Molecular Orbital Theory
Describes bonding in molecules using linear combinations of atomic orbitals (LCAO) to form molecular orbitals
Bond Order Formula
Bond Order = (nb - na) / 2
nb = Bonding Electrons
Number of electrons in bonding molecular orbitals
na = Antibonding Electrons
Number of electrons in antibonding orbitals (marked with *)
Key Principles
1. Orbital Combination
Atomic orbitals combine to form molecular orbitals: same number of MOs as AOs
2. Bonding Orbitals (σ, π)
Lower energy than atomic orbitals; constructive interference; electron density between nuclei
3. Antibonding Orbitals (σ*, π*)
Higher energy; destructive interference; node between nuclei; destabilizes molecule
4. Aufbau Principle
Fill lowest energy MOs first; Hund's rule applies; Pauli exclusion principle
MO Energy Level Order
For O₂, F₂, Ne₂
σ(2s) < σ*(2s) <
σ(2p) < π(2p) <
π*(2p) < σ*(2p)
For B₂, C₂, N₂
σ(2s) < σ*(2s) <
π(2p) < σ(2p) <
π*(2p) < σ*(2p)
Note: π and σ(2p) order switches
Worked Examples
Example 1: O₂ Molecule
Total electrons: 8 + 8 = 16
Configuration:
σ(2s)² σ*(2s)² σ(2p)² π(2p)⁴ π*(2p)²
Bond Order Calculation:
Bonding electrons (nb) = 2+2+4 = 8
Antibonding electrons (na) = 2+2 = 4
Bond Order = (8-4)/2 = 2
Result: Double bond, paramagnetic (2 unpaired e⁻)
Example 2: N₂ Molecule
Total electrons: 7 + 7 = 14
Configuration:
σ(2s)² σ*(2s)² π(2p)⁴ σ(2p)²
Bond Order:
nb = 2+4+2 = 8
na = 2
Bond Order = (8-2)/2 = 3
Result: Triple bond, diamagnetic, very stable
Example 3: He₂ (Does not exist)
Total electrons: 2 + 2 = 4
Configuration: σ(1s)² σ*(1s)²
Bond Order:
Bond Order = (2-2)/2 = 0
Result: No bond formation; He₂ does not exist
Bond Order Interpretation
| Bond Order | Bond Type | Stability | Example |
|---|---|---|---|
| 0 | No bond | Unstable | He₂ |
| 0.5 | Weak bond | Marginally stable | He₂⁺ |
| 1 | Single bond | Moderate | H₂, F₂ |
| 2 | Double bond | Strong | O₂ |
| 3 | Triple bond | Very strong | N₂ |
Note: Higher bond order → shorter bond length and higher bond energy
Common Mistakes
Wrong MO Energy Order
Remember π(2p) and σ(2p) switch order for B₂, C₂, N₂
Forgetting Antibonding Electrons
Must subtract antibonding electrons when calculating bond order
Ignoring Hund's Rule
Fill degenerate π orbitals singly before pairing (affects paramagnetism)
Paramagnetic vs Diamagnetic
Unpaired electrons → paramagnetic; all paired → diamagnetic
Related Tools
MO Calculator
Generate MO diagrams and bond orders
Electron Configuration Calculator
Atomic electron arrangements
Lewis Structures
Alternative bonding theory
Hybridization
Atomic orbital mixing
Electron Configuration
Aufbau and orbital filling
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