Valence Bond Theory: Orbital Overlap, σ & π Bonds
Lewis said atoms share; VBT explains how — two half-filled orbitals walk into each other, their waves overlap, electron density pools between the nuclei, and energy falls. Head-on gives the strong σ bond; sidewise gives the weaker π. Then the theory meets oxygen and cracks.
The Overlap Picture — Complete Theory
Valence bond theory (Heitler–London, 1927; extended by Pauling and Slater) is Lewis sharing made physical. Its core claim: a covalent bond forms when two half-filled valence atomic orbitals overlap, each holding one electron of opposite spin. Where they overlap, electron density pools between the nuclei — both nuclei now attract that shared cloud, energy drops, and the bond exists. Greater the overlap, deeper the energy fall, stronger the bond.
Postulates in four lines. (1) A covalent bond needs overlap of half-filled orbitals with opposite-spin electrons. (2) Overlap releases energy — the bond forms because the overlapped state is lower in energy than the separate atoms. (3) Electron density concentrates between the nuclei — the shared region is the glue. (4) More overlap ⇒ more energy released ⇒ stronger, shorter bond — overlap quality is the theory’s whole measuring stick.
The direction of orbitals matters. p, d and hybrid orbitals point in specific directions, so their bonds form along those directions — the first physical explanation of molecular geometry. H₂’s bond forms along the s orbitals’ (spherical) line of centres; in H₂S the p orbitals of sulphur point roughly at right angles — VBT hints at the bent shape before hybridisation perfects it (§ 4.6).
= overlap condition
Energy released= bond strength
More overlap⇒ stronger bond
Two kinds of overlap — σ and π. Head-on overlap along the internuclear axis (s–s, s–p, or pz–pz) gives a σ (sigma) bond: the electron cloud is cylindrically symmetric about the axis, densest exactly between the nuclei. Sidewise overlap of parallel p orbitals (px–px or py–py, both perpendicular to the axis) gives a π (pi) bond: the cloud splits into two lobes above and below the axis, with a nodal plane containing the nuclei. Every single bond is σ; a double bond is one σ + one π; a triple bond is one σ + two π.
| Property | σ bond | π bond |
|---|---|---|
| Overlap mode | Head-on, along the axis | Sidewise, above/below the axis |
| Overlap extent | Large — maximum | Smaller — grazing |
| Strength | Stronger | Weaker |
| Electron cloud | Cylindrical about the axis | Above & below, nodal plane inside |
| Free rotation | Possible about a σ bond | Blocks rotation (C=C is rigid) |
| Exists alone? | Yes — singles are pure σ | Only with an accompanying σ |
Why σ beats π — in one sentence. Strength is overlap, and head-on overlap between nuclei beats grazing overlap above them. This also explains rigidity: rotating about a σ bond changes nothing (cylinder stays a cylinder); rotating about a π bond breaks the sidewise overlap — which is why ethene is planar and alkanes rotate freely.
The crack. VBT explains H₂ perfectly, predicts direction, and with hybridisation (§ 4.6) nails CH₄’s geometry. But it insists all electrons in O₂ are paired — while liquid oxygen visibly sticks to a magnet. Two unpaired electrons, no explanation. It also stays silent on colour and spectra, and offers no clean stability ranking between molecules. Molecular orbital theory (§ 4.7) was built on exactly these cracks.
Visualising the Overlaps & Ranking Their Quality
Teen overlap, ek bench — head-on vs sidewise drawn to scale, then the strength hierarchy explained line by line.
Overlap Quality Bench
Teen overlap families — har ek ka verdict, strength rank aur VBT-vs-experiment note. Click karo, bench bolta hai.
s–s overlap (H₂) — the textbook clean case: two spherical 1s orbitals, maximum head-on concentration, 436 kJ/mol released. VBT’s poster child — everything here agrees with experiment.
Strength ranking is the head-on (σ) > sidewise (π) rule plus orbital concentration — never raw orbital size alone.
Solved Examples (Step-by-Step)
Bonds → overlaps → verdicts. Jo reasoning yahan chalti hai, wahi bench me live chalti hai.
Bond accounting for ethene, C₂H₄
Describe the bonding in ethene using σ and π bonds — how many of each, and from which orbitals.
- Count4 C–H bonds + 1 C=C → the double bond = 1σ + 1π → total
5σ + 1π. - σ sourcesAll five σ bonds come from sp² hybrid orbitals (§ 4.6) — head-on overlap.
- π sourceThe π bond comes from the unhybridised p orbitals left on each sp² carbon — sidewise overlap above/below the molecular plane.
- ConsequenceThe π bond blocks rotation — ethene is planar, unlike freely-rotating ethane.
5σ (sp²) + 1π (unhybridised p) — and no rotation
N₂’s three bonds, ranked by strength
Nitrogen forms a triple bond. How many σ and π bonds are present, and which is strongest? Why does the triple bond make N₂ so unreactive?
- CountTriple bond = 1σ + 2π — one head-on pz–pz, two sidewise pairs.
- Rankσ strongest (density between nuclei), the two π weaker (grazing) — but all three sum to 946 kJ/mol.
- ReactivityBreaking N₂ demands paying for all three at once — hence its legendary inertness (and why fixing nitrogen is hard chemistry).
1σ + 2π — sum 946 kJ/mol, the inertia of nitrogen
Why ethane spins and ethene doesn’t
Rotation about the C–C bond is free in ethane but blocked in ethene. Explain using σ and π bonds.
- EthaneThe C–C bond is a pure σ — its electron cloud is a cylinder about the axis. Rotate the cylinder: nothing changes → free rotation.
- EtheneThe C=C carries a π bond whose lobes must stay parallel to overlap. Rotating breaks the sidewise overlap → the π bond must be paid for first → rotation blocked.
- ConsequenceThis rigidity is why cis/trans isomerism exists at all — a direct, testable consequence of overlap geometry.
Cylinder rotates · π overlap breaks — rigidity explained
Practice Questions (With Solutions)
Attempt first — options lock after one shot, exactly like the real exam. Then read the working, chahe galti ho ya na ho.
Attempted 0/4 · Correct 0
The number of σ and π bonds in a molecule of ethyne (C₂H₂) are respectively:
Solution
- 2 C–H σ + 1 C≡C (which is 1σ + 2π) → total 3σ + 2π.
- Option A miscounts by treating the triple bond as one unit; D forgets π bonds entirely.
(B) 3σ + 2π
A σ bond is stronger than a π bond because:
Solution
- Strength = overlap extent = electron density between the nuclei. Head-on wins; sidewise only grazes.
- A is wrong (p–p σ bonds exist and are strong); C is backwards (same pair count, less density); D is nonsense chronology.
(B) Density between nuclei
Valence bond theory fails to explain the paramagnetic nature of O₂ because it predicts:
Solution
- VBT’s double bond (1σ + 1π) uses up all four shared electrons in pairs — everything paired, diamagnetic predicted.
- Experiment says paramagnetic with two unpaired electrons — MOT (§ 4.7) gets this right; VBT’s picture is the failure.
(B) All paired — the wrong prediction
Free rotation about a C–C bond is possible in ethane but not in ethene because:
Solution
- Rotating a σ cylinder changes nothing; rotating a π pair destroys the parallel-p orbital overlap → the π bond must break.
- This rigidity is why geometric (cis/trans) isomerism exists across C=C — VBT’s most visible everyday consequence.
(C) π overlap would break
Key Rules & Takeaways
Eight lines that solve this topic
Anchors: H₂ 436 kJ/mol (s–s) · HF 566 (s–p) · N₂ 946 (1σ + 2π) · C₂H₄ = 5σ + 1π · C₂H₂ = 3σ + 2π · π never without σ
- VBT makes sharing physical — Lewis’s pairs become overlapping waves; strength becomes measurable as energy released on overlap.
- σ and π are overlap geometries, not bond types — head-on vs sidewise decides strength, cloud shape, and rotation freedom in one stroke.
- Count with the recipe — singles 1σ; doubles 1σ+1π; triples 1σ+2π; π bonds never travel alone.
- The theory’s failure list is the syllabus map — O₂ paramagnetism, colour, no stability ranking: exactly the doors MOT opens next.
FAQs
What are the main postulates of valence bond theory?
A covalent bond forms by the overlap of half-filled valence atomic orbitals of the two bonded atoms, each containing one unpaired electron. The overlapping orbitals must have opposite spins, and the overlap releases energy — greater the overlap, greater the energy released and stronger the bond. The electron density concentrates between the two nuclei.
What is the difference between a sigma bond and a pi bond?
A sigma bond forms by head-on overlap of orbitals along the internuclear axis — cylindrically symmetric about the axis, and strong because the overlap is maximal. A pi bond forms by sidewise overlap of p orbitals above and below the axis — the overlap is smaller, so a pi bond is always weaker than a sigma bond. Free rotation is possible around a sigma bond but not around a pi bond.
Why is a sigma bond stronger than a pi bond?
Strength follows the extent of overlap. Head-on overlap along the internuclear axis concentrates electron density directly between the nuclei — the region of maximum attraction. Sidewise pi overlap only grazes above and below the axis, giving thinner electron density between the nuclei and less energy release. Hence sigma bonds are stronger and are formed first; pi bonds always accompany an existing sigma bond.
What are the limitations of valence bond theory?
VBT cannot explain the paramagnetism of O2 — it predicts all electrons are paired. It fails for the colour and spectral properties of molecules, gives no quantitative measure of bond stability, and does not explain the equivalence of bonds in molecules like CH4 without invoking hybridisation. Molecular orbital theory resolves each of these failures.
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