Lecture note CHM62-221 Part II

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Sigma bonding orbitals and antibonding orbitals can also be formed between p orbitals (shown
below). Notice that the orbitals have to be in phase inorder to form bonding orbitals. Sigma
molecular orbitals formed by p orbitals are often differentiated from other types of sigma
orbitals by adding the subscript p below it. So the antibonding orbital shown in the diagram
below would be σ*p.

Pi Bonds
The pi bonding bonds as a side to side overlap, which then causes there to be no electron
density along the axis, but there is density above and belong the axis. The diagram below
shows a pi antibonding molecular orbital and a pi bonding molecular orbital.

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2py Orbitals

The two 2py atomic orbitals overlap parallely to form two pi molecular orbitals which are
asymmetrical about the axis of the bond.
2pz orbitals

The two 2pz orbitals overlap to create another pair of pi 2p and pi *2p molecular orbitals. The
2pz-2pz overlap is similar to the 2py-2py overlap because it is just the orbitals of the 2pz
rotated 90 degrees about the axis. The new molecular orbitals have the same potential
energies as those from the 2py-2py overlap.
Drawing Molecular Orbital Diagrams

• Determine the number of electrons in the molecule.
• Fill the molecular orbitals from bottom to top until all the electrons are added.

Describe the electrons with arrows. Put two arrows in each molecular orbital, with the
first arrow pointing up and the second pointing down.
• Orbitals of equal energy are half filled with parallel spin before they begin to pair up.

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Molecular orbital diagram of O2 molecule.
Determining Bond Order
Bond Order= 1/2(a-b)

• where ...
a= number of e- in bonding Molecular Orbitals
b= number of e- in antibondng Molecular Orbitals

Bond Order indicates the strength of the bond. The higher the Bond Order, the stronger the
bond.
Determining the Stability of the Molecule
If the Bond Order is Zero, then no bonds are produced and the molecule is not stable (for
example He2). If the Bond Order is 1, then it is a single covalent bond. The higher the Bond
Order, the more stable the molecule is. An advantage of Molecular Orbital Theory when it
comes to Bond Order is that it can more accurately describe partial bonds (for example in
H2+, where the Bond Order=1/2), than Lewis Structures.

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LIGAND FIELD THEORY
To understand the ligand field theory, the MO diagram must has been considered. In
octahedral environment the metal orbitals (3d, 4s, 4p for 1st row transition metals) divide by
symmetry into 4 sets: s = a1g, p = t1u, axial d = eg, inter-axial d = t2g. The orbitals of the six
ligands can be combined to give six symmetry-adapted linear combinations which are of the
correct symmetry to interact with the s, 3 x p and 2 x axial-d orbitals, but not the inter-axial d
orbitals. The result is that 3 orbitals (the inter-axial d orbitals) are non-bonding, while the rest
(6 metal orbitals and 6 ligand orbitals) combine to form six bonding and six anti-bonding MOs.
This is a much more correct approach than crystal field theory, but is not as easy to use.

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MO energy levels for an octahedral complex (only -bonding considered).
The six bonding orbitals are filled with 12 electrons from the six ligands. Orbital t2g and eg* are
the frontier orbitals where d-electrons reside (which is why transition metal MOs are often
simplified to show only t2g and eg* orbitals).

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-Bonding ligands
For the -acceptor ligands, the bonding is “Synnergic”: -donation to the metal strengthens -
backbonding to the ligand, and -donation from the metal to the ligand strengthens the -
donor component of bonding. This is because -donation leads to increased electron density
on the metal, which allows increased -backdonation. Coversely, -backdonation reduces the
amount of electron density on the metal, which allow more -donation from the ligand to the
metal.

MO energy levels for an octahedral complex with -acceptor

MO of [Cr(CO)6] complex.
From diagram, -backdonation to CO from the t2g orbitals which are non-bonding in the
absence of -interactions between the metal and the ligands. The 3 t2g orbitals and 3 high
lying * orbitals of the CO ligands form 3 bonding MOs and 3 antibonding MOs. Since the CO

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* orbitals are empty, the d-electrons occupy the bonding MO from this interaction. The result
is (1) a very large o, so the eg* orbital is likely to remain empty.

(2) the t2g orbital is strongly bonding (wants to be filled with 6 electrons). Therefore, the
complex strong -acceptor ligands are the most likely to obey the 18 electron rule.
Simplified picture of how -acceptor and -donor interactions affect the MO diagram-
Only the frontier orbitals are shown

-donor ligands
-Donation from the ligands to the t2g orbitals hence the 3 t2g metal orbitals and 3 low lying,
filled ligand orbitals of -symmetry form 3 bonding MOs and 3 antibonding MOs. Thus t2g is
lowered and o increases. Since the interaction ligand orbitals are full, these electron occupy
the bonding MO from this interaction, and the d-electrons occupy the antibonding MO. The
result is (1) a small o (2) the t2g orbital is weakly antibonding.

Principles of Inorganic Chemistry I Part II (CHM62-221)