8.4 Hydrogen bonds and the anomalies of water

The Lennard-Jones potential is isotropic — it depends only on the distance between molecules, not on their orientation. That is adequate for the noble gases, but it fails for water, whose behaviour is dominated by a directional interaction the isotropic potential cannot represent. This lesson introduces the hydrogen bond and traces water’s anomalies back to its directionality.

A strong, directional bond

A water molecule carries a large permanent dipole moment ( $\sim 1.85\,\text{D}$ ): the oxygen pulls electron density away from the two hydrogens, leaving the H atoms slightly positive and the O slightly negative. A positively-charged hydrogen on one molecule is drawn to the negatively-charged oxygen of a neighbour, forming a hydrogen bond — a partially covalent, strongly directional attraction.

where

$\varepsilon_\text{HB}$: hydrogen-bond energy eV
$k_B T$: thermal energy at room temperature eV

Its strength, $\varepsilon_\text{HB} \approx 0.25\,\text{eV} \approx 10\,k_B T$ at room temperature, places it between the weak van der Waals attraction ( $\sim 0.01\,\text{eV}$ ) and a full covalent bond ( $\sim 5\,\text{eV}$ ) — strong enough to organise the liquid, weak enough to break and reform continuously.

Misalignment angle θ = 15°

The hydrogen bond is *directional*: the O–H...O configuration is energetically favourable only when the three atoms are nearly collinear. Misalign by 30° and the bond strength drops by half; misalign by 60° and it nearly vanishes. Contrast with the isotropic Lennard-Jones potential (dashed grey), which has the same energy at every angle. The directionality is what gives water its tetrahedral structure, anomalous density behaviour, high surface tension, and high heat capacity.

The directionality is the essential feature. The bond is strongest when the O–H points straight at the neighbouring oxygen; misalign it by $30^\circ$ and the strength roughly halves, by $60^\circ$ and it nearly vanishes. No isotropic potential — the Lennard-Jones included — can capture an interaction that cares which way the molecule faces.

Where water’s anomalies come from

Each water molecule can form up to four hydrogen bonds: two through its hydrogens (as donor) and two through the oxygen’s lone pairs (as acceptor). Because the bonds are directional, these four point toward the corners of a tetrahedron, and that tetrahedral geometry is the root of water’s famous anomalies:

The density maximum at 4 °C. The open tetrahedral network of ice is less dense than the liquid, so water expands on freezing and is densest a few degrees above the melting point — the reason ice floats and lakes freeze from the top.
The high heat capacity. Warming water spends energy breaking hydrogen bonds rather than raising kinetic energy, so it takes a great deal of heat to warm — a thermal buffer for oceans and organisms.
The high surface tension. A molecule at the surface has unsatisfied hydrogen bonds, making the surface energetically costly; water’s surface tension is among the highest of common liquids.

In the liquid these bonds are not static. They form and break continuously, each lasting on average only about $10^{-12}\,\text{s}$ , so the tetrahedral network is a flickering, ever-rearranging structure rather than a fixed lattice. That transient network is what gives liquid water its unusual combination of fluidity and structure, and it is invisible to the isotropic pair potentials of the earlier lessons.