Valence Bond Theory and Molecular Orbitals

Valence Bond Theory

  • Overview:
    • Asserts that chemical bonds form when orbitals of valence electrons in two atoms overlap spatially.
    • No more than two electrons are shared by both orbitals.
    • Lewis structures and VSEPR cannot fully explain bond formation; quantum mechanics is required.

Bond Energies and Lengths

  • Bond Energies: Average bond energies and bond dissociation energies are crucial for understanding the strength and lengths of bonds.
    • Bond dissociation energy (BDE) is the energy required to break a bond in a molecule.

Directionality in Bonding

  • Directionality:
    • Atom's orbitals bond in the direction they extend in space.
    • There is a balance between maximizing orbital overlap while minimizing nuclear repulsion.

Hybridization of Atomic Orbitals

  • Concept:
    • Orbitals are not physical observables but mathematical abstractions from Schrödinger's equation.
    • Hybridized orbitals are formed by linear combinations of atomic orbitals.
  • Types of Hybrid Orbitals: Various combinations of s, p, and/or d orbitals can create different hybridized orbitals.

Bonding with Hybridized Orbitals

  • Example with BeH2:
    • Be has an sp hybridization to explain its bonding with two hydrogen atoms.
  • Hybridization for Carbon:
    • Carbon ([He] 2s² 2p²) has sp³ hybridization for forming four bonds.

Using VSEPR and Hybridization

  • Procedure for Bonding Description:
    1. Write Lewis electron-dot structure.
    2. Use VSEPR to determine electron geometry (includes bonding and lone pairs).
    3. Identify hybrid orbitals corresponding to electron geometry.
    4. Assign valence electrons to hybrid orbitals following Hund's rule.
    5. Bonds form between singly occupied hybrid orbitals and other atoms' singly occupied orbitals.

Types of Bonds

  • Sigma (σ) Bonds:
    • Cylindrical around the bonding axis; formed first in single and multiple bonds.
  • Pi (π) Bonds:
    • Presence of a node along the bonding axis; formed after σ bonds in double and triple bonds.

Molecular Orbital Theory

  • Concept:
    • Molecular orbitals (MOs) are formed by combining atomic orbitals (AOs).
    • Number of combined AOs equals the number of created MOs.
  • MO Diagrams:
    • Show energy levels of electrons arranged in molecules, similar to AOs in atoms.

Bond Order

  • Definition:
    • Bond order = ½ (number of bonding electrons - number of anti-bonding electrons).
    • Example: H2 has a bond order of 1 (single bond); molecules with resonance can have non-integer bond orders.

Examples of Bonding

  1. He2:
    • Does not form due to a bond order of 0 (one bond - one anti-bond cancels out).
  2. Li2:
    • Can form as bonding MOs are produced from closely situated AOs.
  3. H2 (Excited State):
    • Exciting H2 breaks its bond.

MOs from p Atomic Orbitals

  • Formation of Bonds:
    • Atomic p orbitals form bonding or anti-bonding σ and π MOs based on their phase orientation.

Oxygen Dimer and Magnetism

  • Bond Order of O2:
    • A bond order of 2 signifies a double bond (1 σ and 1 π bond); two unpaired electrons render O2 paramagnetic.