1. Molecular Orbital Theory
Quantum mechanics describes the electrons in an atom using wave functions called atomic orbitals.
Atomic orbital
located on individual atoms
definite energy
contains up to 2 electrons with opposite spins
visualized using a 3-D representation

2. Molecular Orbital Theory
3-D representation of some atomic orbitals: z y y y x x x z z
s orbital
p orbital
d orbital

3. Molecular Orbital Theory
Molecular Orbital Theory describes the electrons in a molecule using wave functions called molecular orbitals.
an allowed state for an e- in a molecule
Molecular orbitals are associated with the whole molecule not with an individual atom.

4. Molecular Orbital Theory
Molecular Orbitals are analogous to atomic orbitals in many ways:
Definite energy
Can hold 2 e- with opposite spins
Visualized using a 3-D representation

5. Molecular Orbital Theory
When 2 atomic orbitals overlap, two new molecular orbitals are formed:
Bonding molecular orbital
Antibonding molecular orbital

6. Molecular Orbital Theory
Bonding molecular orbital
Constructive interference between two atomic orbitals leads to a build up of e- density between the nuclei
lower energy than atomic orbital
Bonding MO

7. Molecular Orbital Theory
Antibonding molecular orbital
Destructive interference leads exclusion of electrons for the region between the nuclei
Highest electron density is located on opposite sides of the nuclei
higher energy than atomic orbital
Antibonding MO
Bonding MO

8. Molecular Orbital Theory
Bonding and antibonding molecular orbitals can be either s or p molecular orbitals:
s molecular orbital:
A molecular orbital in which electron density is centered around the internuclear axis
s bonding MO
s1s
s2p
s antibonding MO
s*1s
s*2p

9. Molecular Orbital Theory
p molecular orbital:
A molecular orbital in which electron density is concentrated on opposite sides of the internuclear axis
p bonding MO:
p2p
p antibonding MO:
p*2p

10. Molecular Orbital Theory
The interaction of atomic orbitals to form bonding and antibonding molecular orbitals can be depicted using a molecular orbital diagram.
Molecular orbital diagram:
an energy level diagram that shows the energy level of molecular orbitals relative to the atomic orbitals from which they’re derived

11. Molecular Orbital Theory
The MO diagram for H2 molecule:
s*1s 1s 1s
H atom
s1s
H atom
bonding electrons
H2 molecule

12. Molecular Orbital Theory
The MO diagram for He2 molecule:
antibonding electrons
s*1s 1s 1s
He atom
s1s
He atom
bonding electrons
He2 molecule

13. Molecular Orbital Theory
The He2 molecule has 2 bonding electrons and 2 antibonding electrons.
The energy decrease from the 2 electrons in the bonding MO is offset by the energy increase from the 2 electrons in the antibonding MO.
He2 is not a stable molecule!

14. Molecular Orbital Theory
In MO Theory, the stability of a covalent bond can be related to its bond order:
Bond order = (# bonding e- - # antibonding e-) 2
Single bond: bond order = 1
Double bond: bond order = 2
Triple bond: bond order = 3
Fractional bond orders also exist!

15. Molecular Orbital Theory
The bond order for H2 molecule:
Bond Order = (2 - 0) = 1 2
The hydrogen atoms in an H2 molecule are held together by a single bond.

16. Molecular Orbital Theory
The bond order for an He2 molecule:
Bond order = (2 - 2) = 0 2
No bond exists between two He atoms.

17. Molecular Orbital Theory
Drawing MO Diagrams:
Start with a “skeleton” MO diagram showing the molecular orbitals
This will be given to you.
Use only the valence electrons of the atoms
Follow the aufbau principle
Each MO can hold a maximum of 2 electrons
Follow Hund’s rule.
Keep electrons unpaired until all MO’s having the same energy have 1 e-.

18. Molecular Orbital Theory
You are responsible for determining the correct # of valence electrons for each atom and placing the electrons into the MO diagram.
You must be able to calculate bond order.
You must be able to predict whether molecule exists or not.

19. Molecular Orbital Theory
Example: Complete the MO diagram for N2. Calculate the bond order.
s*2p
p*2p
s2p
p2p
s*2s
s2s

20. Molecular Orbital Theory
Example: Complete the MO diagram for the O2 molecule. Determine the bond order.
s*2p
p*2p
p2p
s2p
s*2s
s2s

21. Molecular Orbital Theory
The MO diagram for O2 predicts that there are two unpaired electrons.
Molecules like O2 that contain one or more unpaired electron(s) are called paramagnetic
attracted to a magnetic field

22. Molecular Orbital Theory
The MO diagram for N2 predicts that all electrons are paired.
A molecule like N2 that does not contain unpaired electrons is diamagnetic.
Weakly repelled by a magnetic field

23. Molecular Orbital Theory
Example: Is Ne2+ paramagnetic or diamagnetic?
s*2p
p*2p
p2p
s2p
s*2s
s2s