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

Chapter 6: Chemical Bonding II

Introduction to Chemical Bonding Theories

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, bonding, and properties beyond what is possible with Lewis structures alone.

Valence Bond Theory

Fundamental Concepts

Valence Bond (VB) Theory describes chemical bonding as the overlap of atomic orbitals from adjacent atoms, resulting in a shared pair of electrons. The geometry and orientation of these orbitals determine the shape and strength of the bond.

• Atomic Orbitals: Regions in an atom where electrons are likely to be found (s, p, d, f).

• Bond Formation: Occurs when half-filled orbitals from two atoms overlap and their electrons pair with opposite spins.

• Hybridization: Mixing of atomic orbitals to form new, degenerate hybrid orbitals that optimize bonding and molecular geometry.

Example: In methane (CH4), carbon undergoes sp3 hybridization to form four equivalent orbitals arranged tetrahedrally.

Types of Bonds

• Sigma (σ) Bond: Formed by the head-on overlap of orbitals along the axis connecting two nuclei. Strongest type of covalent bond.

• Pi (π) Bond: Formed by the side-by-side overlap of unhybridized p orbitals, with electron density above and below the internuclear axis. Weaker than sigma bonds.

Example: In ethene (C2H4), the double bond consists of one σ bond and one π bond.

Hybridization Schemes

• sp3 Hybridization: Four electron groups, tetrahedral geometry, 109.5° bond angles.

• sp2 Hybridization: Three electron groups, trigonal planar geometry, 120° bond angles.

• sp Hybridization: Two electron groups, linear geometry, 180° bond angle.

• sp3d and sp3d2 Hybridization: Involve d orbitals for expanded octets (e.g., trigonal bipyramidal and octahedral geometries).

Example: In BrF3, bromine uses sp3d hybridization to accommodate five electron groups.

Limitations of Valence Bond Theory

• Cannot accurately predict magnetic properties (e.g., O2 is paramagnetic, but VB theory predicts diamagnetism).

• Does not account for electron delocalization in molecules with resonance.

• Provides only approximate bond angles and strengths.

Molecular Orbital (MO) Theory

Fundamental Concepts

Molecular Orbital Theory applies quantum mechanics to molecules, treating electrons as delocalized over the entire molecule. Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO).

• Bonding Molecular Orbitals: Constructive interference of atomic orbitals, lower energy, increased electron density between nuclei.

• Antibonding Molecular Orbitals: Destructive interference, higher energy, electron density outside the internuclear axis (designated with an asterisk, e.g., σ*).

Example: In H2, two 1s orbitals combine to form one bonding (σ) and one antibonding (σ*) molecular orbital.

Bond Order

Bond order quantifies the strength and stability of a bond:

• Formula:

$\text{Bond Order} = \frac{1}{2} (\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons})$

• Interpretation: Higher bond order means stronger, shorter bonds. Bond order of zero means no bond forms.

• Magnetism: Molecules with unpaired electrons in MO diagrams are paramagnetic; all paired electrons indicate diamagnetism.

Example: O2 has a bond order of 2 and is paramagnetic due to two unpaired electrons in its MO diagram.

MO Diagrams for Diatomic Molecules

MO diagrams show the relative energies and occupancy of molecular orbitals for homonuclear (same atom) and heteronuclear (different atoms) diatomic molecules.

• For second-period elements, the ordering of MO energies can vary due to s-p mixing.

• Electronegativity affects the contribution of atomic orbitals to MOs in heteronuclear molecules.

Sample MO Diagram Table

Molecule	Bonding Orbitals	Antibonding Orbitals	Bond Order	Magnetism
H2	2	0	1	Diamagnetic
He2	2	2	0	Diamagnetic
O2	10	6	2	Paramagnetic
N2	10	4	3	Diamagnetic
NO	11	6	2.5	Paramagnetic

MO Theory and Polyatomic Molecules

For molecules with more than two atoms, MO theory combines all atomic orbitals to form delocalized molecular orbitals over the entire molecule. This approach better explains properties such as resonance and electron delocalization.

Comparison of Bonding Theories

• Lewis Theory: Useful for predicting general trends and drawing structures, but limited in accuracy for bond strengths, angles, and magnetic properties.

• Valence Bond Theory: Improves predictions of molecular geometry and bonding schemes, but does not account for delocalization or some magnetic behaviors.

• Molecular Orbital Theory: Provides the most accurate description of electron distribution, bond order, and magnetic properties, especially for molecules with resonance or unpaired electrons.

Practice Problems and Applications

• Draw Lewis structures and predict hybridization using VSEPR theory.

• Construct MO diagrams for diatomic and simple polyatomic molecules.

• Calculate bond order and predict magnetic properties.

Additional info: The notes are based on lecture slides for Chapter 6 of "Chemistry: Structure and Properties" by Nivaldo J. Tro, focusing on advanced bonding theories relevant for General Chemistry students.