Part B · How stuff sticks

6 · Shapes and the forces between molecules

By its weight, water should be a gas. Hydrogen sulfide, H2S, is almost twice as heavy and boils at −60 °C. Water boils at +100 °C. The difference comes from two facts: water molecules are bent, and their charge is lopsided.

Chapter 5 was about the bonds inside a molecule. This chapter is about the shape those bonds make, and about the much weaker pulls between molecules. Those weaker pulls decide whether a substance is a gas, a liquid or a solid at room temperature, why ice floats and why water climbs up a paper towel.

Shapes: electron groups keep their distance

Methane, CH4, has four bonds around a carbon atom. What shape do they make?

A tetrahedron, with every angle 109.5°. In 3-D, four things can get further apart than in a flat cross: that's the arrangement that keeps the four electron pairs as far from each other as possible. Press "Scramble" below and watch the pairs push each other into it.

Electron groups around a central atom (grey): bonds lead to atoms (coloured balls), lone pairs (unshared electrons) are drawn as translucent lobes. Each group repels every other, and the arrangement slides downhill in energy until it stops. Drag to rotate.

The repulsion here is a simple 1/r rule between points on a sphere, with lone pairs repelling 1.2 times as strongly as bonds. I tuned that number so water and ammonia come out within a degree of their real angles. This rule of thumb is called VSEPR. It works remarkably well for light elements, but it's a summary, not the physics. The real shape is wherever the full quantum energy is lowest.

The pattern: two groups make a straight line, three a flat triangle, four a tetrahedron, five a double pyramid, six an octahedron. Lone pairs count as groups but take up more room, because they're held by only one nucleus and spread out wider. So they squeeze the bonds together: 109.5° in methane, 107° in ammonia (one lone pair), 104.5° in water (two lone pairs).

Lopsided molecules

From chapter 5: oxygen pulls on shared electrons much harder than hydrogen does, so each O–H bond has a slightly negative oxygen end and a slightly positive hydrogen end. Whether the molecule ends up lopsided depends on its shape. Bend it and see.

Thin arrows: each bond's pull of electrons toward the oxygen. Thick arrow: their sum, the molecule's overall lopsidedness (its dipole, here drawn pointing toward the negative end). When the molecule is straight, the two pulls cancel exactly.

Carbon dioxide, O=C=O, is straight, so its two polar bonds cancel and the molecule as a whole isn't polar. Water is bent, so it has a negative end (the oxygen, with its two lone pairs) and a positive end (between the hydrogens). It's a tiny electric dipole: put water molecules in an electric field and they turn to line up with it, which is how a microwave oven heats food, by twisting water molecules back and forth billions of times a second.

Between molecules: the hydrogen bond

Here's the distinction that trips up almost everyone. The O–H bond inside a water molecule is a covalent bond, 463 kJ/mol deep. The attraction between the hydrogen of one water molecule and a lone pair on the oxygen of the next is a hydrogen bond, and it's about 20 times weaker, roughly 20 kJ/mol. It's the strongest of the "between molecules" forces, but still a different, much weaker thing. Boiling breaks the weak ones. The strong ones inside each molecule survive.

Hydrogen bonds only form when hydrogen is attached to a very electronegative atom, which in practice means nitrogen, oxygen or fluorine. That leaves the hydrogen almost bare, a concentrated bit of positive charge that can nestle against a neighbour's lone pair. Compare boiling points down each column of the periodic table:

Show as a table
Boiling points (°C, at 1 atm) of the simple hydrides of four groups of the periodic table, from the lightest (row 2) to the heaviest (row 5). Hover over a point for its value.

Heavier molecules usually boil at higher temperatures: bigger electron clouds have stronger dispersion forces (chapter 1). Methane and its family follow that rule. But the lightest member of three families breaks it badly: NH3, HF, and above all H2O. Those are the three that can hydrogen-bond. Water is the extreme case, because each molecule has two hydrogens to give and two lone pairs to receive, so it can join a network of four hydrogen bonds at once.

Same molecule size, same temperature, different stickiness between molecules:

Left: molecules with a weak pull between them (well depth 0.42 ε, like H2S). Right: a strong pull (well depth 1 ε, like water's hydrogen bonds). Same size, same mass, same temperature. Find a temperature where one box is a liquid and the other a gas.

Real hydrogen bonds are directional: they need the H to point at a lone pair. Here they're just a stronger round stickiness. Directionality is what gives ice its open structure (below), which round particles can't reproduce.

Common trap

"The bubbles in boiling water are hydrogen and oxygen." They're water vapour: whole H2O molecules that have pulled free of their neighbours. Boiling breaks the weak hydrogen bonds between molecules, never the O–H bonds inside them. Pulling water apart into hydrogen and oxygen takes electrolysis or temperatures of thousands of degrees.

Why ice floats

Almost every substance is denser as a solid than as a liquid: the particles pack tighter when they stop moving. Water is the famous exception. In ice, every molecule makes four hydrogen bonds in a rigid tetrahedral arrangement, the same 109.5° geometry as the start of this chapter. The resulting crystal is a hexagonal lattice with a lot of empty space in it. When ice melts, some of those hydrogen bonds break and molecules slump into the gaps, so liquid water is denser.

Ice has a density of about 0.92 g/cm3 against 1.00 for cold water, which is why roughly a tenth of an iceberg shows above the surface. Liquid water is densest at about 4 °C, so in winter the coldest water rises, lakes freeze from the top down, and the ice insulates the water below. Fish survive the winter because of a bond angle. And snowflakes have six arms because of that hexagonal lattice.

Physics / ML bridge

A molecule's shape is the argmin of its potential energy surface: the energy of the electrons as a function of where the nuclei sit (the Born–Oppenheimer picture, chapter 1's curve in 3N dimensions). The first simulation literally runs gradient descent on a toy energy. VSEPR is a cheap hand-built proxy for the real argmin, good enough to sketch most small molecules with no computation at all.

Machine-learned interatomic potentials (models such as MACE) now learn the surface itself from quantum-chemistry data, then let you run gradient descent and molecular dynamics at a tiny fraction of the cost. They're the modern, learned version of VSEPR's hand-made rule.

VSEPR fails for some molecules: gas-phase Li2O is straight, not bent like water; many transition-metal compounds and multiple bonds between heavy atoms don't follow it. Hydrogen bonds also have a partly covalent, quantum character that simple electrostatics doesn't fully capture.

Tell it to a 6-year-old
Look
A coin on a plate, a cup of water, a dropper or a teaspoon, and a drop of washing-up liquid.
Wonder
"How many drops of water can we pile onto this coin before it spills? Five? Twenty?"
Try
Add drops one at a time and count. Look from the side at the dome. Then dry the coin, try again with soapy water, and count again.
True sentence
"The tiny pieces of water hold on to each other, so the top of the water acts like a stretchy skin and makes a dome. Soap gets in between and weakens the skin, so it spills sooner."

This is surface tension: hydrogen bonds pulling the surface molecules inward. Most children guess far too few drops; a coin can often hold twenty or more. "Holding on" is fine; avoid "the water wants to stay together".

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