Chemical Bonding: Shapes and Intermolecular Forces

This guide covers subtopics 3.4 to 3.7 of Topic 3, Chemical bonding, from Cambridge International AS & A Level Chemistry 9701, 2025–2027 series. This is AS Level content.

Before studying this

This resource does not re-teach ionic or covalent bonding from first principles — Ionic, Covalent and Metallic Bonding covers those foundations for IGCSE/O Level, and 9701’s own subtopics 3.1–3.3 (electronegativity, ionic bonding, metallic bonding) build on that before this page begins. What follows is 9701-specific: bonding described in terms of orbitals, not just shared or transferred electron pairs, plus the geometry and intermolecular forces that follow from it.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL CHEMISTRY 9701 — AS Level, Topic 3

3.4 Covalent bonding and coordinate (dative covalent) bonding — covalent bonding as electrostatic attraction between nuclei and a shared electron pair, in molecules including H₂, O₂, N₂, Cl₂, HCl, CO₂, NH₃, CH₄, C₂H₆ and C₂H₄; expanded octets in Period 3 elements (SO₂, PCl₅, SF₆); coordinate bonding, including NH₃ + HCl → NH₄⁺ and the Al₂Cl₆ molecule; σ and π bonds from orbital overlap, and how they form in H₂, C₂H₆, C₂H₄, HCN and N₂; hybridisation (sp, sp², sp³); bond energy and bond length, defined and used to compare reactivity.

3.5 Shapes of molecules — using VSEPR theory to state and explain shape and bond angle for BF₃, CO₂, CH₄, NH₃, H₂O, SF₆ and PF₅; predicting the shape and bond angle of analogous molecules and ions.

3.6 Intermolecular forces, electronegativity and bond properties — hydrogen bonding in N–H and O–H containing molecules (ammonia, water); using hydrogen bonding to explain water/ice’s anomalous melting/boiling points, surface tension and solid-vs-liquid density; electronegativity, bond polarity and dipole moments; van der Waals’ forces as a generic term, split into instantaneous dipole–induced dipole (London dispersion) forces and permanent dipole–permanent dipole forces (including hydrogen bonding); the general rule that ionic, covalent and metallic bonding are stronger than intermolecular forces.

3.7 Dot-and-cross diagrams — using dot-and-cross diagrams for ionic, covalent and coordinate bonding, including species from 3.4 and 3.5, and species with an expanded octet or an odd number of electrons.

Orbital overlap: σ and π bonds

A σ (sigma) bond forms by direct, head-on overlap of orbitals between two bonding atoms; a π (pi) bond forms by sideways overlap of adjacent p orbitals, above and below the σ bond. A single bond is always one σ bond alone; a double bond is one σ bond plus one π bond — which is why the second bond in a C=C double bond is weaker and more reactive than the first: sideways overlap is less effective than head-on overlap.

Hybridisation describes how an atom’s orbitals mix before bonding: an sp³ carbon (as in methane or ethane) has four equivalent hybrid orbitals arranged tetrahedrally; an sp² carbon (as in ethene) has three hybrid orbitals in a plane, leaving one unhybridised p orbital free to form a π bond; an sp carbon has two hybrid orbitals arranged linearly, leaving two unhybridised p orbitals for two π bonds.

Coordinate (dative covalent) bonding

A normal covalent bond is formed from one electron contributed by each bonding atom. A coordinate (dative covalent) bond is a covalent bond in which both shared electrons come from the same atom — the other atom contributes none. Once formed, a coordinate bond behaves exactly like any other covalent bond: it has the same length and strength as an equivalent bond formed the normal way, and cannot be told apart from it once the molecule or ion exists.

Forming the ammonium ion, NH₄⁺. Ammonia’s nitrogen atom has a lone pair of electrons. A hydrogen ion, H⁺, has no electrons at all (it is a bare proton). When NH₃ reacts with H⁺ (for example from HCl), nitrogen’s lone pair is donated entirely into the new N–H bond:

NH₃ + H⁺ → NH₄⁺

The new bond is coordinate, formed from nitrogen’s lone pair alone — but the resulting ammonium ion has four identical N–H bonds; there is no way to distinguish the coordinate bond from the three original covalent N–H bonds once NH₄⁺ has formed.

The Al₂Cl₆ dimer. Aluminium chloride, AlCl₃, is electron-deficient: the aluminium atom in a single AlCl₃ unit has only six electrons around it (three bonding pairs, no lone pair), one short of a full octet. In the vapour phase, two AlCl₃ units pair up to fix this. A lone pair on a chlorine atom of one AlCl₃ unit is donated into a coordinate bond with the aluminium atom of the other unit, and a lone pair on a chlorine of the second unit is simultaneously donated back to the aluminium of the first. This gives two bridging chlorine atoms, each holding the two AlCl₃ units together by one normal covalent bond and one coordinate bond, and the whole dimer, Al₂Cl₆, has both aluminium atoms with a full octet.

Expanded octets

Some central atoms — particularly Period 3 elements such as phosphorus and sulfur — can be surrounded by more than eight electrons, because they are large enough, and have accessible orbitals of a suitable energy, to accommodate extra bonding pairs. This does not happen for Period 2 elements such as carbon, nitrogen or oxygen, which are restricted to a maximum of eight electrons around them.

• SO₂ — sulfur is surrounded by 10 electrons: one lone pair plus two S=O double bonds (each double bond contributing a pair of bonding electrons counted twice, once as a σ pair and once as a π pair, in the electron-counting convention used at this level).
• PCl₅ — phosphorus is surrounded by 10 electrons: five P–Cl single bonds, five bonding pairs.
• SF₆ — sulfur is surrounded by 12 electrons: six S–F single bonds, six bonding pairs.

These expanded-octet species are exactly the ones used to test the trigonal-bipyramidal (PF₅-type) and octahedral (SF₆-type) VSEPR shapes below.

Bond energy and bond length

Bond energy is the energy needed to break one mole of a given covalent bond in the gaseous state; a higher bond energy means a stronger bond. Bond length is the distance between the nuclei of two bonded atoms; a shorter bond is generally a stronger one. The two measures move together: for a given pair of atoms, a triple bond is shorter and stronger than a double bond, which is in turn shorter and stronger than a single bond (compare C–C, C=C and C≡C). Bond energy and bond length are used throughout organic chemistry to compare how reactive different bonds are — a shorter, stronger bond is generally harder to break, and so the site of a reaction is often the longest, weakest bond available.

Shapes of molecules — VSEPR theory

Valence Shell Electron Pair Repulsion (VSEPR) theory says electron pairs around a central atom — bonding and lone pairs alike — arrange themselves as far apart as possible, to minimise repulsion between them. Lone pairs repel more strongly than bonding pairs, which is why replacing a bonding pair with a lone pair compresses the remaining bond angles.

Molecule	Electron pairs (bonding + lone)	Shape	Bond angle
BF₃	3 + 0	Trigonal planar	120°
CO₂	2 + 0	Linear	180°
CH₄	4 + 0	Tetrahedral	109.5°
NH₃	3 + 1	Pyramidal	107°
H₂O	2 + 2	Non-linear (bent)	104.5°
PF₅	5 + 0	Trigonal bipyramidal	120° and 90°
SF₆	6 + 0	Octahedral	90°

The trend from CH₄ (109.5°) to NH₃ (107°) to H₂O (104.5°) is a direct consequence of lone-pair repulsion: each lone pair added in place of a bonding pair squeezes the remaining bond angles a little further.

Intermolecular forces

Every molecule experiences van der Waals’ forces — the generic term for intermolecular forces other than the bonds holding a molecule together. Two kinds matter at AS:

Instantaneous dipole–induced dipole (id-id) forces, also called London dispersion forces, exist between all molecules, arise from momentary, randomly fluctuating electron distributions, and are the only intermolecular force possible between non-polar molecules.

Permanent dipole–permanent dipole (pd-pd) forces exist between polar molecules with a permanent uneven charge distribution. Hydrogen bonding is the strongest kind of permanent dipole–permanent dipole force — it occurs specifically where hydrogen is bonded directly to a small, highly electronegative atom (limited, at this level, to N–H and O–H).

Why water is anomalous

Hydrogen bonding between water molecules explains three properties that would otherwise be surprising for so small a molecule: its relatively high melting and boiling points (extra energy is needed to break the hydrogen bonds between molecules, not just the weaker id-id forces); its relatively high surface tension (surface molecules are pulled inward by hydrogen bonds with fewer neighbours to balance the pull); and ice being less dense than liquid water (in ice, hydrogen bonds lock molecules into a fixed, open lattice with more empty space than the liquid has, so the same mass occupies a larger volume).

All of this is still weaker than a covalent, ionic or metallic bond — hydrogen bonds and van der Waals’ forces act between molecules, not within them, which is the general rule 3.6 closes on.

Dot-and-cross diagrams

A dot-and-cross diagram shows the arrangement of outer-shell (valence) electrons in a species, using dots for the electrons of one atom and crosses for the electrons of another, so the origin of each electron stays visible. It is the standard way of representing ionic bonding, covalent bonding and coordinate bonding at this level.

Ionic bonding (MgCl₂). Magnesium’s two outer electrons (dots) transfer completely, one to each chlorine atom’s outer shell (crosses stay on the chlorine, plus a dot from magnesium added to complete its octet). The resulting ions are drawn separately in square brackets, each with its charge shown: [Mg]²⁺ and two separate [Cl]⁻ ions, each chloride now showing a full octet of eight electrons (seven of its own crosses plus the one donated dot).

Covalent bonding (CH₄). Carbon’s four outer electrons (crosses) and each hydrogen’s single electron (dots) are drawn in the four shared pairs between carbon and each hydrogen, giving carbon a full outer shell of eight electrons (four shared pairs) and each hydrogen a full outer shell of two.

Coordinate bonding (NH₄⁺). Nitrogen’s three N–H bonds are drawn as normal shared pairs (one dot, one cross, from nitrogen and hydrogen respectively). The fourth bond, to the additional H⁺, is drawn as a shared pair made of two dots only (both electrons from nitrogen’s original lone pair) — often marked with an arrow from nitrogen to the new hydrogen to flag that this pair alone was donated, even though the finished ion’s four bonds are otherwise identical.

Expanded-octet species (SF₆). All six S–F bonding pairs are drawn around sulfur, showing twelve electrons around the central atom rather than the usual eight, with each fluorine also showing three lone pairs to complete its own octet.

Odd-electron species (NO). Nitrogen monoxide has an odd total of outer electrons: 5 from nitrogen (dots) and 6 from oxygen (crosses), 11 in all, so not every electron can be paired. The N=O double bond is drawn as two shared pairs, each made of one dot and one cross. Oxygen’s remaining four crosses form two lone pairs, giving oxygen a full octet. Nitrogen’s remaining three dots are drawn as one lone pair plus one single, unpaired dot, so nitrogen is surrounded by only seven electrons. The unpaired electron is what makes a species such as NO a free radical; when drawing any species with an odd number of electrons, count the total first so the unpaired electron is placed deliberately rather than forced into a false octet.

Common mistakes

• Calling all intermolecular forces “van der Waals’ forces” as if that meant only the weak dispersion type. The syllabus uses van der Waals’ forces as the umbrella term that includes hydrogen bonding, not something separate from it.
• Predicting a shape without counting lone pairs. Electron-pair count, not just the number of bonded atoms, determines the shape.
• Confusing bond angle compression with bond strength. NH₃’s smaller angle than CH₄ is about lone-pair repulsion, not about the N–H bond being weaker.
• Explaining ice’s lower density using “hydrogen bonds are strong” alone. The density effect specifically needs the open, ordered lattice argument, not just bond strength.
• Drawing a π bond as if it were a second, identical σ bond. They form by a different kind of orbital overlap and behave differently, particularly in reactivity.

Quick revision checklist

• σ bonds (head-on overlap) vs π bonds (sideways overlap); hybridisation sp, sp², sp³
• Coordinate bonding, and the ammonium ion / Al₂Cl₆ examples
• The seven VSEPR shapes and bond angles: BF₃, CO₂, CH₄, NH₃, H₂O, PF₅, SF₆
• Van der Waals’ forces as the umbrella term; id-id (London) vs pd-pd forces
• Hydrogen bonding as a special case of pd-pd forces, limited to N–H/O–H
• Water/ice’s three anomalous properties, each explained by hydrogen bonding
• Dot-and-cross diagrams, including expanded-octet and odd-electron species

Related resources

• Ionic, Covalent and Metallic Bonding — the IGCSE/O Level foundation this resource builds on
• Atomic Structure: Orbitals and Ionisation Energy — orbital theory behind hybridisation
• Chemical Energetics: Hess’s Law and Enthalpy Cycles — bond energy used quantitatively
• Cambridge AS & A Level Chemistry hub

Written against Cambridge International AS & A Level Chemistry 9701, 2025–2027 series. Always check the current syllabus for your examination year.