Source: Lecture notes / slide deck
Tags: sigma bond, pi bond, double bond, triple bond, bond energy, bond rotation, orthogonal, ethylene, dinitrogen, Lewis dot structure
Difficulty: Intermediate. Prerequisites: orbital hybridisation (sp3, sp2, sp), Lewis dot structures, and a basic understanding of how atomic orbitals overlap to form bonds.
Once you understand hybridisation, the next question is: what kinds of bonds do those orbitals actually form? Sigma and pi bonds are the two fundamental types of covalent bond, and every single, double, or triple bond is made up of some combination of the two. This distinction matters because sigma and pi bonds behave differently: they have different strengths, different rotational properties, and different roles in chemical reactivity. Most of organic chemistry's interesting reactions happen at pi bonds.
Sigma bonds form from head-on overlap of orbitals along the bond axis and allow free rotation. Pi bonds form from side-on overlap of unhybridised p orbitals and do not allow rotation. A double bond is one sigma plus one pi bond (roughly 150 kcal/mol). A triple bond is one sigma plus two pi bonds. Pi bonds are weaker than sigma bonds because the orbital overlap is less direct.
Sigma bond (σ bond)
A covalent bond formed by head-on (end-to-end) overlap of orbitals along the internuclear axis. Think of it as two orbitals pointing straight at each other and merging. Sigma bonds allow free rotation around the bond axis.
Pi bond (π bond)
A covalent bond formed by side-on (lateral) overlap of unhybridised p orbitals above and below the internuclear axis. In simple terms, this is the "second bond" in a double bond. Pi bonds do not allow free rotation because rotating would break the orbital overlap.
Double bond
A bond consisting of one sigma bond plus one pi bond. The sigma bond is formed from hybrid orbitals (sp2); the pi bond is formed from unhybridised p orbitals. Total bond energy is approximately 150 kcal/mol.
Triple bond
A bond consisting of one sigma bond plus two pi bonds. The sigma bond is formed from hybrid orbitals (sp); the two pi bonds are formed from two sets of unhybridised p orbitals. Stronger overall than a double bond.
Orthogonal
At right angles (90 degrees). The pi bond is orthogonal to the sigma bond, meaning the pi bond's electron density sits in a plane perpendicular to the plane of the sigma bond.
Bond energy (bond dissociation energy)
The energy required to break one mole of a particular bond in the gas phase, measured in kcal/mol. In a double bond, the sigma component contributes roughly 90 kcal/mol and the pi component roughly 60 kcal/mol.
Sigma bonds are formed by the head-on overlap of orbitals along the axis connecting two nuclei
They can form from the overlap of two s orbitals, two hybrid orbitals, or a hybrid orbital and an s orbital
In methane's C-H bonds, each sigma bond forms from the overlap of a carbon sp3 orbital with a hydrogen 1s orbital
Each C-H sigma bond contains two electrons: one contributed by carbon, one by hydrogen
The region of greatest electron density sits directly between the two nuclei ("the nub of the bond")
Sigma bonds allow free rotation around the bond axis
Pi bonds form from the side-on overlap of unhybridised p orbitals
The electron density sits above and below the plane of the sigma bond, not along the bond axis
Pi bonds are orthogonal (at 90 degrees) to the sigma bond between the same two atoms
Pi bonds do not allow free rotation, because rotating would break the side-on overlap of the p orbitals
Pi bonds are weaker than sigma bonds because the side-on overlap is less effective than head-on overlap
Each carbon in ethylene is sp2 hybridised
Each carbon has three sp2 orbitals (forming sigma bonds) and one unhybridised 2p orbital (forming the pi bond)
The double bond between the two carbons consists of one sigma bond (from sp2-sp2 overlap) and one pi bond (from 2p-2p side-on overlap)
Total double bond energy: approximately 150 kcal/mol
Sigma component: approximately 90 kcal/mol
Pi component: approximately 60 kcal/mol
The pi bond is weaker because it is lower in energy and has less orbital overlap
The Lewis dot structure of ethylene shows each carbon with one 2p orbital and three sp2 orbitals
In the space-filling model, the pi bond lobes sit above and below the plane formed by the six atoms (two carbons and four hydrogens)
Each nitrogen in N2 is sp hybridised
Nitrogen has 5 valence electrons and one lone pair per atom in N2
The triple bond consists of one sigma bond and two pi bonds
The pi bonds are created from the two unhybridised p orbitals on each nitrogen
N2 requires two unhybridised p orbitals per atom, so only two orbitals (one s + one p) can hybridise, producing two sp orbitals
One sp orbital on each nitrogen forms the sigma bond between them; the other sp orbital holds the lone pair
The sp sigma bond sits between the two nitrogen atoms, the lone pairs point outward, and the two pi bonds are perpendicular to each other and to the sigma bond
Sigma bonds: stronger (approximately 90 kcal/mol in a C-C context), allow free rotation
Pi bonds: weaker (approximately 60 kcal/mol), no rotation
The inability of pi bonds to rotate is why cis/trans isomerism exists around double bonds
Bond Type | Sigma Bonds | Pi Bonds | Total Bond Energy | Hybridisation of Central Atom | Example |
|---|---|---|---|---|---|
Single bond | 1 | 0 | ~90 kcal/mol (C-C) | sp3 | CH4 (C-H bonds) |
Double bond | 1 | 1 | ~150 kcal/mol (C=C) | sp2 | C2H4 (ethylene) |
Triple bond | 1 | 2 | ~200 kcal/mol (N-N) | sp | N2 (dinitrogen) |
Energy breakdown for a C=C double bond: sigma bond contributes roughly 90 kcal/mol, pi bond contributes roughly 60 kcal/mol. The pi bond is weaker because side-on orbital overlap is less effective than head-on overlap.
The restricted rotation of pi bonds is the reason why fats can be "cis" or "trans," which directly affects their biological properties and health effects. Trans fats pack more tightly (like saturated fats) because the rigid double bond holds the carbon chain in a straighter configuration. Understanding sigma and pi bonds also explains why unsaturated compounds (those with double or triple bonds) are more reactive than saturated ones, which is the basis for a huge range of industrial chemical processes.
Students often think a double bond is simply "two sigma bonds." It is not. A double bond is always one sigma bond plus one pi bond. The two bonds in a double bond are fundamentally different from each other.
Students sometimes believe pi bonds are stronger than sigma bonds because they are "extra." Pi bonds are weaker, not stronger, because side-on overlap is less effective than head-on overlap.
Students frequently assume that all bonds in a molecule allow free rotation. Only sigma bonds allow rotation. Pi bonds lock the atoms in place, which is why double bonds are rigid.
Students may think the pi bond sits between the two nuclei. It does not. The pi bond's electron density is above and below the plane of the sigma bond.
Be able to count the number of sigma and pi bonds in any molecule from its Lewis structure.
Know the approximate bond energies: sigma approximately 90 kcal/mol, pi approximately 60 kcal/mol, double bond approximately 150 kcal/mol.
Understand why pi bonds prevent rotation, and be able to connect this to cis/trans isomerism.
Be prepared to explain the relationship between hybridisation type and the number of pi bonds an atom can form.
Know that in ethylene, each carbon has one 2p orbital and three sp2 orbitals.
True or false: A double bond consists of two sigma bonds. (False, it is one sigma and one pi bond.)
Fill in the blank: The approximate energy of a pi bond in a C=C double bond is ______ kcal/mol. (60)
True or false: Pi bonds allow free rotation around the bond axis. (False, they do not.)
Fill in the blank: A triple bond contains ______ sigma bond(s) and ______ pi bond(s). (1 sigma, 2 pi)
True or false: The pi bond electron density sits directly between the two nuclei. (False, it sits above and below the internuclear axis.)
Q: How many sigma and pi bonds are in a C=C double bond?
A: One sigma bond and one pi bond. The sigma bond forms from head-on overlap of sp2 hybrid orbitals; the pi bond forms from side-on overlap of unhybridised p orbitals.
Q: Why is a pi bond weaker than a sigma bond?
A: Because the side-on overlap of p orbitals in a pi bond is less effective (less orbital overlap) than the head-on overlap in a sigma bond. The pi bond's energy is roughly 60 kcal/mol versus approximately 90 kcal/mol for the sigma bond.
Q: Why can you not rotate around a double bond?
A: Rotation would break the side-on overlap of the unhybridised p orbitals that form the pi bond. Maintaining the pi bond requires the p orbitals to remain parallel, so the bond is rigid.
Q: In N2, how many sigma and pi bonds are there, and what orbitals form them?
A: One sigma bond (from sp-sp overlap) and two pi bonds (from two sets of unhybridised p orbitals overlapping side-on). Each nitrogen also has one lone pair in its remaining sp orbital.
Q: What is the relationship between the sigma bond plane and the pi bond in ethylene?
A: They are orthogonal (perpendicular). The sigma bond and the four C-H bonds all lie in the same plane; the pi bond's electron density sits above and below that plane.
Sigma and pi bonding connects to hybridisation (which determines how many of each type an atom can form) and to VSEPR (which predicts the geometry these bonds create). The rigidity of pi bonds is the foundation for understanding cis/trans isomerism (geometric isomerism), conjugation, and aromaticity. Later in the course, you will see that pi bonds are the reactive sites in addition reactions, electrophilic aromatic substitution, and many other organic reaction types.
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