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Shapes of Molecules (VSEPR)

Shapes of simple molecules up to six electron pairs. Electron pairs can be moved to show their repulsion. Bond angles and geometries calculated using VSEPR theory.

Open the Shapes of Molecules (VSEPR) simulation

Teaching notes

Suggested use

Open with methane, which is where the simulation starts. Before saying anything about rules, drag one of the hydrogens well away from where it sits and hold it there. The other three shift while you hold it, and when you let go the whole molecule springs back to exactly the arrangement it started in. Press Shake to throw all four off at once; it recovers just the same. Nothing in the code knows the word "tetrahedral". The shape is what four mutually repelling charges settle into when they are free to move on a sphere.

Establish this before the shapes themselves, because it is the part students most often miss. A tetrahedron in a textbook looks like a fact to memorise. Here it is an outcome, and one you can disturb and watch re-form.

Then work along the molecule row, which is in order of how many electron pairs the central atom has: one, two, three, four, five, six. Ask for a prediction before each click. Two useful pauses:

At CH₄, ask why the four hydrogens do not simply sit at the corners of a square, 90° apart. Most students will have drawn methane flat at some point. Nothing stops you dragging all four hydrogens roughly into a plane to try it; they will not stay.

At NH₃, ask for the bond angle before revealing it. Ammonia has four electron pairs, exactly as methane does, so a reasonable first answer is 109.5°. It reads 107°. Water, with the same four pairs, reads 104.5°. Those two numbers are the evidence that a lone pair is not simply a bonding pair without an atom on the end, and they deserve some time before any explanation is offered.

PCl₅ repays some time. It is the first molecule in the row with two different bond angles, and the reason is better drawn out of the class than stated: five points cannot be spread evenly over a sphere, so two of them have to be different from the other three.

The last entry, AX_nE_m, is not a substance. Two sliders set the number of bonding and lone pairs, up to six between them, and the model builds whatever those pairs settle into. It is the quickest way to work through the whole VSEPR table in one place, and it reaches the shapes that need five or six pairs, which are hard to picture from a flat diagram: the see-saw at four bonding and one lone, the T-shape at three and two, and the square plane at four and two. Ask students to predict the shape from the two numbers before releasing the slider.

Where the lone pairs sit is not looked up. The model costs every way of placing them on the arrangement and keeps the cheapest, which is how it puts a lone pair in a trigonal bipyramid on the equator rather than at a pole, and puts two in an octahedron opposite each other.

Drag the empty space to turn any molecule round. Lone pairs can be dragged too, and they relax back like everything else.

Where the shapes come from

We start from one claim: the electron pairs around a central atom repel each other, so they end up as far apart as they can get. That is the whole of VSEPR, and everything in this simulation follows from it.

For two pairs the answer is immediate. Two charges free to move on a sphere go to opposite poles, 180° apart, and carbon dioxide is linear. Notice, though, what we are counting. Carbon in CO₂ has four bonding pairs, two in each double bond, but the two pairs of a C=O double bond point the same way and cannot separate from each other. They act as a single region of charge. This is why we count regions rather than pairs, and it is the most common place for a prediction to go wrong.

Three regions give a flat triangle at 120°, as in BH₃. Four needs more thought. If we stay in a plane, four charges give 90° each. But we are not confined to a plane, and lifting two of them out of it lets all four get further apart: 109.5°, the tetrahedral angle. You can test this directly in the simulation by dragging the hydrogens of methane towards a square arrangement and releasing them.

So far every pair has held an atom, and the shape of the molecule has been the same as the arrangement of the pairs. Ammonia breaks that. Nitrogen has four pairs, so the pairs are still arranged tetrahedrally, but one of them is a lone pair with no atom on the end. When we name a shape we are describing where the atoms are, and three atoms plus a nitrogen make a trigonal pyramid, not a tetrahedron. Water is the same argument run twice: four pairs, tetrahedral arrangement, two atoms, and the shape we name is bent.

Lone pairs and bond angles

Ammonia is 107° and water 104.5°, both smaller than methane's 109.5°, and all three have four electron pairs on the central atom. If the four pairs were equivalent the angle would be the same in all three, so they are not equivalent: a lone pair presses harder on its neighbours than a bonding pair does.

Two things make that plausible. A bonding pair is held between two nuclei, so it is drawn away from the central atom; a lone pair is attracted by one nucleus only and stays closer in. And a bonding pair is stretched out along the bond, while a lone pair is fatter near the atom it belongs to. Both give a lone pair more presence close to the central atom, where the crowding is.

Here we should be careful about what the simulation is and is not doing. For methane, carbon dioxide, borane, phosphorus pentachloride and sulfur hexafluoride the model is predicting: equal charges repelling on a sphere produce 109.5°, 180°, 120°, and 90° with 120°, and it would produce them whatever we did. For ammonia and water it is not predicting. The strength of the lone pair has been set for each molecule to whatever reproduces the measured angle, because VSEPR tells us the angle should shrink but gives us no way of working out by how much. The shapes are a result; those two angles are an input.

There is also more going on than lone pairs. Nitrogen trifluoride, NF₃, has the same single lone pair as ammonia, so counting pairs predicts a similar angle. It is 102.5°, noticeably tighter than ammonia's 107°. Fluorine is far more electronegative than hydrogen and draws each bonding pair away from the nitrogen; with the bonding pairs held further off, they press on each other less and the lone pair wins more of the argument. Counting lone pairs cannot see this coming, because both molecules have exactly one.

Five electron pairs

Two, three, four and six pairs all have a symmetrical answer, and in every one of them each position is equivalent to every other. Five does not. Set the simulation to PCl₅ and look at the two angle readings: 90° and 120°. Three of the chlorines sit in a triangle round the middle, 120° apart, and two sit above and below at 90° to that triangle. The two axial positions and the three equatorial ones are different places to be, with different numbers of close neighbours.

The model is not at fault here. There is no way to place five points evenly on a sphere, so the best arrangement has to be an uneven one. Six pairs recovers the symmetry: the octahedron of SF₆ puts every fluorine in an identical position with four neighbours at 90° and one opposite at 180°.

Looking ahead

The first thing that changes at university is the reason. VSEPR says electron pairs repel, and it is natural to read that as ordinary electrostatic repulsion between like charges. That is not really it. The dominant effect is the Pauli exclusion principle: two electrons with the same spin cannot occupy the same region, so pairs of electrons keep out of each other's way whether or not we account for their charge. The geometry VSEPR predicts is right far more often than the reason it gives for it.

You will also meet a second language for the same shapes. Hybridisation describes methane's four equivalent bonds as sp³, boron's three as sp², and carbon dioxide's two as sp. Bent's rule, which says that s character concentrates in bonds to less electronegative atoms, handles the NF₃ problem above rather better than counting lone pairs does. Molecular orbital theory goes further again and treats the whole molecule at once, which is the only approach that explains why water is bent and beryllium hydride is linear in terms of orbital energies rather than repulsion. The molecular orbital simulations on this site are the starting point for that.

VSEPR does break down, and phosphine is the clearest case. PH₃ has the same AX₃E arrangement as ammonia, so VSEPR predicts something close to 107°. The measured angle is 93.3°, and H₂S is 92° against water's 104.5°. These are close to 90°, which is what you would expect if the bonds used almost pure p orbitals with the lone pair sitting in a largely unmixed s orbital. Going down a group, the s and p orbitals of the central atom become more different in energy and mix less, and the tetrahedral picture stops applying. VSEPR gives no hint that this is coming.

Model notes and assumptions

The model. Each electron pair around the central atom is a point charge on a sphere, and every pair repels every other with a force that falls off with the square of the distance between them. Nothing tells the pairs where to sit. Each bond also has a preferred length, so an atom pulled in or out springs back.

Angles. The Measured column gives experimental bond angles. For carbon dioxide, borane, methane, phosphorus pentachloride and sulfur hexafluoride, equal charges on a sphere give the measured angles directly, since those angles are fixed by symmetry. For ammonia and water, the extra repulsion of a lone pair is set by hand for each molecule to reproduce the measured angle, 107° and 104.5°. The AX_nE_m entry has no measured angle, so that column shows a dash.