Molecular geometry and bond angles, explained for every shape (electron geometry, molecular geometry, the lone-pair effect, and a self-test)

Molecular geometry is set by the number of electron domains around the central atom, meaning its bonds and lone pairs: 2 domains give a linear shape at 180°, 3 trigonal planar at 120°, 4 tetrahedral at 109.5°, 5 trigonal bipyramidal at 90° and 120°, and 6 octahedral at 90°. Lone pairs take a domain without appearing in the shape, so water's four domains with two lone pairs give a bent molecule at about 104.5°. The full table is below, then the reasoning, then a self-test.

The table: every shape, its electron geometry, molecular geometry and bond angles

Count the domains on the central atom, count how many of them are lone pairs, and read across. The ideal angles are the geometric ones; where lone pairs are present the measured angle is a little smaller, and the table says "about" or "less than".

Domains	Lone pairs	Electron geometry	Molecular geometry	Bond angle(s)	Example
2	0	Linear	Linear	180°	CO₂
3	0	Trigonal planar	Trigonal planar	120°	BF₃
3	1	Trigonal planar	Bent	Less than 120° (about 119° in SO₂)	SO₂
4	0	Tetrahedral	Tetrahedral	109.5°	CH₄
4	1	Tetrahedral	Trigonal pyramidal	About 107°	NH₃
4	2	Tetrahedral	Bent	About 104.5°	H₂O
5	0	Trigonal bipyramidal	Trigonal bipyramidal	90° and 120° (180° between the two axial bonds)	PCl₅
5	1	Trigonal bipyramidal	Seesaw (disphenoidal)	Less than 90° and less than 120°	SF₄
5	2	Trigonal bipyramidal	T-shaped	Less than 90°	ClF₃
5	3	Trigonal bipyramidal	Linear	180°	XeF₂
6	0	Octahedral	Octahedral	90°	SF₆
6	1	Octahedral	Square pyramidal	Less than 90°	BrF₅
6	2	Octahedral	Square planar	90°	XeF₄

Thirteen rows, five electron geometries. If you are here for one molecule, you have your answer. If you are here because there is a test, keep reading: the thirteen rows are five facts and one rule, and the rest of this page is how to carry them in your head rather than on a chart.

Electron geometry vs molecular geometry: the one distinction

Everything on this page turns on one distinction, and most lost marks come from blurring it.

Electron geometry describes how all the electron domains around the central atom arrange themselves, bonds and lone pairs alike. There are only five arrangements, one for each count from 2 to 6: linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral. Call them the five parents.

Molecular geometry describes where the atoms are. A lone pair takes up a domain but is not an atom, so when a molecule has lone pairs on its central atom, its molecular geometry is the parent shape with some positions empty, and it gets a new name. Four domains with no lone pairs is tetrahedral; the same four domains with one lone pair is trigonal pyramidal; with two it is bent. Those are the children of the tetrahedral parent.

When there are no lone pairs, the two geometries coincide and have the same name. When there are lone pairs, they differ, and a question that asks for "the geometry" of water wants you to say which one you mean: tetrahedral electron geometry, bent molecular geometry. Five parents, thirteen children in all, and every child is a parent with lone pairs removed.

Why lone pairs squeeze the angles

The model behind the table is VSEPR, valence shell electron pair repulsion, set out by Gillespie and Nyholm (1957). Its rule is simple: electron domains repel one another, so they spread out around the central atom as far apart as they can. Two domains go to opposite sides, 180°. Three go to the corners of a flat triangle, 120°. Four go to the corners of a tetrahedron, 109.5°, which is the angle at which four points on a sphere are farthest apart.

Lone pairs change the angles because they are not quite like bonding pairs. A bonding pair is shared between two nuclei and is pulled out along the bond. A lone pair belongs to the central atom alone, is held closer to it, and spreads wider. A wider domain pushes its neighbours together, so the bonding pairs end up closer to one another than the ideal angle. Methane, with four bonding pairs, has the ideal 109.5°. Ammonia, with one lone pair, closes to about 107°. Water, with two lone pairs, closes further, to about 104.5°. The same pattern runs through the trigonal planar and octahedral families: a lone pair always squeezes the angles between the bonds that remain.

VSEPR is a model, not a law. Gillespie (2008), reviewing fifty years of it, is clear that it predicts the shapes of most main-group molecules well and has known exceptions, especially among transition-metal compounds, where other models do better. For a Grade 12 or first-year course it is the model you will be asked for, and the table above is what it predicts.

How to work out any shape in four steps

1. Draw the Lewis structure. Count the valence electrons of every atom and add them up. Put the least electronegative atom in the centre (never hydrogen). Join each outer atom to the centre with a single bond, complete the outer atoms' octets, and put any electrons left over on the central atom. If the central atom is short of an octet, move a lone pair from an outer atom in to make a double bond. The SCH4U page places the Lewis-structure idea this depends on in the course; it is the step before this one.
2. Count the electron domains on the central atom. Each bond counts once, whether it is single, double or triple, because the electrons of a multiple bond sit in the same region of space. Each lone pair counts once.
3. Read the electron geometry from the count. Two is linear, three trigonal planar, four tetrahedral, five trigonal bipyramidal, six octahedral.
4. Remove the lone pairs to read the molecular geometry and its angle. Find the row of the table with that domain count and that number of lone pairs. The angle is the parent's, squeezed a little for each lone pair.

With a five-domain parent there is one more decision: a lone pair goes in an equatorial position, around the triangle, not an axial one, because the equatorial position has only two neighbours at 90° while an axial one has three. With a six-domain parent, two lone pairs go opposite each other. Those two rules are why SF₄ is a seesaw and XeF₄ is square planar.

Worked examples: NH₃, SF₄, XeF₄ and CO₂

Each in four lines, the electron count first so you can check it.

Ammonia, NH₃. Valence electrons: nitrogen 5, three hydrogens 3 × 1 = 3, total 8. Nitrogen is central, with three N–H bonds using 6 electrons; the remaining 2 are a lone pair on nitrogen. Domains: 3 bonds + 1 lone pair = 4, so tetrahedral electron geometry. Remove the lone pair: trigonal pyramidal, about 107°.

Sulfur tetrafluoride, SF₄. Valence electrons: sulfur 6, four fluorines 4 × 7 = 28, total 34. Four S–F bonds use 8; each fluorine completes its octet with 6 more, 24 in all, making 32; the last 2 are a lone pair on sulfur. Domains: 4 + 1 = 5, so trigonal bipyramidal electron geometry, and the lone pair takes an equatorial position. Remove it: seesaw, with angles a little under 90° and under 120°.

Xenon tetrafluoride, XeF₄. Valence electrons: xenon 8, four fluorines 28, total 36. Four Xe–F bonds use 8, the fluorines' octets 24, total 32; the remaining 4 are two lone pairs on xenon. Domains: 4 + 2 = 6, so octahedral electron geometry, and the two lone pairs sit opposite each other. Remove them: square planar, 90°.

Carbon dioxide, CO₂. Valence electrons: carbon 4, two oxygens 2 × 6 = 12, total 16. Single bonds leave carbon short of an octet, so each oxygen shares a second pair: two C=O double bonds, and no lone pairs on carbon. Domains: 2 (a double bond is one domain), so linear, 180°.

Notice that the electron count does the work. If your total is wrong, every line below it is wrong, so write the arithmetic down: 5 + 3 = 8; 6 + 28 = 34; 8 + 28 = 36; 4 + 12 = 16.

Polarity follows from the shape

A bond between two different atoms is polar, with the electrons pulled toward the more electronegative one; that pull is a bond dipole. A molecule is polar when its bond dipoles do not cancel, and whether they cancel is a question about the shape.

Symmetric shapes with identical outer atoms are non-polar, because every bond dipole has a partner pulling the other way: linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral and square planar. CO₂ is the standard case: two polar bonds, 180° apart, cancelling to zero.

Shapes with lone pairs on the central atom are usually polar, because the lone pair leaves a gap on one side and the bond dipoles add up on the other: bent, trigonal pyramidal, seesaw, T-shaped and square pyramidal. Water is the standard case: two polar bonds at about 104.5°, adding to a dipole that points through the oxygen.

The two exceptions are the two shapes where the lone pairs sit exactly opposite each other. Linear XeF₂, with three lone pairs around the equator, and square planar XeF₄, with two lone pairs along the axis, are non-polar even though they carry lone pairs. One outer atom different from the rest breaks any of these symmetries: CHCl₃ is tetrahedral and polar.

How to learn the table, not just read it

Do not memorize thirteen rows. Memorize five facts and one rule.

The five facts are the parents and their angles: 2 linear 180°, 3 trigonal planar 120°, 4 tetrahedral 109.5°, 5 trigonal bipyramidal 90° and 120°, 6 octahedral 90°. The rule is: remove lone pairs to get the child, and each lone pair squeezes the angles between the bonds that remain, with the five-domain lone pairs going equatorial and the six-domain pair going opposite. Every row of the table is one of the five facts with the rule applied, and a row you can derive is a row you cannot forget under pressure.

Then make the material do the testing. Write recall cards for the five parents and the rule, and for the handful of children whose names are not obvious (seesaw, T-shaped, square pyramidal); how to write a flashcard keeps the answer off the front. Redraw the shapes from memory on a blank page, with the lone pairs drawn in and the angles labelled, then compare; active recall has the honest-marking rules for that. The science study guide how to study for science has the routine for a whole unit of this kind.

This is the pattern for every table in chemistry: the periodic trends, the strong acids, the solubility rules, the reduction potentials. Find the small set of facts and the rule that generates the rows, learn those, and derive the rest.

Self-test: ten molecules to shape

Shape each of these before you scroll to the answers. For each one, write the electron count, the domain count, the electron geometry, the molecular geometry and the angle. Attempting first is the rule that makes the rest of the page work, and it is chapter 1 of the free playbook.

1. BeCl₂
2. BCl₃
3. SO₃
4. PH₃
5. H₂S
6. CCl₄
7. PF₅
8. BrF₃
9. SF₆
10. IF₅

Mark yourself on three levels: right, struggled, wrong or looked. "I would have got it" is wrong. The ones you missed are tomorrow's first cards.

VSEPR shapes on one screen

• Five parents, five angles: linear 180°, trigonal planar 120°, tetrahedral 109.5°, trigonal bipyramidal 90° and 120°, octahedral 90°.
• One distinction: electron geometry counts every domain; molecular geometry describes the atoms. With lone pairs, they differ.
• One rule: a lone pair takes a domain and squeezes the remaining bond angles; CH₄ 109.5° → NH₃ about 107° → H₂O about 104.5°.
• Two placements: five-domain lone pairs go equatorial; six-domain lone pairs go opposite.
• Polarity: symmetric shapes with identical outer atoms are non-polar; lone pairs usually make a molecule polar, except linear XeF₂ and square planar XeF₄.
• Four steps: Lewis structure, count the domains, read the parent, remove the lone pairs.

Self-test answers

Check your working, not just the name.

1. BeCl₂: 2 + 14 = 16 electrons; 2 bonds, no lone pairs on Be; 2 domains; linear, 180°.
2. BCl₃: 3 + 21 = 24; 3 bonds, no lone pairs on B; 3 domains; trigonal planar, 120°.
3. SO₃: 6 + 18 = 24; three S–O bonds (drawn with double bonds to complete sulfur's octet), no lone pairs on S; 3 domains; trigonal planar, 120°.
4. PH₃: 5 + 3 = 8; 3 bonds and 1 lone pair; 4 domains; tetrahedral electron geometry, trigonal pyramidal, less than 109.5° (measured, phosphine's angle is well below ammonia's).
5. H₂S: 6 + 2 = 8; 2 bonds and 2 lone pairs; 4 domains; tetrahedral electron geometry, bent, less than 109.5° (measured, well below water's angle too).
6. CCl₄: 4 + 28 = 32; 4 bonds, no lone pairs on C; 4 domains; tetrahedral, 109.5°.
7. PF₅: 5 + 35 = 40; 5 bonds, no lone pairs on P; 5 domains; trigonal bipyramidal, 90° and 120°.
8. BrF₃: 7 + 21 = 28; 3 bonds and 2 lone pairs on Br; 5 domains; trigonal bipyramidal electron geometry, T-shaped, a little under 90°.
9. SF₆: 6 + 42 = 48; 6 bonds, no lone pairs on S; 6 domains; octahedral, 90°.
10. IF₅: 7 + 35 = 42; 5 bonds and 1 lone pair on I; 6 domains; octahedral electron geometry, square pyramidal, a little under 90°.

If you got eight or more right with the working shown, the table is yours. If not, the misses name the parent you have not yet learned, and that parent is the card for tonight.