Before we start

0 · Why physicists never quite get chemistry

If you know physics, chemistry can feel like a pile of arbitrary rules: octets, electronegativities, "like dissolves like", acids and bases, curly arrows. You can tell they're true, but not why. This course is an attempt to show the why.

All of chemistry is known, and none of it is solvable

In 1929, Paul Dirac wrote that "the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble."

He was right on both counts. The rulebook is one equation: the Schrödinger equation for nuclei and electrons interacting through Coulomb's law (plus relativity for heavy atoms, which he waved away). But the cost of solving it exactly grows exponentially with the number of electrons. A single caffeine molecule has 102 electrons. A cup of coffee has about 1025 molecules.

So chemistry did what any field does when the true model is intractable: it built compressed models. The octet rule, VSEPR shapes, electronegativity, pKa, functional groups and reaction mechanisms are cheap, approximate, transferable summaries of the full quantum mechanics. They're good enough to design drugs and materials with, and each of them fails somewhere.

Most concepts in chemistry that have proven productive in the design of new experiments are not reducible to physics… aromaticity, the acid–base concept, the idea of a functional group, a substituent effect… And let us not forget the chemical bond. Roald Hoffmann, Nobel laureate in chemistry, 2007

Hoffmann distinguishes vertical understanding, deriving something from deeper laws, from horizontal understanding, relating it to other things at the same level. Chemists mostly reason horizontally, in their compressed concepts, and a physicist reading chemistry keeps asking for the vertical story. This course gives both: every chapter builds the concept from physics you already know, then says plainly where the shortcut breaks.

ML bridge

If you work in machine learning, you already know this situation. Chemistry's concepts behave like learned features: representations that make a hard function easy to approximate, transfer between problems, and generalise well inside their training distribution but not outside it. The octet rule is a feature that works for the second row of the periodic table. VSEPR is a cheap surrogate for the argmin of an energy surface. Electronegativity is a one-dimensional embedding of "how much does this atom want electrons" that turns out to be approximately a chemical potential. Throughout the course, boxes like this one point out these correspondences, and where they stop holding.

Three ideas carry most of the course

  1. Electrical attraction plus quantum rules make energy wells. Atoms attract a little and repel a lot (chapter 1). Electrons in atoms form standing waves in shells (chapter 3), and bonds are electrons arranged to sit between positive nuclei (chapter 5). Breaking a bond always costs energy.
  2. Temperature decides which wells win. Everything jiggles with energy about kT, and the Boltzmann factor e−E/kT, together with counting arrangements (entropy), decides what's stable: solid or gas, reactants or products (chapters 7, 8, 11).
  3. Valleys decide the destination; passes decide the speed. Equilibrium depends only on free energies (chapter 11). How fast you get there depends on the barrier between (chapter 10), which is why catalysts and enzymes matter.

Acids, batteries, rust, water's weirdness, the periodic table and life itself are those three ideas applied to particular molecules.

Map of the course

Chapters build on each other, but not in a straight line. Hover over a chapter to see what it relies on and what relies on it; click to go there.

Each arrow means "the later chapter uses ideas from the earlier one". Columns are depth: how many chapters you need to have read first, at most.
Reading it with a 6-year-old

Every chapter ends with a box like this one, built from what research says works for young children:

Keep it short
One box is a few minutes: a thing to look at, a question, an experiment, one sentence to remember.
Predict first
Always ask "what do you think will happen?" before trying. Being wrong is the interesting part.
True, not fancy
The sentences are simplified but never false, so nothing has to be unlearned later. Say "the pieces pull on each other", not "the atoms want to be together"; say "a fuzzy cloud", not "electrons orbit like planets".
Same idea, again
The anchor sentence comes back in many chapters: "Everything is made of tiny pieces, much too small to see. The pieces aren't in the stuff: they are the stuff."

The experiments use kitchen materials; each box notes what the grown-up should handle. Chapters 1, 7, 8 and 12 have the easiest experiments to start with.