Valence Bond Theory - College Chemistry Guide

What is Valence Bond Theory?

Valence Bond Theory (VBT) is a quantum mechanical model that describes chemical bonding by explaining how atomic orbitals overlap to form covalent bonds. Developed by Linus Pauling and others in the 1930s, VBT uses the concepts of orbital overlap, hybridization, and resonance to explain molecular structure and bonding.

Historical Background

Valence Bond Theory was developed in 1927 by Walter Heitler and Fritz London, who first applied quantum mechanics to explain the hydrogen molecule (H₂). The theory was significantly expanded by Linus Pauling in the 1930s, who introduced the concept of hybridization and won the Nobel Prize in Chemistry (1954) for his work on the nature of the chemical bond.

Fundamental Principles of VBT

Core Concepts:

Orbital Overlap: Covalent bonds form when atomic orbitals on different atoms overlap
Electron Pairing: Each bond involves two electrons with opposite spins
Maximum Overlap: Stronger bonds result from greater orbital overlap
Hybridization: Atomic orbitals mix to form new hybrid orbitals for better bonding
Sigma (σ) and Pi (π) Bonds: Different types of overlap create different bond types
Resonance: Some molecules require multiple bonding structures to describe accurately

The Overlap Principle

According to VBT, a covalent bond forms when:

Two half-filled atomic orbitals overlap
The overlapping region contains a pair of electrons with opposite spins
The electron density between nuclei increases, creating attraction
The greater the overlap, the stronger the bond

Types of Orbital Overlap

1. Sigma (σ) Bonds

Head-on overlap of atomic orbitals along the internuclear axis

s-s overlap (e.g., H₂)
s-p overlap (e.g., HCl)
p-p overlap (end-to-end)
Cylindrically symmetrical around bond axis
Allows free rotation around the bond
Stronger than π bonds

2. Pi (π) Bonds

Sideways overlap of p orbitals perpendicular to the internuclear axis

p-p overlap (side-by-side)
Electron density above and below the internuclear axis
Restricts rotation around the bond
Weaker than σ bonds
Always accompanied by a σ bond in multiple bonds

Bond Composition Examples:

Single Bond: 1 σ bond (e.g., C-C in ethane)

Double Bond: 1 σ + 1 π bond (e.g., C=C in ethene)

Triple Bond: 1 σ + 2 π bonds (e.g., C≡C in ethyne)

Hybridization

Hybridization is the mixing of atomic orbitals to form new hybrid orbitals with equivalent energy and specific geometries, allowing for better overlap and stronger bonds.

sp Hybridization

1s + 1p → 2 sp orbitals

Geometry: Linear

Bond Angle: 180°

Examples: BeCl₂, C₂H₂ (acetylene)

Bonds: 2 σ bonds

Unhybridized: 2 p orbitals (can form π bonds)

sp² Hybridization

1s + 2p → 3 sp² orbitals

Geometry: Trigonal Planar

Bond Angle: 120°

Examples: BF₃, C₂H₄ (ethene), CO₃²⁻

Bonds: 3 σ bonds

Unhybridized: 1 p orbital (can form π bond)

sp³ Hybridization

1s + 3p → 4 sp³ orbitals

Geometry: Tetrahedral

Bond Angle: 109.5°

Examples: CH₄, NH₃, H₂O

Bonds: 4 σ bonds or bonding pairs/lone pairs

Unhybridized: None

sp³d Hybridization

1s + 3p + 1d → 5 sp³d orbitals

Geometry: Trigonal Bipyramidal

Bond Angles: 90°, 120°, 180°

Examples: PCl₅, PF₅

Bonds: 5 σ bonds

Note: Requires d orbitals (period 3+)

sp³d² Hybridization

1s + 3p + 2d → 6 sp³d² orbitals

Geometry: Octahedral

Bond Angle: 90°, 180°

Examples: SF₆, [Co(NH₃)₆]³⁺

Bonds: 6 σ bonds

Note: Common in coordination compounds

dsp² Hybridization

1d + 1s + 2p → 4 dsp² orbitals

Geometry: Square Planar

Bond Angle: 90°, 180°

Examples: [Ni(CN)₄]²⁻, [PtCl₄]²⁻

Bonds: 4 σ bonds

Note: Inner orbital complex

VBT Applied to Coordination Compounds

Valence Bond Theory was historically used to explain the structure and bonding in transition metal complexes before Crystal Field Theory became dominant.

Inner Orbital vs. Outer Orbital Complexes

Property	Inner Orbital Complex	Outer Orbital Complex
d Orbitals Used	(n-1)d orbitals	nd orbitals
Hybridization	d²sp³ (octahedral) dsp² (square planar)	sp³d² (octahedral)
Ligand Field	Strong field ligands	Weak field ligands
Magnetic Nature	Low spin (fewer unpaired e⁻)	High spin (more unpaired e⁻)
Bond Strength	Stronger (more covalent)	Weaker (more ionic)
Example	[Co(NH₃)₆]³⁺ (d²sp³)	[CoF₆]³⁻ (sp³d²)

Example: [Co(NH₃)₆]³⁺ Complex

Co³⁺: d⁶ configuration (3d⁶)

Hybridization: d²sp³ (inner orbital)

Geometry: Octahedral

Magnetic: Diamagnetic (no unpaired electrons)

Reason: NH₃ is a strong field ligand causing electron pairing in 3d orbitals

                "Valence Bond Theory provides an intuitive picture of chemical bonding through orbital overlap and hybridization, making it essential for understanding molecular geometry and structure."
            

Resonance in VBT

Resonance occurs when a single Lewis structure cannot adequately describe a molecule. The actual structure is a hybrid of multiple resonance structures.

Key Points about Resonance:

Resonance structures differ only in electron placement, not atom positions
The actual molecule is a resonance hybrid (average of all structures)
All resonance structures must obey octet rule (with exceptions)
More resonance structures = greater stability
Equivalent structures contribute equally to the hybrid

Classic Resonance Examples:

Benzene (C₆H₆): Two equivalent structures with alternating double bonds

Carbonate Ion (CO₃²⁻): Three equivalent structures

Nitrate Ion (NO₃⁻): Three equivalent structures

Ozone (O₃): Two equivalent structures

Comparison: VBT vs. MOT vs. CFT

Aspect	Valence Bond Theory	Molecular Orbital Theory	Crystal Field Theory
Basic Approach	Localized bonds from orbital overlap	Delocalized electrons in molecular orbitals	Electrostatic ligand-metal interactions
Bond Type	Covalent	Covalent	Ionic (simplified)
Geometry Prediction	Excellent (via hybridization)	Good	Limited
Magnetism	Good	Excellent	Excellent
Color Explanation	Limited	Good	Excellent
Complexity	Moderate	High	Moderate
Best For	Organic molecules, simple structures	Paramagnetic species, O₂	Transition metal complexes

Strengths of Valence Bond Theory

Provides an intuitive, visual model of chemical bonding
Excellently predicts molecular geometry through hybridization
Explains directionality of covalent bonds
Successfully describes sigma and pi bonding
Accounts for bond strength through orbital overlap
Introduces resonance concept for molecules with delocalized electrons
Works well for organic chemistry applications

Limitations of Valence Bond Theory

Paramagnetism of O₂: Cannot explain why oxygen is paramagnetic
Electron delocalization: Poor treatment of delocalized π systems
Quantitative predictions: Limited ability to predict bond energies and lengths
Transition metal complexes: Less accurate than CFT for color and magnetism
Hypervalent molecules: Controversial use of d-orbital participation
Metallic bonding: Cannot adequately explain properties of metals
Computational difficulty: Harder to implement in quantum calculations

These limitations led to the development of Molecular Orbital Theory, which provides a more complete quantum mechanical description of bonding.

Important Formulas and Rules

Determining Hybridization:

Hybridization = Steric Number = (Bonded atoms + Lone pairs)

Steric Number 2 → sp (linear)
Steric Number 3 → sp² (trigonal planar)
Steric Number 4 → sp³ (tetrahedral)
Steric Number 5 → sp³d (trigonal bipyramidal)
Steric Number 6 → sp³d² (octahedral)

VSEPR and VBT Connection:

VSEPR (Valence Shell Electron Pair Repulsion) predicts geometry based on electron pair repulsion, which corresponds to VBT hybridization:

VSEPR geometry → Determines hybridization type
Lone pairs occupy hybrid orbitals
Lone pairs repel more than bonding pairs

Study Tips for VBT

Master drawing orbital overlap diagrams for σ and π bonds
Practice determining hybridization from molecular formulas
Understand the relationship between hybridization and geometry
Learn to draw resonance structures correctly
Know which orbitals remain unhybridized for each type
Connect VSEPR theory with VBT hybridization schemes
Understand when VBT is appropriate vs. when to use MOT or CFT
Practice with coordination compound examples

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