Foundations — VSEPR theory — geometry from electron pairs (linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral, etc

Before we can watch clouds "spread out on a sphere," we must agree on what every word, letter, and picture in the parent note actually means. This page assumes you know nothing and builds each tool only when the next one needs it. We go bottom-up: charge → cloud → domain → counting → angles → geometry.

1. Charge and repulsion — the engine of everything

Why the topic needs this: the entire theory is one sentence — "like charges repel, so electron clouds spread out." If you don't feel repel in your bones, nothing else lands. See Formal Charge for how we track charge on atoms more carefully later.

2. The central atom and its neighbours

Why the topic needs this: "geometry of the molecule" really means "geometry of the spokes around one hub." Finding the central atom is always step zero.

3. Electrons in pairs — bonding pairs and lone pairs

Why the topic needs this: the parent note's key rule — that lone pairs "squeeze" angles more than bonding pairs — only makes sense once you see why they are different clouds. A lone pair is held by one nucleus, so its cloud puffs out fatter and closer; a bonding pair is stretched thin between two nuclei. Where do these pairs come from? From the dot-diagram of the molecule — that is Lewis Structures.

4. The electron domain — the real unit VSEPR counts

Why the topic needs this: this is the single most-missed idea (the parent's first "steel-manned mistake"). Count directions, not electrons.

5. Counting — the steric number $SN$

Now we meet our first real formula. Before writing it, know what each symbol means.

Why the topic needs this: the parent claims "$SN$ ALONE fixes the electron geometry." So $SN$ is the master dial: turn it to 2, 3, 4, 5, 6 and the shape falls out.

6. Angles and the degree symbol ${}^{\circ }$

Why the topic needs this: "maximise the angle" is literally the goal of the whole theory. Every shape is named by the special angle it produces.

7. Points on a sphere — what "spread out in 3D" means

• $N=2$ → opposite poles → a straight line, angle $180^{\circ }$.
• $N=3$ → a flat triangle → $120^{\circ }$.
• $N=4$ → a tetrahedron (a 3-sided pyramid) → $109.5^{\circ }$.
• $N=5$ → trigonal bipyramid (two special angles, $90^{\circ }$ and $120^{\circ }$).
• $N=6$ → octahedron → $90^{\circ }$.

Why the topic needs this: the shapes in the parent's big table are not arbitrary — they are the natural answers to this "spread the balloons" puzzle. Chemistry sets $N$ (via $SN$); geometry decides the rest.

8. Two geometries — electrons vs atoms

Why the topic needs this: confusing these two is the parent's third steel-manned mistake. They agree only when there are zero lone pairs.

The one tool from beyond this page: $\cos \theta$

The parent derives the tetrahedral angle with a dot product and $\arccos$. Those belong to a separate foundations page — for now just know:

• $\theta$ (Greek letter "theta") is the name we give the unknown angle between two spokes.
• $\cos \theta$ and $\arccos$ are the machinery that turns a spoke's directions into that angle number, giving $109.47^{\circ }$. You will meet them fully when you need them; here just trust that the tetrahedron's angle is exactly $\arccos (-\frac{1}{3})$.

How the foundations feed the topic

Read it top to bottom: repulsion makes pairs matter, pairs become domains, domains get counted into $SN$, $SN$ picks a sphere-arrangement, and the arrangement (bent by lone pairs) becomes the final shape.

Related tools you will meet next

• Lewis Structures — where the dots and lines (bonds, lone pairs) come from in the first place.
• Formal Charge — a bookkeeping check on where electrons sit.
• Hybridization — a companion picture that also predicts $109.5^{\circ }$, $120^{\circ }$, $180^{\circ }$.
• Bond Polarity and Dipole Moment — how the shape decides whether the molecule is polar.
• Molecular Orbital Theory — a deeper electron-cloud model.
• Back to the parent: VSEPR — geometry from electron pairs.

Equipment checklist

Test yourself — cover the right side and answer each before revealing.