Why Liquid Oxygen Clings to a Magnet but Liquid Nitrogen Does Not

The Lewis structure of oxygen, O=O, shows every electron neatly paired. Yet liquid oxygen is attracted by a magnet, which only happens when a molecule has unpaired electrons.

Molecular orbital theory treats electrons as belonging to the whole molecule, and it predicts oxygen's magnetism, why He${}_2$ does not exist, and how strong each bond is.

This part covers the postulates of MO theory, MO diagrams for diatomic molecules, bond order and its uses, and hydrogen bonding.

In molecular orbital theory, atomic orbitals of similar energy and matching symmetry combine by linear combination to form an equal number of molecular orbitals spread over the whole molecule — a lower-energy bonding orbital from constructive overlap and a higher-energy antibonding orbital from destructive overlap.

Postulates:

- Electrons in a molecule occupy molecular orbitals, each belonging to the whole molecule
- Only atomic orbitals of comparable energy and proper symmetry combine effectively
- The number of molecular orbitals formed equals the number of atomic orbitals combined
- Molecular orbitals fill by the Aufbau principle, Pauli exclusion principle and Hund's rule

Bonding and antibonding. Adding the wave functions, ${\psi }_A+{\psi }_B$, piles electron density between the nuclei — a bonding orbital ($\sigma$ or $\pi$). Subtracting them, ${\psi }_A-{\psi }_B$, leaves a node between the nuclei — an antibonding orbital (${\sigma }^{\ast }$ or ${\pi }^{\ast }$).

Worked example — counting orbitals. Two hydrogen 1s orbitals give $2$ molecular orbitals. Two second-period atoms each bring $1s$, $2s$ and three $2p$ orbitals — $10$ atomic orbitals in total, giving **$10$ molecular orbitals.

An everyday example. Two tabla strokes in step sound louder together, while strokes exactly out of step partly cancel — like wave functions adding or subtracting.

The substance. An antibonding orbital is raised in energy slightly more than the bonding orbital is lowered**, so filling both gives no net bonding.

**Fill molecular orbitals in order of increasing energy; for up to $14$ electrons (as in N${}_2$) the $\pi 2p$ orbitals lie below $\sigma 2p_z$, while for O${}_2$ and F${}_2$ the $\sigma 2p_z$ lies below the $\pi 2p$ pair.

Energy order for Li${}_2$ to N${}_2$:**

$$\sigma 1s<{\sigma }^{\ast }1s<\sigma 2s<{\sigma }^{\ast }2s<(\pi 2p_x=\pi 2p_y)<\sigma 2p_z<({\pi }^{\ast }2p_x={\pi }^{\ast }2p_y)<{\sigma }^{\ast }2p_z$$

**For O${}_2$ and F${}_2$**, $\sigma 2p_z$ moves below $(\pi 2p_x=\pi 2p_y)$.

Worked examples (KK stands for the filled $\sigma 1s^2{\sigma }^{\ast }1s^2$):

- **H${}_2$**: $\sigma 1s^2$
- **He${}_2$**: $\sigma 1s^2{\sigma }^{\ast }1s^2$
- **B${}_2$**: KK $\sigma 2s^2{\sigma }^{\ast }2s^2\pi 2p_x^1\pi 2p_y^1$
- **C${}_2$**: KK $\sigma 2s^2{\sigma }^{\ast }2s^2\pi 2p_x^2\pi 2p_y^2$
- **N${}_2$**: KK $\sigma 2s^2{\sigma }^{\ast }2s^2\pi 2p_x^2\pi 2p_y^2\sigma 2p_z^2$
- **O${}_2$**: KK $\sigma 2s^2{\sigma }^{\ast }2s^2\sigma 2p_z^2\pi 2p_x^2\pi 2p_y^2{\pi }^{\ast }2p_x^1{\pi }^{\ast }2p_y^1$
- **O${}_2^{-}$** adds one more electron to ${\pi }^{\ast }$; **O${}_2^{+}$** removes one from ${\pi }^{\ast }$

An everyday example. Filling seats in a bus that has double seats — passengers spread out one per seat before pairing up — matches how the two ${\pi }^{\ast }$ orbitals of O${}_2$ each take one electron.

The substance. **The switch in energy order between N${}_2$ and O${}_2$** comes from mixing of 2s and 2p orbitals, which is strong for lighter atoms.

**Bond order $=\frac{1}{2}(N_b-N_a)$, where $N_b$ and $N_a$ are electrons in bonding and antibonding orbitals; a positive bond order means a stable molecule, a higher bond order means a shorter and stronger bond, and any unpaired electrons make the species paramagnetic.

Worked example 1 — oxygen.** Bonding electrons: $\sigma 1s^2,\sigma 2s^2,\sigma 2p_z^2,\pi 2p^4$, so $N_b=10$. Antibonding: ${\sigma }^{\ast }1s^2,{\sigma }^{\ast }2s^2,{\pi }^{\ast }2p^2$, so $N_a=6$.

$$\text{bond order}=\frac{1}{2}(10-6)=2$$

The two ${\pi }^{\ast }$ electrons are unpaired, so **O${}_2$ is paramagnetic.

Worked example 2 — the series.

- H${}_2$**: $\frac{1}{2}(2-0)=1$, diamagnetic
- **He${}_2$**: $\frac{1}{2}(2-2)=0$ — does not exist
- **B${}_2$**: bond order $1$, paramagnetic
- **C${}_2$**: bond order $2$, diamagnetic
- **N${}_2$**: $\frac{1}{2}(10-4)=3$, diamagnetic, the strongest bond here
- **F${}_2$**: bond order $1$, diamagnetic

Worked example 3 — oxygen ions. O${}_2^{+}$ $2.5$, O${}_2$ $2$, O${}_2^{-}$ $1.5$, O${}_2^{2-}$ $1$, so bond length follows

$${\text{O}}_2^{2-}>{\text{O}}_2^{-}>{\text{O}}_2>{\text{O}}_2^{+}$$

An everyday example. The nitrogen in air is very unreactive, which fits its triple bond order of $3$ and very high bond dissociation enthalpy.

The substance. **MO theory correctly predicts O${}_2$ is paramagnetic**, which a simple Lewis structure cannot.

A hydrogen bond is an attraction between a hydrogen atom bonded to a highly electronegative atom (F, O or N) and a lone pair on another such atom; it is much weaker than a covalent bond but strong enough to raise boiling points and change structures.

- Intermolecular hydrogen bonds link different molecules — water, HF, alcohols — and raise boiling points
- Intramolecular hydrogen bonds form within one molecule — as in ortho-nitrophenol — and reduce association between molecules

Worked example 1 — boiling points.

- **H${}_2$O** boils at $100$ °C, while heavier **H${}_2$S** boils at about $-60$ °C — a difference of $160$ °C
- HF boils at about $19.5$ °C, while HCl boils at about $-85$ °C

Without hydrogen bonding, water would be a gas at room temperature, like H${}_2$S.

Worked example 2 — nitrophenols. Para-nitrophenol forms intermolecular hydrogen bonds and has a higher boiling point; ortho-nitrophenol bonds within itself and is more volatile.

Ice. Each water molecule in ice hydrogen-bonds to four others in an open cage, so ice is less dense than liquid water.

An everyday example. Ice cubes float in a glass of nimbu-pani because hydrogen bonds hold ice in that open, low-density structure.

The substance. Intramolecular hydrogen bonding lowers boiling point, the opposite effect to intermolecular hydrogen bonding.