Summary of Molecular Orbitals and Their Applications

Summary of Molecular Orbitals and Their Applications

1. Concept of a Molecular Orbital

• Definition: A molecular orbital (MO) is a region of space where electrons in a molecule are most likely to be found. It is formed by the combination of atomic orbitals (AOs) from bonded atoms.

• Key Points:

  • MOs extend over the entire molecule rather than being localized to a single atom.

  • Electrons in MOs determine molecular bonding, stability, and reactivity.

2. Linear Combination of Atomic Orbitals (LCAO)

• Formation of Molecular Orbitals:

  • Bonding Orbital: Constructive interference of atomic orbitals; increases electron density between nuclei, stabilizing the molecule.

  • Antibonding Orbital: Destructive interference of atomic orbitals; creates a node (region of zero electron density) between nuclei, destabilizing the molecule.

• Combination Rules:

  • Orbitals combine if they have similar energy and symmetry.

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

3. Molecular Orbitals in Stability and Reactivity

• Bond Order:

  • Formula: Bond Order=(nbonding−nantibonding)2\text{Bond Order} = \frac{(n_\text{bonding} - n_\text{antibonding})}{2}Bond Order=2(nbonding​−nantibonding​)​

  • nbondingn_\text{bonding}nbonding​: Number of electrons in bonding orbitals.

  • nantibondingn_\text{antibonding}nantibonding​: Number of electrons in antibonding orbitals.

  • Interpretation:

    • Bond order > 0: Molecule is stable.

    • Bond order = 0: Molecule is unstable and does not exist under normal conditions.

• Reactivity:

  • Molecules with partially filled or low-energy molecular orbitals are often more reactive.

4. Molecular Orbital Energy Level Diagrams

• Energy Levels:

  • Bonding orbitals are lower in energy than the original atomic orbitals.

  • Antibonding orbitals are higher in energy.

• Order of Orbitals (for diatomic molecules up to oxygen):

  • For Li2\text{Li}_2Li2​ through N2\text{N}_2N2​: σ2s<σ2s∗<π2p<σ2p<π2p∗<σ2p∗\sigma_{2s} < \sigma_{2s}^* < \pi_{2p} < \sigma_{2p} < \pi_{2p}^* < \sigma_{2p}^*σ2s​<σ2s∗​<π2p​<σ2p​<π2p∗​<σ2p∗​

  • For O2\text{O}_2O2​ and F2\text{F}_2F2​: σ2s<σ2s∗<σ2p<π2p<π2p∗<σ2p∗\sigma_{2s} < \sigma_{2s}^* < \sigma_{2p} < \pi_{2p} < \pi_{2p}^* < \sigma_{2p}^*σ2s​<σ2s∗​<σ2p​<π2p​<π2p∗​<σ2p∗​

• Steps to Analyze:

  1. Fill orbitals with the total number of electrons (bonding first, then antibonding).

  2. Calculate bond order to determine stability.

  3. Identify unpaired electrons to determine magnetic properties.

5. Diamagnetic vs. Paramagnetic Species

• Diamagnetic: All electrons are paired; the molecule is weakly repelled by a magnetic field.

  • Example: N2\text{N}_2N2​ (bond order = 3).

• Paramagnetic: Contains unpaired electrons; the molecule is attracted to a magnetic field.

  • Example: O2\text{O}_2O2​ (bond order = 2).

6. HOMO and LUMO

• HOMO (Highest Occupied Molecular Orbital):

  • Contains the highest-energy electrons.

  • Important in determining how the molecule donates electrons in reactions.

• LUMO (Lowest Unoccupied Molecular Orbital):

  • The lowest-energy orbital available to accept electrons.

  • Determines how the molecule accepts electrons in reactions.

• Significance:

  • The HOMO-LUMO gap indicates reactivity:

    • Smaller gap = Higher reactivity (e.g., good nucleophiles or electrophiles).

    • Larger gap = Lower reactivity.