Shapes of molecules

Electron-Pair Repulsion Theory

The shape of a covalent molecule is determined by electron-pair repulsion theory, which states that electron pairs around a central atom repel each other and arrange themselves as far apart as possible.

This minimises repulsion and gives the molecule its lowest-energy geometry. Each region of electron density counts as one repelling unit.

A bonding pair is a shared pair of electrons in a covalent bond. A lone pair is a non-bonded pair of electrons localised on the central atom.

Lone pairs are held closer to the central atom than bonding pairs, so they exert greater repulsion. The repulsion order is:

lone pair–lone pair > lone pair–bond pair > bond pair–bond pair

Each lone pair therefore compresses the bond angle between adjacent bonding pairs by approximately 2.5° per lone pair compared with the ideal angle.

A double bond or triple bond counts as a single region of electron density for the purposes of predicting shape, because both electron pairs occupy the same direction in space.

MisconceptionStudents often count each bond in a double bond separately. In CO₂, the two C=O double bonds count as two regions, not four, giving a linear shape and not tetrahedral.

Exam TipCount regions of electron density, not individual electrons or bonds.

Bond Length and Bond Angle

Two key descriptors of molecular geometry are bond length and bond angle, which together define the spatial arrangement of atoms in a molecule.

Bond length is the distance between the nuclei of two covalently bonded atoms, typically measured in nanometres or picometres.

Shorter bonds are generally stronger because the bonded nuclei are closer to the shared electron pair. A C=C bond is shorter and stronger than a C–C bond.

Bond angle is the angle between two covalent bonds that share a common atom, measured in degrees.

The bond angle depends on the number of bonding pairs and lone pairs around the central atom and follows the repulsion order described above.

Shapes of Specified Molecules and Ions

Applying electron-pair repulsion theory to BeCl₂, BCl₃, CH₄, NH₃, NH₄⁺, H₂O, CO₂, PCl₅(g), SF₆ and C₂H₄ gives a set of standard shapes and bond angles that must be known precisely.

The procedure is to count bonding pairs and lone pairs on the central atom, then apply the repulsion rules to deduce shape and angle.

NH₃ has one lone pair on N, which compresses the H–N–H angle from the ideal tetrahedral 109.5° down to 107°.

H₂O has two lone pairs on O, which compress the H–O–H angle further to 104.5° because lone pair–lone pair repulsion is greatest.

NH₄⁺ has the same shape as CH₄ because the lone pair on NH₃ has been used to form a dative covalent bond to H⁺, leaving four equivalent bonding pairs.

PCl₅(g) is described as gaseous because in the solid state it exists as ionic [PCl₄]⁺[PCl₆]⁻; the trigonal bipyramidal shape applies to the gas-phase molecule.

C₂H₄ has a C=C double bond; each carbon has three regions of electron density (the double bond plus two C–H bonds), giving trigonal planar geometry around each carbon and an overall planar molecule.

Examiner InsightWhen asked to “name the shape”, the precise term is required. “Pyramidal” alone is not accepted for NH₃; write “trigonal pyramidal”. “Bent” is acceptable for H₂O alongside “non-linear”.

Exam TipAlways pair the shape name with the exact bond angle.

Predicting Shapes of Analogous Species

Electron-pair repulsion theory can be used to predict the shape of any simple molecule or ion that is analogous to one of the standard examples by counting electron pairs around the central atom.

The procedure is:

• Determine the number of bonding pairs around the central atom (count each multiple bond as one region).
• Determine the number of lone pairs on the central atom.
• Match the total number of electron domains to the standard geometry.
• Adjust the bond angle downward by ≈2.5° for each lone pair present.

For example, BF₃ is analogous to BCl₃ and is trigonal planar with 120° bond angles, because B has three bonding pairs and no lone pairs.

H₃O⁺ is analogous to NH₃ because both have three bonding pairs and one lone pair on the central atom; both are trigonal pyramidal with bond angles of 107°.

PH₃ is analogous to NH₃ and is trigonal pyramidal, with a bond angle slightly smaller than 107° due to the larger central atom.

SO₂ is analogous to bent geometry: S has two regions of bonding (treating S=O as one region) and one lone pair, giving a bent shape with a bond angle near 120° before lone-pair compression.

XeF₄ is analogous to no listed standard but follows the same logic: six regions (four bonding, two lone pairs) give a square planar arrangement.