Molecular Orbitals and Hydrogen Bonding: Quick Revision

A brief note on Molecular Orbitals and Hydrogen Bonding. Read it before a test. Try each question at the end before you open its answer.

Molecular orbitals

• Atomic orbitals combine into the same number of molecular orbitals.
• Bonding: $\psi_A + \psi_B$, lower energy. Antibonding: $\psi_A - \psi_B$, higher energy, starred.
• They combine only with similar energy, the same symmetry and good overlap.
• Up to $\text{N}_2$: $\sigma 2s$, $\sigma^* 2s$, $\pi 2p$, $\sigma 2p$, $\pi^* 2p$, $\sigma^* 2p$.
• For $\text{O}_2$ and $\text{F}_2$: $\sigma 2p$ comes before $\pi 2p$.
• Fill by the Aufbau, Pauli and Hund rules.

Bond order and magnetism

• Bond order $= \dfrac{1}{2}(N_b - N_a)$.
• Zero: no stable molecule ($\text{He}_2$, $\text{Be}_2$, $\text{Ne}_2$).
• Higher bond order: stronger and shorter bond.
• Unpaired electrons: paramagnetic ($\text{O}_2$, $\text{B}_2$). All paired: diamagnetic ($\text{N}_2$, $\text{C}_2$).
• $\text{O}_2^+$, $\text{O}_2$, $\text{O}_2^-$ and $\text{O}_2^{2-}$ have bond orders $2.5$, $2$, $1.5$ and $1$.

The hydrogen bond

• $\text{H}$ joined to $\text{F}$, $\text{O}$ or $\text{N}$, attracted to a lone pair on another such atom.
• Intermolecular: HF chains, the water network. Intramolecular: ortho-nitrophenol.
• It lifts the boiling points of $\text{H}_2\text{O}$, HF and $\text{NH}_3$, and makes ice less dense than water.

A worked example

Find the bond order and the magnetism of the superoxide ion, $\text{O}_2^-$.

1. Electrons. Oxygen has $16$, plus one: $17$.
2. Fill. $\sigma 1s^2$ $\sigma^* 1s^2$ $\sigma 2s^2$ $\sigma^* 2s^2$ $\sigma 2p^2$ $\pi 2p^4$ $\pi^* 2p^3$.
3. Count. Bonding $2 + 2 + 2 + 4 = 10$; antibonding $2 + 2 + 3 = 7$.
4. Bond order. $\dfrac{10 - 7}{2} = 1.5$.
5. Magnetism. Three electrons in two $\pi^*$ orbitals leave one unpaired: paramagnetic.

Practice with new numbers

A program to try

The program lists the bond order, bond length and bond enthalpy of $\text{N}_2$, $\text{O}_2$ and $\text{F}_2$, and sorts them by bond order.

Mistakes to avoid

• One energy order for all. Oxygen and fluorine put $\sigma 2p$ below $\pi 2p$.
• Forgetting to halve the difference. Two electrons make one bond.
• *Pairing oxygen's $\pi^$electrons.** They stay unpaired, so$\text{O}_2$ is paramagnetic.
• Every ion weaker than its molecule. $\text{O}_2^+$ is stronger than $\text{O}_2$.
• Hydrogen bonds with carbon or chlorine. Strong ones need $\text{F}$, $\text{O}$ or $\text{N}$.

Check yourself

1. What is the bond order of $\text{Li}_2$, and is it paramagnetic?

2. Why does $\text{N}_2^+$ have a weaker bond than $\text{N}_2$, while $\text{O}_2^+$ has a stronger bond than $\text{O}_2$?

3. Why does ammonia dissolve so well in water?

4. Which is the more volatile of the two nitrophenols, and why?