1. Molecular Orbital Theory
Molecule:
Simplest: overlap of unchanged atomic orbitals (atoms stuck together)
Hybridization: overlap of hybridized atomic orbitals localized between nuclei
MO Theory: collection of nuclei with delocalized molecular orbitals
Linear combination of atomic orbitals in the molecule to form molecular orbitals.
Atomic orbitals must overlap to form molecular orbitals.
Wave functions can constructively and destructively interfere.
Conservation of the number of orbitals – the number of molecular orbitals equals the total number of molecular orbitals.

2. Overlap of 1s wavefunctions
[ΨA – ΨB]2
[ΨA + ΨB]2
[ΨA2 + ΨB2]

3. Hydrogen MOs Combining hydrogen 1s orbitals to form H2.
MO diagram for H2. The dots are the nuclei in the orbitals.

4. MO Theory: Important Points
Once the molecule is formed, the atomic orbitals no longer “exist”.
Bonding orbitals are lower in energy than 1s orbitals of the free H atoms. Anti-bonding orbitals are higher in energy.
Thus, forming H2 is more stable than two free hydrogen atoms.
Similar rules:
Each MO can hold two electrons of opposite spin.
Orbitals are conserved.
For H2 the symmetry of the overlap results in a sigma (σ) bond.
H2: σ1s2

5. MO Theory: Important Points
A molecule forms if it has lower energy than the separated atoms.
In MO theory: it must have more bonding electrons than antibonding electrons.
Bond order: [#bonding e– – #antibonding e–]/2
Look at He2.
#bonding e– = #antibonding e–.
Bond order = 0.
But He2+ is stable!
Bond order = 0.5.
Odd number of electrons (no Lewis structure).
Molecular ion. +

6. Diatomic hydrogen
H2 H2+ H2–

7. How well does it work? Bond order Length (Å) Bond energy (kJ/mol) H2 1
0.74
432
H2+
0.5
1.06
255
He2+
1.08
250
He2 --
H2–

8. Period 2 Diatomics
The 1s orbitals are not involved in forming MOs (there is no overlap).
The MO diagram for Li2 predicts a stable molecule.
Bond order = 1
Bond energy = 110 kJ/mol
Bond length = 2.67 Å
Not the most stable form of lithium.

9. Period 2 Diatomics: 2p overlap

10. Period 2 Diatomics: 2p overlap

11. “Simple” MOs for 2p overlap
Because σp overlap has increased electron density between nuclei, it would be expected to be lower in energy than pi overlap.
There is some p-s mixing that occurs which complicates matters.
The s orbital can mix with the p orbital with σ symmetry.