the s-bonds are made from the overlap of the metal atom orbitals and the ligand orbitals that lie along these axes. For the first row of transition metals, these would be the 4s (which points in all directions equally), 4px, 4py, 4pz, 3dx2-y2, and 3dz2 orbitals. We will only consider the ligand orbital that is involved in the s bonding and ignore the rest. For ammonia, this would be the lone pair sp3 orbital. For Cl- or CN-, this would be the sp orbital that is pointed at the metal. (The p and pi orbitals on these ligands will not be involved in the sigma bonding, but will be involved in the pi bonding which we will consider later.) The dxy, dxz, dyz orbitals have the wrong symmetry to interact with ligand orbital involved in sigma bonding. Thus, they are unaffected by the sigma bonding and do not change energy.

3. As we have done before, we will use the energies of the AO�s to produce a correlation diagram that has the MO�s in the middle. To the left we have the metal ion orbitals that are higher in energy than the ligand lone pair orbitals shown at the right. The lone pair orbitals interact with the metal orbitals along the axes to form six s bonding orbitals that are lower in energy and are primarily of ligand orbital character. (These can have slightly different energies with respect to each other, but for simplicity they are shown as having the same energy.) The six s anti-bonding orbitals that are formed are higher in energy and are primarily of metal orbital character. Here we show the anti-bonding orbitals at different energies resulting from the energy differences of the 3d, 4s, and 4p orbitals. The two d-orbitals (3dx2-y2, 3dz2) contribute primarily to the first s* orbital so it is labeled sd*; this orbital then has mostly d orbital character. Likewise, the 4s orbital contributes most to the ss* orbital and the 4p orbitals contribute the most to the sp* orbitals. Because the 3dxy, 3dxz, 3dyz orbitals are not involved in the s bonding, they come over as non-bonding orbitals in the molecule. If we take the correlation diagram away to just leave the MO energy diagram, we can clearly see that we have the six s bonding orbitals. These are filled with the 12 electrons from the 6 lone pairs from the ligands. (In this model we can ignore the other electrons in the ligands because they will just stay where they are.) The remaining electrons are the d electrons on the transition metal ion. If we look at the remaining orbitals we see that we have the 3 non-bonding d orbitals and the s* orbitals. We can ignore the ss*and sp* orbitals because they are too high in energy. The sd* orbitals are close enough in energy to consider. Note that the 3d non-bonding orbitals and the sd* orbitals form the 2-3 splitting pattern that we got for the d-orbitals from crystal field theory. The d electrons will then go into these two MO�s pairing or not pairing depending on the energy difference between these orbitals and the electron pair repulsion energy. We now better understand these orbitals and their energy difference. The two higher energy orbitals are antibonding orbitals primarily of d character and the lower energy orbitals are non-bonding d orbitals. The difference in energy between these orbitals is then the difference in energy between anti-bonding and non-bonding orbitals: ?oct = E(sd*) � E(3d). The magnitude of ?oct when only considering sigma bonding depends upon how anti-bonding the sd*orbitals are. The greater the interaction of the d orbitals with the ligand orbitals the more anti-bonding these orbitals will be. The more positive charge on the metal (the greater the oxidation state) the closer the ligands are drawn into the metal ion causing a greater interaction between these orbitals. Therefore, for the same ligand, the higher the oxidation number, the greater the energy splitting and the larger ?oct. As we have done before, we will use the energies of the AO�s to produce a correlation diagram that has the MO�s in the middle. To the left we have the metal ion orbitals that are higher in energy than the ligand lone pair orbitals shown at the right. The lone pair orbitals interact with the metal orbitals along the axes to form six s bonding orbitals that are lower in energy and are primarily of ligand orbital character. (These can have slightly different energies with respect to each other, but for simplicity they are shown as having the same energy.) The six s anti-bonding orbitals that are formed are higher in energy and are primarily of metal orbital character. Here we show the anti-bonding orbitals at different energies resulting from the energy differences of the 3d, 4s, and 4p orbitals. The two d-orbitals (3dx2-y2, 3dz2) contribute primarily to the first s* orbital so it is labeled sd*; this orbital then has mostly d orbital character. Likewise, the 4s orbital contributes most to the ss* orbital and the 4p orbitals contribute the most to the sp* orbitals. Because the 3dxy, 3dxz, 3dyz orbitals are not involved in the s bonding, they come over as non-bonding orbitals in the molecule. If we take the correlation diagram away to just leave the MO energy diagram, we can clearly see that we have the six s bonding orbitals. These are filled with the 12 electrons from the 6 lone pairs from the ligands. (In this model we can ignore the other electrons in the ligands because they will just stay where they are.) The remaining electrons are the d electrons on the transition metal ion. If we look at the remaining orbitals we see that we have the 3 non-bonding d orbitals and the s* orbitals. We can ignore the ss*and sp* orbitals because they are too high in energy. The sd* orbitals are close enough in energy to consider. Note that the 3d non-bonding orbitals and the sd* orbitals form the 2-3 splitting pattern that we got for the d-orbitals from crystal field theory. The d electrons will then go into these two MO�s pairing or not pairing depending on the energy difference between these orbitals and the electron pair repulsion energy. We now better understand these orbitals and their energy difference. The two higher energy orbitals are antibonding orbitals primarily of d character and the lower energy orbitals are non-bonding d orbitals. The difference in energy between these orbitals is then the difference in energy between anti-bonding and non-bonding orbitals: ?oct = E(sd*) � E(3d). The magnitude of ?oct when only considering sigma bonding depends upon how anti-bonding the sd*orbitals are. The greater the interaction of the d orbitals with the ligand orbitals the more anti-bonding these orbitals will be. The more positive charge on the metal (the greater the oxidation state) the closer the ligands are drawn into the metal ion causing a greater interaction between these orbitals. Therefore, for the same ligand, the higher the oxidation number, the greater the energy splitting and the larger ?oct.

4. We have seen that the magnitude of ?oct on the same metal depends upon the ligand. We have strong field and weak field ligands and those in between. We can explain the different splitting energies by considering the p bonding between the metal ion and the ligands. The s bonding still occurs as was given on the previous slide. But now, the dxy, dyz, dxz orbitals have the right symmetry to interact with orbitals on the ligands that can form p orbitals. We have seen that the magnitude of ?oct on the same metal depends upon the ligand. We have strong field and weak field ligands and those in between. We can explain the different splitting energies by considering the p bonding between the metal ion and the ligands. The s bonding still occurs as was given on the previous slide. But now, the dxy, dyz, dxz orbitals have the right symmetry to interact with orbitals on the ligands that can form p orbitals.

5. Cl- is a weak field ligand. We can understand this small ?oct by considering the p bonding which raises the energy of the dxy, dyz, dxz orbitals. We begin with the sigma bonding molecular orbital energy diagram that we produced before. There are two p orbitals on each Cl- not involved in the s bonding that have the right orientation to form p bonding and anti-bonding orbitals with the d orbitals. With 6 ligands, that gives us 12 p orbitals which are at lower in energy than the metal orbitals and are placed on the right side of the diagram above the sp orbitals which form the sigma bonds. Because the ligand p orbitals are lower in energy than the metal d orbitals, 12 bonding p orbitals are formed that are primarily of Cl- p orbital in character. (These orbitals are weakly bonding and can be considered to be primarily non-bonding p orbitals on the Cl-. The electrons remaining on the Cl- not used in the s bonding go into these orbitals.) Because the dxy, dyz, dxz orbitals are higher in energy than the ligand p orbitals, 3 antibonding p* orbitals are formed that are primarily of metal d orbital character. Most importantly, these anti-bonding orbitals are higher in energy than the metal atom d orbitals; the 3 orbitals are pushed closer to the sd*. The splitting in energy between these orbitals, ?oct , is reduced! Cl- is a weak field ligand because the ligand p orbitals cause the metal d orbitals to become p* antibonding orbitals that are closer in energy to the sd* orbitals. We now understand the anti-bonding nature of these orbitals, the types of orbitals that they are, and the energy difference between them. Cl- is a weak field ligand. We can understand this small ?oct by considering the p bonding which raises the energy of the dxy, dyz, dxz orbitals. We begin with the sigma bonding molecular orbital energy diagram that we produced before. There are two p orbitals on each Cl- not involved in the s bonding that have the right orientation to form p bonding and anti-bonding orbitals with the d orbitals. With 6 ligands, that gives us 12 p orbitals which are at lower in energy than the metal orbitals and are placed on the right side of the diagram above the sp orbitals which form the sigma bonds. Because the ligand p orbitals are lower in energy than the metal d orbitals, 12 bonding p orbitals are formed that are primarily of Cl- p orbital in character. (These orbitals are weakly bonding and can be considered to be primarily non-bonding p orbitals on the Cl-. The electrons remaining on the Cl- not used in the s bonding go into these orbitals.) Because the dxy, dyz, dxz orbitals are higher in energy than the ligand p orbitals, 3 antibonding p* orbitals are formed that are primarily of metal d orbital character. Most importantly, these anti-bonding orbitals are higher in energy than the metal atom d orbitals; the 3 orbitals are pushed closer to the sd*. The splitting in energy between these orbitals, ?oct , is reduced! Cl- is a weak field ligand because the ligand p orbitals cause the metal d orbitals to become p* antibonding orbitals that are closer in energy to the sd* orbitals. We now understand the anti-bonding nature of these orbitals, the types of orbitals that they are, and the energy difference between them.

6. CN- is a strong field ligand with a large magnitude for ?oct. Instead of p orbitals on the ligand, there are p* orbitals that interact with the metal dxy, dyz, dxz orbitals. Similar to the Cl-, there are two of these p* orbitals on each ligand. With 6 ligands we then have 12 p* which, because they are anti-bonding orbitals, are higher in energy than the metal atom d orbitals. When these orbitals interact with the dxy, dyz, dxz orbitals, they form antibonding p* in the complex that are higher in energy than the ligand p* orbitals. When the dxy, dyz, dxz orbitals interact with the ligand p* orbitals, 3 p bonding orbitals are formed that are primarily of metal d character and are lower in energy than the dxy, dyz, dxz orbitals. Thus, the splitting in energy between these orbitals and the sd* is greater causing ?oct to increase. The p bonding causes CN- to be a strong field ligand. We now know why ligands that have p* orbitals are strong field ligands and what the nature of these upper orbitals are. CN- is a strong field ligand with a large magnitude for ?oct. Instead of p orbitals on the ligand, there are p* orbitals that interact with the metal dxy, dyz, dxz orbitals. Similar to the Cl-, there are two of these p* orbitals on each ligand. With 6 ligands we then have 12 p* which, because they are anti-bonding orbitals, are higher in energy than the metal atom d orbitals. When these orbitals interact with the dxy, dyz, dxz orbitals, they form antibonding p* in the complex that are higher in energy than the ligand p* orbitals. When the dxy, dyz, dxz orbitals interact with the ligand p* orbitals, 3 p bonding orbitals are formed that are primarily of metal d character and are lower in energy than the dxy, dyz, dxz orbitals. Thus, the splitting in energy between these orbitals and the sd* is greater causing ?oct to increase. The p bonding causes CN- to be a strong field ligand. We now know why ligands that have p* orbitals are strong field ligands and what the nature of these upper orbitals are.

7. In summary, the 2-3 splitting of the d orbitals is caused by the sigma bonding interacting with just 2 of the d orbitals to form sd* orbitals which are higher in energy than the d atomic orbitals. Ligands with p orbitals available for p bonding with the metal are weak field ligands because they turn the three d non-bonding orbitals into p* orbitals that go up in energy, closer to sd* orbital. Ligands with p* orbitals available for p bonding with the metal are strong field ligands because they turn the three d non-bonding orbitals into p bonding orbitals that go down in energy, further away from the sd* orbital. Ligands that have no orbitals available for p bonding with the metal are medium field ligands lying somewhere between these strong and weak field ligands. The splitting in energy depends just upon the s bonding. In summary, the 2-3 splitting of the d orbitals is caused by the sigma bonding interacting with just 2 of the d orbitals to form sd* orbitals which are higher in energy than the d atomic orbitals. Ligands with p orbitals available for p bonding with the metal are weak field ligands because they turn the three d non-bonding orbitals into p* orbitals that go up in energy, closer to sd* orbital. Ligands with p* orbitals available for p bonding with the metal are strong field ligands because they turn the three d non-bonding orbitals into p bonding orbitals that go down in energy, further away from the sd* orbital. Ligands that have no orbitals available for p bonding with the metal are medium field ligands lying somewhere between these strong and weak field ligands. The splitting in energy depends just upon the s bonding.