3.3 Molecular Orbital Theory

Molecular Orbital Theory explains chemical bonding by combining atomic orbitals to form molecular orbitals. It treats electrons as moving under the influence of all nuclei in a molecule, not just individual bonds. This approach offers insights into delocalized electrons and magnetic properties.

Molecular orbital diagrams show energy levels and electron occupancies in molecules. For diatomics, orbitals form from atomic orbital overlap. In polyatomics, symmetry and overlap of constituent orbitals are considered. These diagrams help predict bond order, stability, and magnetic properties.

Molecular Orbital Theory Principles

Quantum Mechanical Model of Chemical Bonding

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• Molecular orbital theory describes chemical bonding in molecules by considering the combination of atomic orbitals to form molecular orbitals
• Electrons are treated as moving under the influence of the nuclei in the whole molecule, not assigned to individual bonds between atoms
• Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO) and can be bonding, antibonding, or nonbonding
  • Bonding orbitals have lower energy than the constituent atomic orbitals and are populated by electrons first, resulting in a net stabilization of the molecule (H2 molecule)
  • Antibonding orbitals have higher energy than the constituent atomic orbitals and are populated by electrons after all bonding orbitals are filled, resulting in a net destabilization of the molecule (He2 molecule)
  • Nonbonding orbitals have the same energy as the constituent atomic orbitals and do not contribute to bonding (lone pairs on oxygen in H2O)

Advantages over Valence Bond Theory

• Molecular orbital theory can better explain the properties of molecules with delocalized electrons, such as resonance structures, compared to valence bond theory (benzene)
• Molecular orbital theory can predict the magnetic properties of molecules based on the number of unpaired electrons in molecular orbitals (O2 molecule)
• Valence bond theory struggles to explain the properties of molecules with an odd number of electrons or with more complicated bonding arrangements (NO molecule)

Molecular Orbital Diagrams

Constructing Diagrams for Diatomic Molecules

• Molecular orbital diagrams show the relative energies and electron occupancies of molecular orbitals in a molecule
• For diatomic molecules, molecular orbitals are formed by the combination of atomic orbitals of the same symmetry and comparable energy
  • Sigma (σ) molecular orbitals are formed by the end-on overlap of atomic orbitals along the internuclear axis and can be bonding (σ) or antibonding (σ*) (H2 molecule)
  • Pi (π) molecular orbitals are formed by the side-on overlap of atomic orbitals perpendicular to the internuclear axis and can be bonding (π) or antibonding (π*) (N2 molecule)
• The order of increasing energy for molecular orbitals in diatomic molecules is typically: (1sσ) < (1sσ*) < (2sσ) < (2sσ*) < (2pπ) < (2pπ*) < (2pσ) < (2pσ*)

Constructing Diagrams for Simple Polyatomic Molecules

• For simple polyatomic molecules, the molecular orbital diagram is constructed by considering the symmetry and overlap of the constituent atomic orbitals
  • In linear molecules (BeH2), the molecular orbitals are classified as σ, π, or δ (delta) based on their symmetry with respect to the molecular axis
  • In bent molecules (H2O), the molecular orbitals are classified as a1, b1, or b2 based on their symmetry with respect to the molecular plane
• The molecular orbital diagrams for polyatomic molecules can be more complex due to the increased number of atomic orbitals and possible combinations (CO2 molecule)
• Group theory can be used to determine the symmetry and energy ordering of molecular orbitals in polyatomic molecules (NH3 molecule)

Bond Order, Stability, and Magnetism

Calculating Bond Order and Predicting Stability

• Bond order is the number of bonding electron pairs shared between two atoms in a molecule and can be calculated using the formula: (number of bonding electrons - number of antibonding electrons) / 2
  • A bond order of 1 corresponds to a single bond, 2 to a double bond, and 3 to a triple bond (N2 molecule)
  • Molecules with higher bond orders are generally more stable and have shorter bond lengths (CO molecule)
• The stability of a molecule can be predicted by the total number of electrons in bonding and antibonding molecular orbitals
  • Molecules with more electrons in bonding orbitals than antibonding orbitals are stable (F2 molecule)
  • Molecules with more electrons in antibonding orbitals than bonding orbitals are unstable (He2 molecule)

Determining Magnetic Properties

• The magnetic properties of a molecule can be determined by the number of unpaired electrons in the molecular orbitals
  • Molecules with no unpaired electrons are diamagnetic and are weakly repelled by a magnetic field (N2 molecule)
  • Molecules with one or more unpaired electrons are paramagnetic and are attracted to a magnetic field (O2 molecule)
• The presence of unpaired electrons in molecular orbitals can be determined by constructing a molecular orbital diagram and filling the orbitals according to the Aufbau principle and Hund's rule (NO molecule)