Building an MO diagram
An MO diagram graphically represents the energies of atomic orbitals (side columns) and molecular orbitals (central column), connected by lines indicating AO contributions.
Construction steps for a diatomic molecule AB:
1. Draw the AO energy levels of A (left) and B (right). 2. Identify combinations allowed by symmetry and energy matching. 3. Place bonding MOs (lower) and antibonding MOs (higher, labelled *). 4. Fill MOs with available electrons following the Aufbau principle and Hund's rule. 5. Calculate bond order and deduce magnetic properties.
Notation convention: σ, π for bonding MOs; σ, π for antibonding MOs. Non-bonding MOs (same energy as the parent AO) are labelled n.
Bond order and bond energy
Bond order (BO) is defined as:
BO = (N_b − N_a) / 2
where N_b = electrons in bonding MOs, N_a = electrons in antibonding MOs.
General empirical correlations: - Higher BO → shorter and stronger bond. - BO = 0 → the molecule does not form. - Half-integer BO is possible (e.g. H₂⁺, BO = 1/2; O₂⁺, BO = 5/2).
| Species | BO | d(X−X) / pm | E_bond / kJ·mol⁻¹ |
|---|---|---|---|
| N₂ | 3 | 110 | 945 |
| N₂⁺ | 2.5 | 112 | 840 |
| O₂ | 2 | 121 | 498 |
| O₂⁺ | 2.5 | 112 | 643 |
| O₂⁻ (superoxide) | 1.5 | 133 | 395 |
| O₂²⁻ (peroxide) | 1 | 149 | 204 |
| F₂ | 1 | 143 | 159 |
Magnetic properties — the case of O₂
Lewis theory predicts diamagnetic O₂ (all electron pairs paired). Experiment shows that O₂ is paramagnetic: it is attracted to a magnet.
The MO diagram explains this: the two π2p MOs are degenerate* (same energy) and, by Hund's rule, each fills with one electron of parallel spin. These two unpaired electrons give a net spin magnetic moment → paramagnetism.
The magnetic moment μ = √(n_e(n_e + 2)) Bohr magnetons (μ_B), where n_e = number of unpaired electrons. For O₂: μ = √(2 × 4) = 2.83 μ_B, consistent with measurements.
Applications: ions and reactivity
MO theory predicts how ionising a molecule changes its properties:
- N₂⁺ (remove one electron from bonding σ2p MO) → BO = 2.5; weaker and longer bond than N₂.
- O₂⁻ (superoxide ion): one extra electron in π*2p → BO = 1.5; found in mitochondria.
- O₂²⁻ (peroxide ion): two extra electrons in π*2p → BO = 1; hydrogen peroxide H₂O₂.
The reactivity of Oxygen (O) in biological systems is directly tied to these frontier MOs: superoxide radicals O₂⁻· are key reactive oxygen species (ROS) in oxidative stress.