Atomic orbitals are the building blocks of molecular structure. They combine to form molecular orbitals, shaping how electrons behave in molecules. Understanding these orbitals is key to grasping chemical bonding and reactivity.

Molecular orbital theory explains how atomic orbitals merge, creating new energy levels. This process determines a molecule's stability, shape, and properties. It's crucial for predicting and understanding molecular behavior in various chemical systems.

Atomic and Molecular Orbitals

Atomic Orbital Characteristics

• Atomic orbitals are mathematical functions describing the wave-like behavior of electrons in an atom
• Characterized by unique shapes and orientations in space (s, p, d, f)
• Each orbital has a specific energy level and can hold up to two electrons with opposite spins (Pauli exclusion principle)
• Electrons fill orbitals in order of increasing energy (Aufbau principle)

Molecular Orbital Formation

• Molecular orbitals form when atomic orbitals combine through the linear combination of atomic orbitals (LCAO) method
• LCAO involves adding or subtracting wave functions of atomic orbitals to create new molecular orbitals
• Bonding orbitals are lower in energy than the original atomic orbitals and contribute to the stability of the molecule
• Antibonding orbitals are higher in energy than the original atomic orbitals and can destabilize the molecule if occupied
• The number of molecular orbitals formed equals the number of atomic orbitals combined

Molecular Orbital Energy Diagrams

• Energy diagrams illustrate the relative energies of molecular orbitals
• Electrons fill molecular orbitals in order of increasing energy, following the Aufbau principle and Hund's rule
• The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are important for determining chemical reactivity and electronic properties
• The energy difference between HOMO and LUMO is the band gap, which influences electrical conductivity and optical properties

Types of Molecular Bonds

Sigma (σ) and Pi (π) Bonds

• Sigma (σ) bonds form when atomic orbitals overlap head-on, creating a single region of electron density between the nuclei
• Sigma bonds are the strongest type of covalent bond and are present in all single bonds (C-C, C-H)
• Pi (π) bonds form when parallel p orbitals overlap laterally, creating two regions of electron density above and below the bond axis
• Pi bonds are weaker than sigma bonds and are present in double and triple bonds (C=C, C≡C) alongside sigma bonds

Hybridization

• Hybridization is the mixing of atomic orbitals to form new hybrid orbitals with specific geometries
• Hybrid orbitals allow for better overlap and stronger bonds compared to pure atomic orbitals
• Common hybridization states include sp³ (tetrahedral), sp² (trigonal planar), and sp (linear)
• The hybridization state influences the bond angles and molecular geometry of a molecule (CH₄: sp³, 109.5°; BF₃: sp², 120°)

Theoretical Approach

Valence Bond Theory

• Valence bond theory describes bonding as the overlap of atomic orbitals to form localized electron pairs
• Focuses on the individual bonds between atoms and the hybridization of orbitals
• Provides a qualitative understanding of molecular geometry and bonding
• Limitations include the inability to accurately describe delocalized electrons and the energies of excited states
• Complementary to molecular orbital theory, which offers a more quantitative approach to bonding and electronic structure