Shapes of molecules and ions

Electron pairs push apart

The shape of a molecule is set by the electron pairs round its central atom. Every pair is a region of negative charge, the pairs repel each other, and the molecule takes the shape in which the pairs are as far apart as possible. That is electron-pair repulsion theory, known by its initials as VSEPR, valence shell electron pair repulsion. Four balloons tied together by their necks settle with their ends at the corners of a tetrahedron for the same kind of reason: each is pushed by the other three until none can get further from its neighbours.

The pairs do not all repel equally. A lone pair is held by one nucleus only, so it sits closer to the central atom and spreads more widely round it than a bonding pair, which is drawn out between two nuclei. Lone pairs therefore repel more strongly. The order is lone pair–lone pair repulsion, then lone pair–bonding pair, then bonding pair–bonding pair, and each lone pair squeezes the bonding pairs a little closer together.

The shape is named from the positions of the atoms, not the positions of the electron pairs. Ammonia has four pairs arranged roughly tetrahedrally, but one of them is a lone pair, so its four atoms form a pyramid. Lone pairs decide where the atoms go, and do not appear in the name of the shape.

Electron-pair repulsion theory

The theory that the electron pairs round a central atom repel each other and move as far apart as possible, which fixes the shape of the molecule.

Bond angle

The angle between two bonds that meet at the same atom.

Bonding pair

A pair of electrons shared between the central atom and another atom in a covalent bond.

Lone pair

A pair of outer electrons on the central atom that is not shared in a bond, and repels more strongly than a bonding pair.

The five parent shapes

With only bonding pairs round the central atom, five shapes cover two to six pairs. Each is the arrangement that puts the pairs furthest apart.

Describe the drawing

Five molecules, each a central atom with bonds and no lone pairs, with the shape name and bond angle beneath. Beryllium chloride is linear at 180°. Boron trifluoride is trigonal planar at 120°. Methane is tetrahedral at 109.5°, drawn with two bonds in the plane, one wedge and one hatched wedge. Phosphorus pentachloride is a trigonal bipyramid with 120° round its middle and 90° to the poles. Sulfur hexafluoride is octahedral at 90°.

In a trigonal bipyramid the five positions are not all the same. Three equatorial positions lie in a triangle round the middle, at 120° to each other, and two axial positions lie above and below, at 90° to the equator. In an octahedron all six positions are equivalent: every angle between neighbouring bonds is 90°, and each bond is at 180° to the one opposite.

Four of the five examples break the octet rule, and the method copes with all of them. Beryllium in BeCl₂ has only four outer electrons round it and boron in BF₃ only six, so they have two and three pairs. Phosphorus in PCl₅ has ten and sulfur in SF₆ twelve, possible because both are in Period 3. Electron-pair repulsion counts pairs, whatever the total.

A molecule is drawn in three dimensions on flat paper with three kinds of line. A plain line is a bond in the plane of the paper. A solid wedge is a bond coming out of the paper towards the reader, its narrow end at the central atom. A hatched wedge, or a dashed line, is a bond going back behind the paper. Methane is drawn with two plain bonds in the plane, one wedge and one hatched wedge, and every tetrahedral carbon in organic chemistry is drawn that way.

Describe the drawing

A key of three bond styles: a plain line in the plane of the paper, a solid wedge coming towards the viewer and a hatched wedge going away, each narrow at the atom it starts from. Beside it methane drawn with two plain C–H bonds up-left and up-right, a solid wedge down-left and a hatched wedge down-right. Below, a side view with the paper as a vertical line and an eye on the left: the two plain bonds run up the line, the wedge hydrogen sits in front of it and the hatched hydrogen behind it.

Wedge bond

A bond drawn as a solid wedge, showing that it points out of the plane of the paper towards the viewer.

Dash bond

A bond drawn as a hatched wedge or dashed line, showing that it points behind the plane of the paper.

Equatorial position

One of the three positions in a trigonal bipyramid that lie in a triangle round the central atom, at 120° to each other.

Axial position

One of the two positions in a trigonal bipyramid directly above and below the central atom, at 90° to the equatorial positions.

Lone pairs close the angle

Methane, ammonia and water each have four pairs of electrons round the central atom, so all three are based on a tetrahedron. Methane's four pairs are all bonding pairs and every angle is 109.5°. Ammonia has three bonding pairs and one lone pair. The lone pair repels the bonding pairs more strongly than they repel each other, pushing them together to 107°, and the shape is pyramidal.

Water has two bonding pairs and two lone pairs. The extra repulsion closes the angle further, to 104.5°, and the shape is bent, also called non-linear or V-shaped. Each lone pair takes about 2.5° off the tetrahedral angle.

An answer that explains a shape needs three statements: how many bonding pairs and lone pairs are on the central atom, that electron pairs repel and move as far apart as possible, and, if there are lone pairs, that lone pairs repel more strongly than bonding pairs. The name of the shape and the angle follow from those. Write 'electron pairs repel', not 'bonds repel' or 'atoms repel': the pairs are what the theory is about.

Describe the drawing

Methane, ammonia and water side by side, each drawn from the same tetrahedral arrangement with wedge and hatched bonds. Methane has four C–H bonds and an arc of 109.5°. In ammonia the top position is an amber lone-pair lobe holding two electrons and the arc closes to 107°. Water has two lone-pair lobes at the top and two O–H bonds below with an arc of 104.5°. Beneath each, its shape name and its count of bonding and lone pairs.

Ions follow the same rules. In NH₄⁺ nitrogen has four bonding pairs and no lone pair, so the ion is tetrahedral with angles of 109.5°, exactly like methane, even though one of its bonds formed as a dative bond. In H₃O⁺ oxygen has three bonding pairs and one lone pair, so the ion is pyramidal with angles of about 107°, like ammonia.

A shape can change when a dative bond forms. Boron in BF₃ has three bonding pairs and is trigonal planar, 120°. When ammonia gives its lone pair to boron, forming H₃N→BF₃, boron has four bonding pairs and the bonds round it become tetrahedral, about 109.5°. Nitrogen's lone pair is now a bonding pair, so the H–N–H angle opens from 107° to about 109.5° as well.

With five or six pairs, lone pairs take the positions that keep them furthest from other pairs. In a trigonal bipyramid they go equatorial, where each has two neighbours at 90° rather than three. ClF₃ has three bonding pairs and two lone pairs, both equatorial, and its fluorine atoms form a T-shape with F–Cl–F angles a little under 90°. In an octahedron two lone pairs go opposite each other. XeF₄ has four bonding pairs and two lone pairs, and its four fluorine atoms form a square planar shape with angles of 90°.

A method for any molecule or ion

The shape of any species with one central atom comes from four steps. Count the outer electrons of the central atom, from its group. Add one for each atom joined to it by a single bond, since each of those atoms supplies one electron to its bond. Add one for each negative charge and take away one for each positive charge. Divide by two to get the number of electron pairs: the number of bonds gives the bonding pairs, and the rest are lone pairs.

Species with the same number of electrons, arranged alike, have the same shape, which gives a quick check. CH₄, NH₄⁺ and BH₄⁻ each have ten electrons and four bonding pairs on the central atom, and all three are tetrahedral at 109.5°. The amide ion, NH₂⁻, has 5 + 2 + 1 = 8 electrons round nitrogen, two bonding pairs and two lone pairs, so it is bent at about 104.5°, like water, with which it is isoelectronic.

Double bonds and larger molecules

Double bonds need one change to the method. A double bond holds two pairs, but both point in one direction, so it counts as one region of electron density when deciding the shape. In CO₂, carbon uses all four outer electrons in two double bonds, has no lone pair and two regions, so the molecule is linear, 180°.

In SO₂, sulfur uses four of its six outer electrons in two double bonds and keeps one lone pair. That is three regions, one of them a lone pair, so the molecule is bent, with an angle of about 119°. Adding one electron per bonded atom only works when every bond to the central atom is single; with doubly bonded oxygen atoms, count regions instead.

A double bond holds four electrons, so as a region it repels a little more than a single bond. In ethene the H–C–H angle is 117°, not 120°, because the C=C region pushes the two C–H bonds together. The angle round a doubly bonded carbon is quoted as 120° for the shape; the extra repulsion of the double bond explains a measured value a few degrees smaller.

BF₃, CO₃²⁻ and NO₃⁻ each have 32 electrons. The central atom in each has three regions of electron density and no lone pair, so all three are trigonal planar at 120°.

Larger molecules have more than one central atom, and the method is applied to each in turn. In ethanol, CH₃CH₂OH, both carbon atoms have four bonding pairs, so the bonds round each are tetrahedral at 109.5°. The oxygen has two bonding pairs and two lone pairs, so the C–O–H angle is about 104.5°, as in water. In ethene, CH₂=CH₂, each carbon has three regions, one of them the double bond, so each end is trigonal planar with angles of about 120°, and the whole molecule is flat.

Benzene, C₆H₆, extends the same reasoning round a ring. Each of its six carbon atoms is bonded to two carbons and one hydrogen and has no lone pair: three regions, trigonal planar, 120°. A ring of six such carbons can only be a flat regular hexagon, with every hydrogen in the same plane. Ethyne, HC≡CH, has two regions on each carbon, a single bond and a triple bond, so the molecule is linear, 180°.

Region of electron density

A lone pair, a single bond, a double bond or a triple bond, each counted once when deciding the shape round a central atom.

Other boards: hybridisation and analogous species

Cambridge describes the carbons in organic molecules through hybridisation as well as electron-pair repulsion. Four regions of electron density make a carbon sp³ and tetrahedral, as in ethane and ethanol. Three make it sp² and trigonal planar, as in ethene and every carbon of benzene, with the unhybridised p orbital at right angles to the plane forming the π bond. Two, as in ethyne, make it sp and linear. The shapes and angles are the ones VSEPR gives; hybridisation names the orbitals that point along them.

A Cambridge answer on the shape of ethene or benzene is expected to name the hybridisation of each carbon and say that the σ bonds lie in one plane, as well as giving the 120° angle.

Edexcel asks for the shapes of species analogous to the named examples to be predicted from the count of electron pairs, which is what the isoelectronic comparisons do: BH₄⁻ from CH₄, NH₂⁻ from H₂O, and CO₃²⁻ and NO₃⁻ from BF₃.