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Review: structures, charges, electrons donated by the ligands in Table 6.7
Bonding in linear molecules
The molecule BeH2 has D
h symmetry:
| Dh
| E | C2
| C
| i | 
| 
|
| A1g | 1 | 1 | 1 | 1 | 1 | 1 |
| A1u | 1 | -1 | 1 | -1 | 1 | -1 |
There are two hydrogen group orbitals
- {H1(1s) + H2(1s)}, A1g
- {H1(1s) - H2(1s)}, A1u
The Be 2s orbital has the same symmetry as the first group orbital and the Be 2pz has the symmetry of the second group orbital. The orbitals with the same symmetry will combine. The other Be p orbitals are non-bonding.
All molecules with D
h symmetry that have only s and p orbitals will have the sigma framework above.What about a transition metal with d orbitals? What is the symmetry of d orbitals in this point group? Only the dz2 orbital has electron density along the z (bond) axis. If we look at the symmetry operations for the group, we can see that this orbital transforms like A1g.
Consider the linear molecule [Cu(NH3)2]+. There will be orbital mixing between a copper s orbital, a copper d orbital and a ligand group orbital to make 3 sigma molecular orbitals.
Molecular orbitals of trigonal complexes
What about trigonal planar molecules in the D3h point group? We know that the 2s orbital in BH3 has the same symmetry as one of the group orbitals from the hydrogen 1s orbitals. The boron 2px has the same symmetry as another group orbital and the 2py has the same symmetry as the third group orbital. The boron 2pz is non-bonding.
What about the trigonal planar complex [Cu(PPh3)3]+? Two of the d orbitals have the same symmetry as the px and py orbitals.
This results in orbital mixing. The sigma bonding molecular orbtials are shown below. (The non-bonding orbital are not included for clarity here. You would add those and the electrons to a molecular orbital diagram.)
Molecular orbitals of tetrahedral complexes
We examined the molecular orbital diagram of methane previously. The carbon 2s orbital has the same symmetry as one of the group orbitals {H1(1s) + H2(1s) + H3(1s) + H4(1s)}. Each of the p orbitals on carbon has the same symmetry as one of the other group orbitals.
In tetrahedral TiCl4 the 3dxy, 3dxz and 3dyz orbitals also have the same symmetry in the T2 point group as one of the group orbitals.
The 3dxz, 3py, and one of the group orbitals are shown below.
Again, we see orbital mixing. The sets of mixed molecular orbitals are shown below.
Here are the rest of the molecular and atomic orbitals.
Molecular orbitals of octahedral complexes
What if you had octahedral CH6? What would the molecular orbitals look like? The six hydrogen orbitals 1s orbitals would form 6 group orbitals. The lowest energy (completely symmetric) one would have the same symmetry as the carbon 2s orbital. There would be 3 group orbitals with one nodal place each that would have the same symmetry to combine with the 3 p orbitals on carbon. Two of the group orbitals would be non-bonding. Those would each have 2 nodal planes.
What about WH6? With a transition metal, 2 of the d orbitals have the same symmetry as the 2 remaining hydrogen group orbitals. You can see these below.
The remaining d orbitals (dxy, dxz, and dyz) are non-bonding.
