Difficulty: Intermediate
Prerequisites: Parts 1 and 2 of these notes (atomic structure, orbitals, Lewis structures, formal charge, resonance). You need to be able to draw Lewis structures confidently before tackling hybridisation and molecular geometry.
Knowing what bonds exist (Part 2) is only half the story. This section explains how those bonds are arranged in three-dimensional space, why certain geometries arise, and how unequal electron sharing creates polar bonds and molecular dipole moments. Hybridisation is the model that ties orbital theory to observed bond angles, and molecular orbital (MO) theory provides a deeper account of bonding and antibonding interactions. These concepts are essential for predicting reactivity, understanding spectroscopy, and visualising how molecules interact with each other.
Molecular geometry is predicted by counting groups and lone pairs around a central atom (VSEPR). Hybridisation (sp³, sp², sp) explains the bond angles: four groups give tetrahedral (109.5°), three give trigonal planar (120°), two give linear (180°). Sigma bonds form from head-on orbital overlap; pi bonds form from side-to-side overlap. Polar bonds arise when atoms of different electronegativity share electrons unequally, and the molecular dipole moment is the vector sum of all individual bond dipoles.
Bond length
The distance between the nuclei of two bonded atoms. Governed by the period (row) of the atoms, the bond order, and the column (group). Shorter bonds are generally stronger. In simple terms, it is how far apart two bonded atoms sit.
Bond angle
The angle between two bonds that share a common atom. Determined by the number of groups (atoms + lone pairs) around the central atom.
Dihedral angle (torsion angle)
The angle between bonds on adjacent atoms, measured by looking down the bond connecting those atoms. Required to fully specify three-dimensional molecular geometry. Think of it as the "twist" around a bond.
Hybridisation
The mixing of atomic orbitals (s and p) to form new hybrid orbitals that better explain observed bond angles and molecular shapes. The notation spⁿ describes the ratio of p to s character: n = f_p / f_s.
sp³ hybridisation
Four hybrid orbitals formed from one s and three p orbitals. Gives tetrahedral geometry with bond angles of 109.5°. Found in methane, ethane, and saturated carbons generally.
sp² hybridisation
Three hybrid orbitals formed from one s and two p orbitals, with one unhybridised 2p orbital remaining. Gives trigonal planar geometry with bond angles of 120°. Found in ethylene, carbonyl groups, and aromatic rings.
sp hybridisation
Two hybrid orbitals formed from one s and one p orbital, with two unhybridised 2p orbitals remaining. Gives linear geometry with a bond angle of 180°. Found in acetylene, nitriles, and allene's central carbon.
Sigma (σ) bond
A bond formed by the head-on (end-to-end) overlap of orbitals along the internuclear axis. All single bonds are sigma bonds. It is cylindrically symmetrical around the bond axis.
Pi (π) bond
A bond formed by the side-to-side overlap of two parallel p orbitals. Found in double bonds (one σ + one π) and triple bonds (one σ + two π). Not cylindrically symmetrical.
Molecular orbital (MO)
An orbital that extends over an entire molecule, formed by combining atomic orbitals of the constituent atoms. MOs can be bonding (lower energy, stabilising) or antibonding (higher energy, destabilising).
Bond dipole
The unequal sharing of electrons in a polar covalent bond, resulting from a difference in electronegativity. Represented as a vector pointing from the less electronegative atom toward the more electronegative one.
Dipole moment (μ)
The vector sum of all bond dipoles in a molecule. A molecule with a nonzero dipole moment is polar. Measured in debyes (D). μ = q × r, where q is the separated charge and r is the distance between the charges.
Electronegativity
A measure of an atom's ability to attract bonding electrons. Increases from left to right and from bottom to top of the periodic table (fluorine is the most electronegative element).
Electrostatic potential map (EPM)
A visual representation of the distribution of charge across a molecule's surface. Red regions are electron-rich (partial negative charge), blue regions are electron-poor (partial positive charge).
Count all groups around the central atom: bonded atoms and lone pairs each count as one group.
Groups repel each other and arrange themselves as far apart as possible.
Four groups (e.g. CH₄, NH₃, H₂O): tetrahedral electron geometry, bond angles near 109.5°.
Four bonding groups, zero lone pairs: tetrahedral shape (methane).
Three bonding groups, one lone pair: trigonal pyramidal shape (ammonia). The lone pair compresses the bond angle slightly below 109.5°.
Two bonding groups, two lone pairs: bent shape (water).
Three groups (e.g. BF₃, ethylene carbons): trigonal planar, bond angles of 120°.
Two groups (e.g. CO₂, acetylene carbons): linear, bond angle of 180°.
Hybridisation is a model that explains observed bond angles by mixing atomic orbitals.
sp³: one s + three p orbitals mix to give four equivalent hybrid orbitals pointing to the corners of a tetrahedron (109.5°). Each can overlap with another orbital to form a σ bond. Methane has an sp³-hybridised carbon.
sp²: one s + two p orbitals mix to give three hybrid orbitals in a plane (120°), leaving one unhybridised 2p orbital perpendicular to the plane. The unhybridised p orbital forms a π bond by side-to-side overlap. The carbons of ethylene are sp².
sp: one s + one p orbital mix to give two hybrid orbitals pointing in opposite directions (180°), leaving two unhybridised 2p orbitals. These form two π bonds. The carbons of acetylene are sp.
Fractional hybridisation: the spⁿ notation does not require n to be a whole number. n = f_p / f_s, where f_p and f_s are the fractional p and s character. For example, the nonbonding orbital on ammonia's nitrogen has about 27% s character, giving sp²·⁷ hybridisation, while the bonding N-H orbitals are approximately sp³·¹².
A single bond = one σ bond.
A double bond = one σ bond + one π bond.
A triple bond = one σ bond + two π bonds.
σ bonds form from head-on overlap of any combination of orbitals: s-s, s-sp³, sp³-sp³, sp²-sp², sp-sp, etc. They are cylindrically symmetrical around the bond axis.
π bonds form from side-to-side overlap of parallel p orbitals. They have a nodal plane along the bond axis and are not cylindrically symmetrical. Rotation around a π bond would break it, which is why double bonds are rigid.
MO theory combines atomic orbitals from all atoms in a molecule to form molecular orbitals that span the entire molecule.
Mixing j atomic orbitals gives j molecular orbitals: some bonding (lower energy) and some antibonding (higher energy).
Electrons fill MOs from lowest to highest energy (aufbau), obeying the Pauli principle and Hund's rule.
Bond order = (electrons in bonding MOs − electrons in antibonding MOs) / 2. A positive bond order indicates a stable species.
Example: H₂ has two electrons in the bonding MO, zero in antibonding. Bond order = (2−0)/2 = 1.
Example: He₂ would have two electrons in bonding and two in antibonding MOs. Bond order = 0, so He₂ does not exist as a stable molecule.
O₂ has a bond order of 2, with two unpaired electrons in degenerate antibonding π* orbitals, making it paramagnetic.
A bond between atoms of different electronegativity is polar: electrons are shared unequally, creating a bond dipole.
The dipole moment μ = q × r, where q is the amount of separated charge and r is the bond length. Measured in debyes (D). 1 D = 1 × 10⁻¹⁰ esu × 1 Å.
For HCl: μ = 1.08 D, bond length = 127.4 pm. The calculated charge separation is 0.18 electron, meaning about 18% of a full electron charge is transferred from H to Cl.
The molecular dipole moment is the vector sum of all bond dipoles. Symmetric molecules can have polar bonds but zero overall dipole moment (e.g. CCl₄, CO₂).
Molecules with non-cancelling dipoles are polar (e.g. H₂O, NH₃, CH₂Cl₂).
Dipole moment: μ = q × r where q = magnitude of separated charge, r = distance between the charges.
Bond order (MO theory): Bond order = (electrons in bonding MOs − electrons in antibonding MOs) / 2
Fractional hybridisation: n = f_p / f_s where spⁿ is the hybridisation, f_p is the fraction of p character, and f_s is the fraction of s character. For sp³, f_s = 0.25, f_p = 0.75, n = 3. For sp², f_s = 0.33, f_p = 0.67, n = 2.
1 debye: 1 D = 1 × 10⁻¹⁰ esu × 1 Å = 1 × 10⁻⁸ esu pm In SI: 1 D = 3.34 × 10⁻³⁰ C·m
The rigid geometry of double bonds (no free rotation around a π bond) is why cis and trans isomers exist. This matters in drug design: the cis form of a molecule can have completely different biological activity from the trans form.
Dipole moments determine how molecules interact with solvents. Polar molecules dissolve in polar solvents (like water), nonpolar molecules dissolve in nonpolar solvents (like hexane). This is the molecular basis of "like dissolves like."
MO theory explains why O₂ is paramagnetic (attracted to a magnet), which a Lewis structure alone cannot account for. This was one of the early triumphs of MO theory.
Students often confuse bond angle with dihedral angle. A bond angle involves three atoms (A-B-C); a dihedral angle involves four atoms (A-B-C-D) and describes the twist around the B-C bond.
Hybridisation is frequently treated as a physical process ("the atom hybridises its orbitals"). It is a mathematical model, not something that happens in real time. The atom does not "decide" to hybridise; we use hybridisation to explain the geometry we observe.
Students sometimes think that a polar bond always means a polar molecule. Symmetric arrangements of polar bonds can cancel out, giving a nonpolar molecule (CCl₄ has four polar C-Cl bonds but zero dipole moment).
A common error is assuming that lone pairs do not affect hybridisation. They do. The nitrogen in ammonia is sp³, not sp², because the lone pair counts as a group occupying one of the four sp³ orbitals.
⚠️ Predicting hybridisation and geometry from a Lewis structure is one of the most common exam question types. Practise until it is automatic: count groups, assign hybridisation, state the geometry and approximate bond angle.
⚠️ Distinguishing σ and π bonds in a molecule is routinely tested. Remember: a double bond = 1σ + 1π; a triple bond = 1σ + 2π.
⚠️ Dipole moment questions often ask whether a molecule is polar or nonpolar. Draw all bond dipoles as vectors and check whether they cancel.
⚠️ MO diagrams for simple diatomics (H₂, He₂, Li₂, N₂, O₂) and their ions are fair game. Know how to fill them and calculate bond order.
⚠️ Bond length comparisons (which bond is shorter/longer) come up regularly. The key factors in decreasing order of importance: period of the atoms, bond order, then column of the periodic table.
Fill in the blank: An sp²-hybridised carbon has ______ bond angle(s) of approximately ______ degrees.
Three bonds at approximately 120°.
True or false: A triple bond consists of three sigma bonds.
False. A triple bond consists of one sigma bond and two pi bonds.
Fill in the blank: The bond order of He₂ is ______.
Zero. (2 bonding electrons − 2 antibonding electrons) / 2 = 0.
True or false: CCl₄ has a nonzero dipole moment because its C-Cl bonds are polar.
False. The four C-Cl bond dipoles cancel by symmetry, giving a net dipole moment of zero.
Fill in the blank: In allene (H₂C=C=CH₂), the central carbon is ______ hybridised.
sp hybridised (linear, bonded to two groups).
Q: What is the hybridisation and geometry at each labelled atom in acetonitrile (CH₃C≡N)?
A: The methyl carbon (CH₃) is sp³ with tetrahedral geometry (bond angles near 109.5°). The carbon of the C≡N group is sp with linear geometry (bond angle 180°). The nitrogen is also sp, with a lone pair in an sp hybrid orbital.
Q: In allene (H₂C=C=CH₂), explain why the two CH₂ planes are perpendicular to each other.
A: The central carbon is sp-hybridised with two unhybridised 2p orbitals that are perpendicular to each other. Each 2p orbital forms a π bond with a different terminal carbon. Since the two π bonds use mutually perpendicular p orbitals, the two CH₂ planes must also be perpendicular.
Q: The dipole moment of water is 1.84 D and the bond angle is 104.5°. Using vector addition, calculate the magnitude of each O-H bond dipole.
A: The x-components of the two O-H dipoles cancel by symmetry. The resultant comes from the y-components only. Using the law of cosines with the supplement of the bond angle (180° − 104.5° = 75.5°), each O-H bond dipole is approximately 1.50 D.
Q: Draw the MO diagram for the H₂⁻ ion (three electrons). Is this species stable? What is its bond order?
A: Two electrons go in the bonding MO and one in the antibonding MO. Bond order = (2 − 1) / 2 = 0.5. The bond order is positive, so H₂⁻ should be a marginally stable species, with about half the bond strength of H₂.
Q: Why is the C-O-H bond angle in methanol (109°) smaller than 120° even though oxygen could be considered sp²-hybridised?
A: Oxygen in methanol is better described as sp³-hybridised, with two bonding pairs and two lone pairs. The lone pairs occupy orbitals with slightly more s character (they are held closer to the nucleus), which pushes more p character into the bonding orbitals, compressing the bond angle toward 109° or slightly below.
Hybridisation and geometry connect directly to stereochemistry (Chapters 6-7): the tetrahedral geometry of sp³ carbon is why chirality exists. Sigma and pi bond character becomes central when you study reaction mechanisms (Chapters 3-4), particularly additions to alkenes and alkynes. Dipole moments and polarity feed into intermolecular forces and physical properties (boiling points, solubility) discussed later. MO theory returns in depth when you study conjugated systems, aromaticity (Chapter 15+), and UV-Vis spectroscopy.
bond length, bond angle, dihedral angle, torsion angle, VSEPR, tetrahedral, trigonal planar, trigonal pyramidal, linear, bent, hybridisation, sp3, sp2, sp, hybrid orbital, sigma bond, pi bond, molecular orbital, bonding MO, antibonding MO, bond order, bond dipole, dipole moment, debye, electronegativity, electrostatic potential map, EPM, polar bond, nonpolar molecule, CCl4, methane, ethylene, acetylene, allene, fractional hybridisation, paramagnetic, O2 MO diagram