Organic Chemistry · Structure and Bonding
Describing Chemical Bonds: Valence Bond Theory
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The previous topic ended with a quantum insight: a bond forms when atomic orbitals overlap. valence bond (VB) theory Model in which a covalent bond is the overlap of half-filled atomic orbitals Full entry → makes it precise: a covalent bond forms when half-filled orbitals on two atoms overlap, and the shared electron pair lives in that overlap, concentrated between the nuclei.
VB theory distinguishes two overlap types. A sigma (σ) bond Bond from head-on orbital overlap along the internuclear axis forms when orbitals overlap head-on along the internuclear axis The imaginary line connecting two bonded nuclei Full entry → — every single bond. A pi (π) bond Bond from side-by-side overlap of parallel p orbitals forms when parallel p orbitals overlap side-by-side, above and below the axis — the second bond of a double bond One σ bond plus one π bond Full entry →, the second and third of a triple bond One σ bond plus two π bonds Full entry →. This distinction explains bond lengths, strengths, and shapes, and why molecules rotate around single bonds but not double bonds.
Why this matters
Valence bond theory is the theory that organic chemists actually use, all the time:
- It explains bond strength and length. A double bond is not "two single bonds": a σ bond is stronger than a π bond The sideways-overlap bond above and below the σ bond; it locks the alkene flat. Full entry →, and their sum gives double bonds their distinctive lengths and energies.
- It explains rotation. Single (σ-only) bonds rotate freely; double bonds (σ + π) cannot without breaking π overlap — the basis of cis/trans isomerism in alkenes.
- It explains molecular geometry. The directionality of overlap — refined by hybridization in the next topics — determines bond angles.
- It underlies reactivity. π bonds are weaker and more exposed than σ bonds — exactly why alkenes and alkynes react and alkanes do not.
The college version
Core Concepts
The sigma bond: head-on overlap
A σ bond forms when two orbitals point directly at each other, overlapping along the line between the nuclei:
- s–s (two 1s orbitals, as in H₂)
- s–p (as in C–H bonds of methane)
- p–p head-on (as in the C–C bond of ethane)
Because its electron density is concentrated between the nuclei, a σ bond is strong and cylindrical — looking down the axis, the electron cloud looks the same from every angle. That symmetry permits free rotation Rotation about a bond axis that does not change the bond's electron distribution Full entry →: rotating one end doesn't disturb the overlap.
The pi bond: side-by-side overlap
A π bond forms when two parallel p orbitals overlap sideways, creating two lobes of electron density — above and below the plane of the atoms:
- A π bond is weaker than a σ bond because its electron density sits farther from the nuclei.
- Its two lobes are not cylindrically symmetric: rotating one atom about the axis destroys the p orbitals' parallel alignment and breaks the overlap.
- A π bond forms only in addition to a σ bond, which holds the atoms at the right distance.
Single, double, and triple bonds
- Single bond = one σ bond (C–C in ethane).
- Double bond = one σ + one π (C=C in ethylene).
- Triple bond = one σ + two π (C≡C in acetylene).
The trend in bond lengths (standard reference values):
| Bond | Type | Length (pm) | Strength (kJ/mol) |
|---|---|---|---|
| C–C (ethane) | σ only | 154 | 348 |
| C=C (ethylene) | σ + π | 134 | 614 |
| C≡C (acetylene) | σ + 2π | 120 | 839 |
Two patterns stand out. Adding π bonds shortens the bond (more electron density pulls nuclei together) and strengthens it — but each extra π bond adds less than the last (614 − 348 = 266 kJ/mol for the first, 839 − 614 = 225 kJ/mol for the second), because π overlap is inherently weaker than σ overlap.
Rotation and geometry: the π bond's fingerprint
Ethane's C–C single bond rotates freely at room temperature; ethylene's C=C bond does not, because the p orbitals forming the π bond must stay parallel — rotation would break their overlap at enormous energy cost. This locked geometry is why alkenes exist as cis and trans isomers. You will meet this again in the alkenes and stereochemistry chapters.
How It Works / Step-by-Step Process
To describe any C–C or C–heteroatom bond with VB theory:
- Identify the bond order: single, double, or triple.
- Assign one σ bond (head-on overlap) to every bond, regardless of order.
- Add one π bond per additional bond order: double → 1 π, triple → 2 π.
- Predict properties: more π bonds → shorter bond, higher strength, no rotation, higher reactivity.
- Check geometry: σ bonds are cylindrically symmetric; π bonds fix the atoms in a plane.
Common Confusions
| Common Confusion | Correct Understanding |
|---|---|
| "A double bond is twice as strong as a single bond." | Stronger, but not double: 614 vs. 348 kJ/mol. The π component is weaker than the σ. |
| "A double bond is two σ bonds." | A double bond is one σ + one π; a triple bond is one σ + two π. Only one σ bond can exist between a pair of atoms. |
| "Rotation around a double bond is slow but possible." | Effectively impossible at ordinary temperatures — rotation breaks the π overlap, costing hundreds of kJ/mol. |
| "The π bond holds the atoms together; the σ bond is secondary." | The σ bond is the primary framework; the π bond adds to it and controls geometry and reactivity. |
| "All p orbital overlaps are π bonds." | Head-on p–p overlap along the axis is σ; only parallel, side-by-side overlap is π. |
| "Triple bonds are rigid in all directions." | Acetylene's geometry is linear, but the two π bonds still block rotation — the molecule is fixed. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Two atoms bonding is like two people holding hands. A sigma bond is a firm handshake: they grip right between them and can spin around together freely. A pi bond is a gentler second hold — two more hands placed above and below. If one person spins, the extra hands come apart, so they must stay facing the same way. Double bonds are two hands; triple bonds are three.
Worked example
Example 1: Counting bonds in ethylene and acetylene
Ethylene, C₂H₄, has a C=C double bond. The formula before substitution:
bonds per connection = 1σ+ (bond order - 1)π
Substituting the double bond (order 2):
C=C = 1σ+ (2 - 1)π= 1σ+ 1π
Acetylene, C₂H₂, has a C≡C triple bond (order 3):
C≡C = 1σ+ (3 - 1)π= 1σ+ 2π
So ethylene has 1σ + 1π between the carbons; acetylene has 1σ + 2π. The extra π bonds pull the carbons closer (134 pm, then 120 pm) and lock the geometry — ethylene is planar, acetylene is linear.
Example 2: Why the second bond of a double bond is weaker than the first
Compare the incremental strength of adding the first and second π bonds to a C–C σ framework, using the standard bond strengths (348, 614, and 839 kJ/mol).
The formula before substitution:
ΔEπ = E(new bond) - E(old bond)
Substituting — first π bond (single → double):
ΔEπ1 = 614 kJ/mol - 348 kJ/mol = 266 kJ/mol
Second π bond (double → triple):
ΔEπ2 = 839 kJ/mol - 614 kJ/mol = 225 kJ/mol
The first π bond adds 266 kJ/mol; the second only 225 kJ/mol. Because π overlap is side-by-side and less efficient than head-on σ overlap, each added π contributes less — why chemists describe alkenes and alkynes as a strong σ "skeleton" plus weaker, more reactive π "ornament."
Example 3: Bond length trend as bond order increases
Using the reference bond lengths (C–C 154 pm, C=C 134 pm, C≡C 120 pm), the shortening per added π bond:
154 pm - 134 pm = 20 pm (single → double)
134 pm - 120 pm = 14 pm (double → triple)
Each added bond pulls the nuclei closer, but by a smaller increment — consistent with the diminishing energy gains above.
Key takeaways
- VB theory: a bond is the overlap of half-filled atomic orbitals, concentrating electron density between nuclei.
- σ bond = head-on overlap (s–s, s–p, or p–p along the axis); every single bond is σ.
- π bond = side-by-side overlap of parallel p orbitals, above and below the bond axis.
- Single = 1σ; double = 1σ + 1π; triple = 1σ + 2π.
- π bonds are weaker than σ; each added π shortens and strengthens the bond, but by diminishing amounts.
- Free rotation around σ-only single bonds; none around double bonds → cis/trans isomerism.
- C–C 154 pm, C=C 134 pm, C≡C 120 pm; 348, 614, 839 kJ/mol (standard reference values).
- π electrons sit farther from the nuclei → alkenes/alkynes react more readily than alkanes.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
Define σ and π bonds in terms of orbital overlap The region where two atomic orbitals reinforce, concentrating electron density Full entry →.
Show answer
A σ bond is head-on overlap of orbitals along the internuclear axis (s–s, s–p, or p–p); a π bond is side-by-side overlap of parallel p orbitals, placing electron density above and below the axis.
How many σ and π bonds are in a C≡C triple bond?
Show answer
One σ and two π bonds.
Why can ethane rotate freely about its C–C bond but ethylene cannot rotate about its C=C bond?
Show answer
The C–C single bond is σ-only and cylindrically symmetric, so rotation preserves the overlap. The C=C double bond includes a π bond between parallel p orbitals; rotating one carbon breaks that parallelism and destroys the π overlap.
Arrange the bonds C–C, C=C, C≡C in order of increasing bond length and increasing bond strength.
Show answer
Length: C≡C (120 pm) < C=C (134 pm) < C–C (154 pm). Strength: C–C (348 kJ/mol) < C=C (614 kJ/mol) < C≡C (839 kJ/mol).
Which is stronger, a σ bond or a π bond, and why?
Show answer
A σ bond is stronger, because its electron density lies directly between the nuclei; π electron density sits farther out, above and below the axis, so it binds less tightly.
Why are alkenes (with π bonds) generally more reactive than alkanes (σ only)?
Show answer
π electrons are farther from the nuclei and less tightly held, so they are more available to react (with electrophiles); σ electrons are buried in the bond axis and much less accessible.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- valence bond (VB) theory
- Model in which a covalent bond is the overlap of half-filled atomic orbitals
- sigma (σ) bond
- Bond from head-on orbital overlap along the internuclear axis
- pi (π) bond
- Bond from side-by-side overlap of parallel p orbitals
- internuclear axis
- The imaginary line connecting two bonded nuclei
- orbital overlap
- The region where two atomic orbitals reinforce, concentrating electron density
- double bond
- One σ bond plus one π bond
- triple bond
- One σ bond plus two π bonds
- free rotation
- Rotation about a bond axis that does not change the bond's electron distribution
- π bond
- The sideways-overlap bond above and below the σ bond; it locks the alkene flat.
- σ (sigma) bond
- Bond formed by head-on orbital overlap along the internuclear axis
Sources & references
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
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