Study Notes on Molecular Orbital Theory of Bonding

CHEM 1066: Molecular Orbital Theory of Bonding - Study Notes

Predict shape and bonding types using Valence Bond Theory
- Understanding the differences in bond types.
- Utilizing knowledge of electron configurations and molecular geometries.
Explain Atomic Orbital Overlap
- The principle that atomic orbitals can overlap to form bonds.
- This overlap leads to a sharing of electrons between atoms.
Explain Hybridisation
- The process of mixing atomic orbitals to create new hybrid orbitals.
- Helps in predicting the geometry of molecules.
Construct MO diagrams for:
- Homonuclear diatomic molecules (e.g., H₂)
- Heteronuclear diatomic molecules (e.g., CO)
- Homo and heteronuclear triatomic molecules (e.g., O₃)
Predict properties of molecules based on their MO
- Understanding parameters like bond order, magnetism, and electronegativity based on the molecular orbital configuration.

Introduction:
- Valence bond theory, pioneered by Linus Pauling, focuses on localized bonding arrangements among atoms.
- It proposes hybridization which allows atomic orbitals to combine, resulting in hybrid orbitals that match the experimental bond angles observed.
Applications:
- Utilized when VSEPR (Valence Shell Electron Pair Repulsion) fails, particularly for complex molecules.
- Example: Analyzing transition metal compounds and the halides in group 2 elements.
Isoelectronic Species:
- Provide insight into molecular structure using species that have the same electron configuration.
Observed Deviations:
- Collect empirical data that may deviate from expected geometries. Example: For Tellurium fluoride, Te-F bond lengths show discrepancy from predicted values, indicating an octahedral geometry instead of the expected pentagonal bipyramidal.

Core Concept:
- Focuses on electron pairs localized in space around the bonded atoms.
Hybridisation:
- Employs atomic orbitals to construct new hybrid orbitals adapted to achieve the optimal shape according to VSEPR theory.
- The mathematical representation for the combination of wavefunctions in bonding is given as:
  Y = FA(1)FB(2) + FA(2)FB(1)
- According to the Pauli Principle, electrons must possess paired spins within a bonding orbital to ensure stability (energy minimization).
Energy Considerations:
- Hybrid pairs create a lower energy system as compared to individual atomic orbitals.

Definition of Hybridisation:
- The mixing of different atomic orbitals to form hybrid orbitals tailored for bonding.
Case Study: CH₄:
- Carbon configuration: 1s^2 2s^2 2p^2 (Four valence electrons needing to form four bonds).
- Process: 1s and 3p orbitals hybridize to produce four sp³ orbitals utilized in bonding with hydrogen atoms.
- Each sp³ orbital is singly filled to accommodate hydrogen bonds.
Shape and Bond Angles:
- The arrangement from sp³ hybridization leads to a tetrahedral shape with bond angles of approximately 109.5°.
General Hybridisation Processes:
- sp: 2 hybrid orbitals (linear); 50% s, 50% p. Example: BeCl₂.
- sp²: 3 hybrid orbitals (trigonal planar); 33.3% s, 66.67% p. Example: BF₃.
- sp³: 4 hybrid orbitals (tetrahedral); 25% s, 75% p. Example: CH₄.

Introduction:
- Developed by Robert Mulliken, this theory utilizes a linear combination of atomic orbitals (LCAO) to explain molecular bonding.
Principles:
1. The number of molecular orbitals equals the number of atomic orbitals combined.
2. For every bonding molecular orbital (lower energy), a corresponding anti-bonding molecular orbital exists (higher energy).
3. Electrons are filled into the lowest energy orbitals first (Aufbau principle).
4. Maximum occupancy of each orbital is limited to 2 electrons (Pauli Exclusion Principle).
5. Electrons will fill degenerate orbitals singly before pairing up (Hund's Rule).
Types of Molecular Orbitals:
- Bonding Orbitals: Lower energy, stable configurations that promote bonding.
- Anti-bonding Orbitals: Higher energy configurations that destabilize interactions.
- Non-Bonding Orbitals: No energy lowering compared to atomic orbitals (e.g., lone pairs).

Example: H₂:
- Bonding MO (σ) has lower energy than AOs.
- Anti-bonding MO (σ*) has higher energy than AOs.
Molecular Orbital Diagrams for Diatomics:
- Understand the order of energy levels in different molecules such as O₂ and N₂ and how mixing of orbitals can influence bonding.
- The inclusion of dipole moments can also assist in determining molecular stability and reactivity.
Energy Differences in Multi-electron Atoms:
- The energy separation between different subshells ([e.g., 2s-2p]) is key in understanding electron configurations. For example, for F the ΔE is 27.65 eV and for N it is 12.2 eV.
- Observe the shifting energy levels of σ and π orbitals in elements from Li to Ne.

Bond Order Calculation:
- Bond order can be determined using the formula:
  Bond Order = rac{1}{2} [ ext{Number of bonding electrons} - ext{Number of antibonding electrons}]
Magnetic Properties:
- Understanding paramagnetism vs. diamagnetism based on electron configurations (presence of unpaired electrons). Paramagnetic species exhibit attractive interactions in a magnetic field.
Symmetry in Molecular Orbitals:
- MOs can be classified based on symmetry properties (gerade vs. ungerade).

Diagrams for elements previous to the transition metals observed changes, highlighting the impact of molecular structure on electronic distribution and detached bonding/no bonding configurations.
Effect of bonding/anti-bonding orbitals on molecular properties such as stability and reactivity must be considered in practical applications of molecular orbital theory in chemical contexts.

Review cases of hybridization transitions, energy states for molecular orbitals, bond lengths, and types of interactions exhibited across the periodic table based on atomic composition.