Molecular Orbitals Theory

Molecular Orbitals (MO) Theory

  • Definition of MO Theory: MO = Linear Combination of Atomic Orbitals (LCAO).

    • Number of initial Atomic Orbitals (AOs) equals the number of final Molecular Orbitals (MOs).

  • For 2-atom molecules:

    • Each MO can be represented as either AO1 ± AO2:
    • Bonding Molecular Orbital (MO):
      • Defined as (MO = AO1 + AO2)
      • Probability of finding electrons (ē) between nuclei is HIGH.
      • Bonding MO is lower in energy compared to antibonding MO.
    • Anti-bonding Molecular Orbital (MO):
      • Defined as (MO = AO1 - AO2)
      • Probability of finding ē between nuclei is LOW, which can reach 0.
      • Anti-bonding MO is higher in energy compared to bonding MO.

Electrons in Molecular Orbitals

  • Population of Electrons:

    • The number of electrons in atomic orbitals (AOs) equals the number of electrons in molecular orbitals (MOs).
    • MOs are populated according to principles also applied to AOs:
    • Aufbau Principle: Electrons fill the lowest energy orbitals first.
    • Pauli Exclusion Principle: No two electrons can have the same set of quantum numbers.
    • Hund’s Rule: Electrons will occupy degenerate orbitals singly before pairing up.

  • Molecular Orbital Energy Diagrams:

    • Diagrams depict the relative energies and number of electrons in each MO.
    • Electronic configurations can be written in a manner analogous to that of AOs.

  • Bond Order Calculation:

    • Bond order is determined using the formula:
    • Bond ext{ } order = \frac{# \text{ of } ē ext{ in bonding } MO - # \text{ of } ē ext{ in anti-bonding } MO}{2}
    • Interpretations:
    • If bond order > 0, the molecule is more stable than the separate atoms.
    • If bond order = 0, the molecule is as stable as separate atoms (indicating that the molecule will not form).

Comparison of VB Theory and MO Theory

  • Valence Bond (VB) Theory vs. Molecular Orbital (MO) Theory:
    • Bonds:
    • VB theory considers bonds as localized between each pair of atoms.
    • MO theory describes electrons as delocalized throughout the entire molecule.
    • Method of Bond Formation:
    • VB theory forms bonds through the overlap of atomic orbitals (s, p, d, etc.) and hybrid atomic orbitals (sp, sp2, sp3, etc.).
    • MO theory combines AOs to form Molecular Orbitals (σ, σ, π, π).
    • Bonding Types:
    • VB theory forms sigma (σ) or pi (π) bonds.
    • MO theory forms bonding and antibonding molecular orbitals.
    • Bond Order Calculation:
    • In VB theory, bond order is the number of electron pairs between atoms.
    • In MO theory, the same formula for bond order applies as mentioned earlier.
    • Predictions:
    • VB theory predicts molecular shape based on the number of regions of electron density.
    • MO theory predicts the arrangement of electrons in molecules and does not use the concept of resonance.
    • Terminology:
    • Definitions: AO = Atomic Orbital, MO = Molecular Orbital, HAO = Hybrid Atomic Orbital.

Types of Molecular Orbitals

  • Types of MOs:
    • Bonding MOs: e.g., $ ext{σ}_{1s}$
    • Anti-bonding MOs: e.g., $ ext{σ}^*_{1s}$
    • Characteristics of MOs:
    • Bonding MOs have constructive interference of wave functions.
    • Anti-bonding MOs have destructive interference of wave functions.

Energy of MOs for 2nd Period Homonuclear Molecules

  • Molecular Orbitals for 2nd Period Molecules:

    • The analysis ignores 1s AOs and associated molecular orbitals (s1s and s*1s), as those are fully occupied and do not affect bond orders.

  • Energy Levels for 2nd Period Homonuclear Diatomic Molecules:

    • The focus is primarily on the arrangement of MOs, applied using the Aufbau principle and Hund’s rule for electron configuration calculations.

Summary of Molecular Orbitals

  • Example: Li2 molecule

    • Bond order = 1
    • Energy = 102 kJ/mol
    • Bond length = 267 pm
    • Description: Li2 is diamagnetic.

  • Example: Be2 molecule

    • Bond order = 0
    • Description: Be2 does not exist due to its unstable nature.

Molecular Orbitals for Heteronuclear Diatomic Molecules

  • Characteristics:

    • Atomic orbital energy levels differ, even among the same types of orbitals due to differences in nuclear charge and electronegativity.
    • Higher effective nuclear charge (zeff) leads to lower energy AOs.
    • Resulting MO energy levels are asymmetrical relative to AOs.
    • Bonding MOs are closer in energy to lower-energy AOs (e.g., more electronegative atoms).
    • Anti-bonding MOs are closer in energy to higher-energy AOs.
    • Formation of MOs:
    • MOs are formed using LCAO, but coefficients differ:
      • MOi = c1 AO1 ext{ } ± ext{ } c2 AO_2
    • Non-bonding MOs:
    • These derive from atomic orbitals that do not participate in bonding, analogous to lone electron pairs in VB theory.

  • Bond Order Calculation for Heteronuclear Diatomic Molecules:

    • As previously defined, bond order is calculated using the formula for bonding and antibonding electrons:
    • Bond ext{ } order = \frac{# \text{ of } ē ext{ in bonding } MO - # \text{ of } ē ext{ in anti-bonding } MO}{2}
    • Importance of this calculation in defining the stability of the molecule based on its electronic structure.