Chapter 6: Chemical Bonding II - Valence Bond Theory and Molecular Orbital Theory

Chapter 6: Chemical Bonding II – Advanced Theories

Introduction

This chapter explores advanced models of chemical bonding, focusing on Valence Bond Theory and Molecular Orbital Theory. These theories provide deeper insight into molecular structure, electron delocalization, and the nature of chemical bonds beyond the Lewis and VSEPR models.

6.1 Oxygen: A Magnetic Liquid

Paramagnetism in Oxygen

• Paramagnetic substances contain unpaired electrons, which generate tiny magnetic fields due to the spin of the electron.

• Oxygen (O2) is paramagnetic because it has two unpaired electrons in its molecular orbitals, as shown by molecular orbital theory.

• Liquid oxygen is attracted to a strong external magnetic field, a property not explained by Lewis or VSEPR models.

6.2 Valence Bond Theory: Orbital Overlap as a Chemical Bond

Fundamentals of Valence Bond Theory

• Valence Bond Theory: A chemical bond forms through the overlap of two half-filled atomic orbitals, resulting in a region of increased electron density between the nuclei.

• Quantum-Mechanical Atomic Orbitals: Valence bond theory uses s, p, d, and f orbitals or hybridized atomic orbitals (combinations of standard orbitals).

Energy Interactions and Bond Formation

• When two atoms approach, their electrons and nuclei interact. If these interactions lower the system's energy, a chemical bond forms.

• Bond Length and Bond Energy: The bond length is the distance at which the system is most stable, with significant orbital overlap and minimal repulsion.

Summarizing Valence Bond Theory

• Valence bond theory is a quantum-mechanical model that explains bonding as the overlap of atomic orbitals.

• It accounts for molecular shape and bond strength, but does not fully describe electron delocalization in molecules.

Conceptual Connection 6.1: What Is a Chemical Bond?

• According to valence bond theory, a covalent chemical bond is the overlap between two half-filled atomic orbitals on two atoms.

• The Lewis model describes a chemical bond as a shared electron pair between two atoms.

• A lone electron pair is not considered a chemical bond in any bonding model.

6.3 Valence Bond Theory: Hybridization of Atomic Orbitals

Hybridization Concept

• Hybridization: The mixing of atomic orbitals to form new, equivalent hybrid orbitals suitable for bonding.

• Standard atomic orbitals (s, p, d) alone cannot explain the bonding in many molecules; hybridization accounts for observed molecular geometries.

sp3 Hybridization

• Tetrahedral Geometry in CH4: The tetrahedral geometry of methane (CH4) is explained by the hybridization of one 2s orbital and three 2p orbitals on the carbon atom.

• Formation of sp3 Hybrid Orbitals: The process results in four sp3 hybrid orbitals, each with mixed s and p character and identical energy.

Conceptual Connection 6.2: Number of Hybrid Orbitals

• The number of hybrid orbitals formed equals the number of atomic orbitals combined.

• Combining one s orbital and three p orbitals results in four sp3 hybrid orbitals.

sp2 Hybridization and Double Bonds

• sp2 hybridization involves mixing one s and two p orbitals, forming three sp2 hybrid orbitals and one unhybridized p orbital.

• The unhybridized p orbital forms a π (pi) bond in double-bonded molecules.

• Rotation about a double bond is restricted due to the side-by-side overlap of p orbitals in a π bond.

sp Hybridization and Triple Bonds

• sp hybridization involves mixing one s and one p orbital, resulting in two sp hybrid orbitals and two unhybridized p orbitals.

• Triple bonds consist of one σ (sigma) bond and two π (pi) bonds.

sp3d and sp3d2 Hybridization

• Elements in the third period and beyond can expand their octets through hybridization involving d orbitals.

• sp3d hybridization leads to trigonal bipyramidal geometry; sp3d2 hybridization leads to octahedral geometry.

Writing Hybridization and Bonding Schemes

• Determine the number of electron groups around the central atom using the Lewis structure.

• Apply VSEPR theory to predict the geometry and assign the correct hybridization.

• Label all bonds, lone pairs, and hybrid orbitals.

6.4 Molecular Orbital Theory: Electron Delocalization

Introduction to Molecular Orbital Theory

• Molecular Orbital Theory treats electrons as delocalized over the entire molecule, rather than localized between two atoms.

• Atomic orbitals combine to form molecular orbitals (MOs) that extend over the whole molecule.

Linear Combination of Atomic Orbitals (LCAO)

• Molecular orbitals are formed by combining atomic orbitals mathematically (LCAO).

• Bonding Orbital: Formed by constructive interference, resulting in increased electron density between nuclei.

• Antibonding Orbital: Formed by destructive interference, resulting in a node between nuclei and higher energy.

Summarizing LCAO–MO Theory

• Molecular orbitals can be approximated as linear combinations of atomic orbitals (AOs).

• The number of MOs formed equals the number of AOs combined.

• Electrons fill the lowest energy MOs first, following the Aufbau principle.

Second-Period Homonuclear Diatomic Molecules

MO Diagrams and Bonding

• Second-period homonuclear diatomic molecules (e.g., O2, N2, F2) have between 2 and 16 valence electrons.

• Bonding is explained using higher-energy molecular orbitals formed from valence atomic orbitals.

• MO diagrams show the relative energies and electron configurations of bonding and antibonding orbitals.

Energy Ordering Differences

• For B2, C2, and N2: σ2s is lower in energy than π2p.

• For O2, F2, and Ne2: σ2p is lower in energy than π2p.

Bond Order Calculation

• Bond order is calculated as:

$\text{Bond Order} = \frac{\text{Number of electrons in bonding MOs} - \text{Number of electrons in antibonding MOs}}{2}$

• Bond order indicates the stability and strength of a bond; higher bond order means a more stable bond.

Conceptual Connection 6.5: Bond Order

• Bond order correlates with bond strength and bond length.

• As bond order increases, bond strength increases and bond length decreases.

• Examples:

Molecule	Bond Order	Bond Energy (kJ/mol)	Bond Length (pm)
N2	3	946	110
O2	2	498	121
F2	1	159	142

Second-Period Heteronuclear Diatomic Molecules

MO Theory for Heteronuclear Molecules

• Molecular orbital theory can be applied to molecules with different atoms, such as NO and HF.

• Energy levels and electronegativity differences affect the distribution of electrons in molecular orbitals.

6.5 Molecular Orbital Theory: Polyatomic Molecules

Electron Delocalization in Polyatomic Molecules

• Molecular orbital theory explains the delocalization of electrons over an entire molecule, which is crucial for understanding resonance and stability.

• Example: Benzene (C6H6) has delocalized π electrons over six carbon atoms, resulting in equal bond lengths and enhanced stability.

Conceptual Connection 6.6: What Is a Chemical Bond? (Part II)

• Molecular orbital theory states that electrons can have their energy spread over many atoms in the molecule.

• Unlike valence bond theory, chemical bonds in molecular orbital theory are not always localized between two atoms.

Key Terms

• Valence Bond Theory: Describes how atomic orbitals overlap to form bonds.

• Hybridization: The mixing of atomic orbitals to form new hybrid orbitals for bonding.

• Molecular Orbital (MO): An orbital that extends over the entire molecule.

• Bonding Orbital: An MO that is lower in energy and leads to bond formation.

• Antibonding Orbital: An MO that is higher in energy and works against bond formation.

Concepts

Valence Bond Theory

• A chemical bond is the overlap of half-filled atomic orbitals or a filled orbital with an empty orbital.

• Hybridization explains observed molecular geometries.

• Types of bonds: σ (sigma) bonds (direct overlap) and π (pi) bonds (side-by-side overlap).

Molecular Orbital Theory

• Molecular orbitals are linear combinations of atomic orbitals (LCAOs).

• Bonding and antibonding MOs are formed, and electrons fill the lowest energy orbitals first.

• The stability and bond strength of the molecule depend on the number of electrons in bonding versus antibonding orbitals.

Equations and Relationships

• Bond order is calculated using the formula:

$\text{Bond Order} = \frac{\text{Number of electrons in bonding MOs} - \text{Number of electrons in antibonding MOs}}{2}$

• Bond order indicates the strength and stability of a bond in a diatomic molecule.

• Bond order can be a fractional value, reflecting resonance or partial bonding.

• Bonding molecular orbitals (MOs) contribute to bond formation, while antibonding MOs work against bond formation.