Chemistry: Atoms First 2e · Advanced Theories of Bonding

Valence Bond Theory

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On this page 9 sections

In 30 seconds
Why this matters
The college version
Eli explains
Worked example
Key takeaway
Check yourself
Study tools
Sources & references

In 30 seconds

Lewis structures describe bonds as shared electron pairs, but not why a pair of electrons holds two atoms together. Valence bond (VB) theory answers that: a covalent bond forms when half-filled atomic orbitals of two atoms , and the shared electron pair occupies the overlap region. The greater the overlap, the stronger the bond. VB theory also introduces the two fundamental bond types — sigma (σ) and pi (π) bonds — which differ in how orbitals overlap. It is the first of two quantum-based theories in this chapter; molecular orbital theory, the second, spreads electrons over the whole molecule instead of one bond.

Why this matters

VB theory explains what Lewis structures cannot: why a double bond is not twice as strong as a single bond (one σ plus one weaker π), why rotation around a double bond is restricted (π overlap would break), and why H₂ is stable. The σ/π distinction governs the planarity of alkenes, the rigidity of protein peptide bonds, and the reactivity of double bonds in fats and drugs. Bond strength tracking orbital overlap also explains bond-energy trends and sets up hybridization, the next topic, which fixes VB theory's major weakness.

The college version

Core Concepts

Orbital overlap and bond formation

In VB theory, a bond forms when two atomic orbitals — each with one — overlap, and the electrons pair with opposite spins in the shared region. The system's energy drops below the separated atoms' because both electrons are attracted to both nuclei. Bond strength depends on overlap: more overlap, stronger bond, and overlap is greatest when orbitals point directly at each other — which is why s and p orbitals bond along the line between nuclei.

Sigma bonds: head-on overlap

A forms from head-on (end-to-end) overlap: s–s (H₂), s–p (H–F), or p–p (F₂). Its electron density lies along the axis between the nuclei. Sigma bonds have three key properties: they are the strongest bond type; every single bond is σ; and rotation around them is free, because the cylindrical electron cloud is unchanged by rotation — why ethane rotates freely around its C–C bond.

Pi bonds: side-by-side overlap

A forms from side-by-side (parallel) overlap of two p orbitals; its electron density sits in two lobes above and below the internuclear axis. Pi bonds are weaker than σ bonds because parallel overlap is less complete than head-on overlap. A double bond is one σ plus one π; a triple bond is one σ plus two π. Rotation around a double bond would break the π overlap, so double bonds are rigid — the basis of cis/trans isomerism in alkenes and the fixed planar peptide bond in proteins.

Spin pairing and the bonding capacity of atoms

Each covalent bond uses one half-filled orbital per atom. Hydrogen (one 1s electron) forms one bond; fluorine (one unpaired 2p) forms one; oxygen (two unpaired 2p) forms two; nitrogen (three unpaired 2p) forms three. This is the orbital-level basis of the bonding capacities in Lewis structures. Bonding electrons must have opposite spins, so two electrons can share one overlap region without violating the Pauli exclusion principle.

Strengths and limits of VB theory

VB theory correctly explains bond formation, bond-strength trends, and the σ/π distinction. Its weakness is geometry: pure atomic orbitals predict water bonds at 90° (the angle between p orbitals), but the measured angle is 104.5°, and it cannot explain methane's four identical C–H bonds at 109.5°. Hybridizing atomic orbitals into directional orbitals that match observed geometry — the next topic — fixes this.

How It Works / Step-by-Step Process

Write the Lewis structure to see how many bonds and lone pairs each atom has.
Identify which atomic orbitals hold the bonding electrons (s and p for main-group atoms).
Match each bond to its overlap type: head-on = σ; parallel p orbitals = π.
Assign one σ bond to every single bond; add one π per multiple-bond order beyond one.
Verify the atom's unpaired-electron count matches its bonding capacity.

Common Confusions

Do Not Confuse	With	The Difference
σ bond	π bond	σ is head-on overlap along the axis (strong); π is parallel overlap above/below (weaker)
Double bond	Two σ bonds	A double bond is one σ + one π; two σ bonds between the same pair is impossible
Bond strength	Bond length alone	Stronger bonds are usually shorter, but overlap and orbital size matter too
Overlap	Sharing a lone pair	Bonding overlap involves one electron from each atom; a lone pair belongs to one atom
VB theory	Molecular orbital theory	VB localizes electrons between two atoms; MO delocalizes them over the molecule
"π bond is weak"	"π bond is unimportant"	π bonds are weaker than σ but control shape, rigidity, and reactivity of double bonds

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine two kids reaching for the same toy: when their hands overlap, they can both hold it — that is how atoms bond. If they grab it end-to-end, that is a sigma bond; if they hold it side-by-side from above and below, that is a pi bond, and their grip is a little weaker. The more their hands overlap, the tighter they hold, which is why some bonds are strong and some are weak.

Worked example

Example 1: The hydrogen molecule (H₂)

Each hydrogen atom contributes one 1s orbital with one unpaired electron. The two 1s orbitals overlap head-on, the electrons pair with opposite spins, and a σ bond forms. The bond energy is 436 kJ/mol — breaking one mole of H–H bonds needs 436 kJ. Converting to energy per individual bond with Avogadro's number:

$436 kJ mol \times 1000 J 1 kJ \times 1 mol 6.022 \times 1023 bonds = 7.24 \times 10 -19 J per bond$

The strong overlap of two small 1s orbitals is why H₂ is a stable single bond — and the most abundant molecule in the universe.

Example 2: The triple bond in nitrogen (N₂)

Nitrogen has three unpaired 2p electrons (2pₓ, 2p_y, 2p_z). Two nitrogen atoms form a triple bond: one σ from head-on overlap of the 2p orbital along the axis, plus two π from the other two pairs of parallel 2p orbitals. The bond energy is 945 kJ/mol — the strongest common bond — because three overlaps hold the atoms. The two π bonds make N₂ rigid and unreactive, which is why nitrogen gas makes up 78% of the atmosphere without reacting away. Compare F₂ (159 kJ/mol, one σ from weak p–p overlap): its weak bond is a major reason fluorine is so reactive.

Example 3: Bond type inventory for ethylene (C₂H₄)

Ethylene's Lewis structure shows a C=C double bond plus four C–H bonds. The double bond is one σ (head-on overlap along the C–C axis) plus one π (parallel p orbitals above and below the plane); the four C–H bonds are σ (s–p overlap). Because the π bond pins the carbons and their attached atoms in one plane, ethylene is flat and cannot rotate around the double bond — the same rigidity that holds protein peptide bonds flat.

Key takeaways

A covalent bond = overlap of half-filled atomic orbitals, electrons paired with opposite spins.
More overlap = stronger bond; head-on overlap beats parallel overlap.
σ bonds: s–s, s–p, p–p head-on; every single bond is σ; free rotation.
π bonds: parallel p–p overlap; weaker than σ; double = 1σ + 1π, triple = 1σ + 2π.
Double bonds do not rotate (π overlap would break) → cis/trans isomerism.
Bond capacity = number of unpaired electrons (H:1, F:1, O:2, N:3).
Pure-orbital VB fails for geometry (predicts 90° for water) → hybridization needed.

Check yourself

5 review questions from the chapter. Try each one, then open the answer.

What two things must be true for a covalent bond to form in VB theory?
Show answer
Two atoms must each have a half-filled orbital that overlaps, and the two electrons must pair with opposite spins.
Why is a π bond weaker than a σ bond?
Show answer
Parallel (side-by-side) p-orbital overlap is less complete than head-on overlap, so the electron density shared is smaller.
How many σ and π bonds are in a C≡C triple bond?
Show answer
One σ bond and two π bonds.
Why can't a molecule rotate freely around a double bond?
Show answer
Rotation would require breaking the side-by-side π overlap; the π bond locks the atoms in place.
What is the key failure of VB theory that hybridization (next topic) fixes?
Show answer
With pure atomic orbitals it predicts wrong bond angles (e.g., 90° for water instead of 104.5°) and cannot explain equivalent bonds like the four C–H bonds of methane.

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Study tools & related lessonsKey vocabulary · Related

Key vocabulary

valence bond theory: Model in which bonds form by overlap of half-filled atomic orbitals
overlap: The region where two atomic orbitals share space and electrons
sigma (σ) bond: Bond from head-on orbital overlap, electron density along the internuclear axis
pi (π) bond: Bond from parallel p-orbital overlap, density above and below the axis
unpaired electron: Single electron in an orbital, available for pairing in a bond
spin pairing: Two electrons of opposite spin sharing one orbital region
π (pi) bond: Bond formed by side-by-side overlap of parallel p orbitals, with density above/below the axis.

Sources & references

openstax.org — Chemistry Atoms First 2e

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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