Chemical Bonding

Chapter 14: Introduction to Chemical Bonding

Recommended Textbook Problems

• Chapter 13 - Bonding: General Concepts
  • Lewis Structures and Resonance: 63, 67, 73, 75, 77
  • Formal Charge: 85, 87, 89
• Chapter 14 - Covalent Bonding: Orbitals
  • The LE Model and Hybrid Orbitals: 13, 15, 21, 23, 27
  • The MO Model: 35, 39, 43, 45, 51

Chemical Bonding and Lewis Theory

• Lewis Theory:
  • Works reasonably well for light atoms in main-group compounds (s and p block elements).
  • Emphasizes the electron pair bond and octets.
  • Based on chemical reactivity and structure patterns, not on a fundamental physical model.
  • Many exceptions noted for main-group elements.
  • Fails for transition metals and rare Earth elements (d+f block).
• Historical Context:
  • Lewis formulated his concepts without a complete description of bonding at the time.
• Quantum Mechanics:
  • The 1920s/30s saw the discovery and development of quantum mechanics.
  • First applied to atoms and then molecules, providing a complete physical description of bonding.

The Schrödinger Equation: A Simplified Overview

• Schrödinger Equation:
  • $HΨ = EΨ$
  • Where:
    • $H$ is the Hamiltonian operator (contains kinetic energy $T$ and potential energy $V$ terms).
    • $Ψ$ is the wavefunction.
    • $E$ is the energy of a given state.
• Interactions in $H_2$:
  • Potential energy terms: electron-electron repulsion, proton-proton repulsion, electron-proton attraction.
  • Kinetic energy terms.
• Orbitals:
  • Energy is the only observable; therefore, there are orbitals when describing electrons.
• Wavefunction:
  • $Ψ$ has no physical meaning itself.
  • $Ψ^2$ gives a probability distribution.
• Utility:
  • A very useful tool for tackling chemical bonding.

Review of Atomic Orbitals and Orbital Phases

• Quantum Numbers:
  • Principal quantum number $n$: 1, 2, 3, … (energy level)
  • Angular momentum quantum number $l$: 0, 1, …, $n-1$ (shape)
  • Magnetic quantum number $m_l$: -$l$, …, +$l$ (direction/orientation)
  • Electron spin quantum number $m_s$: +1/2, -1/2
• Example: Oxygen Atom
  • Electron configuration: $1s^2 2s^2 2p^4$
  • 2p orbitals: $2p<em>x$, $2p</em>y$, $2p_z$
• Pauli Exclusion Principle:
  • No two electrons can have the same four quantum numbers.
• Orbital Phase:
  • Phase is important! (+ + = constructive interference, + - = destructive interference)

Two Major Approximations of the Schrödinger Equation

• Challenge:
  • The Schrödinger equation is too complex mathematically to be solved for molecules larger than $H_2$.
  • Need to make approximations.
• Approximations to be Discussed:
  • Molecular Orbital (MO) theory: delocalized view of chemical bonding.
    • Bonding without bonds.
  • Valence Bond (VB) theory: localized view of bonding.

Molecular Orbital Theory: The Basic Idea

• Helium Atom Example:
  • Pull nucleus apart. Approach $He_2^{2+}$ as $H-H$.
• Molecular Orbitals:
  • Molecular orbitals are solutions to the molecular problem.
• Linear Combination of Atomic Orbitals (LCAO):
  • A way to make MO theory useful.
  • Example:
    • $Ψ<em>1 = 1s + 1s = σ</em>g + σ_g$ (same phase, constructive)
    • $Ψ<em>2 = 1s - 1s = σ</em>u + σ_u$ (opposite phase, destructive)
• Key Principles:
  • Number of atomic orbitals (AO's) in = Number of molecular orbitals (MO's) out.
  • For atomic orbitals to combine, they must be of similar energy and symmetry.
  • Overlap: O + O →
    σ, O + O_{out
    of
    phase} → π

Molecular Orbital Symmetry and Labels

• Symmetry Requirement:
  • Orbitals must have the same symmetry to combine.
• Defining MO Symmetry:
  • Symmetry is determined by how the orbital 'looks' following rotation about a bond.
• Symmetry Labels:
  • $σ$: symmetric with a full 360° rotation (sigma).
  • $π$: antisymmetric with a 180° rotation (pi).
  • By definition, the atomic z-axis is oriented along the bond.