Valence-Bond Theory and Localised Bonds

Introduction

Valence-bond theory pictures a covalent bond as electron pairing in overlapping orbitals associated with two atoms. It gives a useful local account of sigma and pi bonds and connects readily to structural formulas. Its local picture is not the only way to represent molecular electrons.

Core explanation

For H₂, each H atom supplies an electron in a 1s orbital. As the orbitals overlap, electrons of opposite spin can form a bonding pair concentrated between the nuclei in a simple valence-bond description. Increased between-nucleus electron density stabilises the arrangement relative to separated atoms at a suitable distance. Repulsion at too-short distance yields an equilibrium bond length.

The overlap must have appropriate symmetry. Two orbitals meeting head-on along the internuclear axis can support a sigma bond. Parallel p orbitals overlapping side-on can support a pi bond. In ethene, a local model uses one C–C sigma bond, four C–H sigma bonds and one C–C pi bond. In ethyne, one C–C sigma, two C–H sigma and two C–C pi components appear. The structural double and triple lines are shorthand for these bonding patterns, not literal parallel sticks.

Spin pairing matters because two electrons occupying a shared bonding region cannot have identical quantum states. An elementary valence-bond picture often begins with one electron from each atom, but coordinate bonds show another route: one donor can supply a pair to an acceptor. Once formed, the covalent bond does not carry a physical label recording the electron source.

Hybridisation extends the local approach by constructing directional orbitals that match observed geometry. For methane, four equivalent tetrahedrally directed carbon bonding orbitals are described as sp³ hybrids. For ethene, three planar sigma directions plus one p orbital for pi bonding suggest sp² at each carbon. These are chosen representations of a quantum state, not orbital objects physically mixing in sequence before a molecule forms.

Localised valence-bond descriptions can become cumbersome for delocalised systems. Benzene, nitrate and carbonate need resonance to spread bonding character across several positions. Molecular-orbital theory treats orbitals extending over a whole molecule and naturally handles some delocalisation and O₂ magnetism. Both frameworks can describe aspects of the same molecule; a choice of model follows the property to be explained.

Step-by-step reasoning

1. Identify the bonded atom pair and their relevant valence orbitals. 2. Check orientation for sigma or pi overlap. 3. Describe electron pairing and stabilising density between nuclei. 4. Relate local bond components to a structural formula. 5. Recognise when resonance or MO treatment is needed for delocalisation or magnetism.

Visual explanation

Draw two H 1s clouds overlapping along a line and label the paired bonding region. Next show head-on hybrid overlap in C–C sigma and side-on p overlap above/below for C–C pi in ethene. Add a faded ring picture to signal that benzene's pi density is not limited to one pair.

Real-world analogy

A neighbourhood map shows direct links between neighbouring houses clearly, while a citywide map shows traffic spread across many routes. Local valence-bond and molecular-orbital models offer similarly different scales of electron description.

Real-world example

Organic chemists use local sigma/pi language to discuss alkene additions and bond rotations. The model helps explain why C=C rotation is restricted: twisting misaligns the p orbitals responsible for pi overlap.

Why?

Why does overlap direction matter? Orbital wavefunctions have shapes and signs. Suitable combinations place electron density in stabilising regions; misaligned p orbitals provide little side-on overlap and weaken the pi interaction.

Common misconception

“Valence-bond theory proves electrons are permanently confined to one bond line.” A localised representation is useful, but real electrons can be delocalised and different orbital representations can describe the same physical state.

Worked example

Use a local valence-bond account for ethene CH₂=CH₂. Each carbon forms two C–H sigma bonds and one C–C sigma bond, giving three approximately planar sigma directions. A remaining p orbital on each carbon overlaps side-on to make a pi bond. Total for the molecule is five sigma and one pi bond. This explains restricted rotation around C=C in the simple model, while an MO account could represent the pi electrons across both carbons as a molecular orbital.

Quick check

1. What is the local orbital-overlap pattern of a pi bond? Answer: Side-on overlap of suitably aligned p orbitals.

Exam focus

Distinguish sigma from pi overlap and count each correctly. State that hybrid labels are models for local geometry. Use resonance or MO theory when a localised picture alone cannot capture delocalisation or paramagnetism.

Advanced insight

Modern valence-bond calculations can be quantitatively sophisticated and include resonance between different local arrangements. The classroom model is a simplified entry point, not the full scope of valence-bond theory.

Summary

Valence-bond theory models local covalent bonds through appropriate orbital overlap and electron pairing. Sigma and pi patterns explain simple bond geometry and rotation, while delocalised electronic properties may need resonance or molecular-orbital treatment.

Practice questions

1. How do sigma and pi overlaps differ? Answer: Sigma is head-on along the bond axis; pi is side-on with density off the axis. 2. How many sigma and pi bonds are in ethene? Answer: Five sigma and one pi. 3. Does a coordinate bond remain a fundamentally different force after it forms? Answer: No. Coordinate describes the electron-pair source during formation. 4. Why can benzene challenge a single localised double-bond drawing? Answer: Its pi bonding is delocalised across the ring, so one fixed local pattern is incomplete.