2.2 Atomic and molecular orbitals

Atomic orbitals are the building blocks of chemical bonding. They represent where electrons hang out around atoms, defined by quantum numbers that describe their energy and shape. These orbitals combine to form molecular orbitals in compounds.

Molecular orbitals show where electrons likely exist in molecules. They form through atomic orbital combinations, creating bonding, antibonding, or non-bonding orbitals. Understanding these concepts is key to grasping chemical structure and reactivity.

Atomic Orbitals

Atomic and molecular orbital properties

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• Atomic orbitals represent regions in space where electrons likely reside around an atom described by quantum numbers (n, l, ml, ms) characterizing energy levels and shapes
• Molecular orbitals depict regions where electrons probably exist in a molecule formed by atomic orbital combinations resulting in bonding, antibonding, or non-bonding orbitals (H₂, O₂)

Types of atomic orbitals

• s orbitals exhibit spherical shape with one orbital per energy level and no angular nodes (1s, 2s, 3s)
• p orbitals display dumbbell shape with three orbitals per energy level (px, py, pz) and one angular node
• d orbitals show complex shapes (cloverleaf and doughnut) with five orbitals per energy level and two angular nodes
• f orbitals present more intricate shapes with seven orbitals per energy level and three angular nodes

Molecular Orbitals

Formation of molecular orbitals

• Linear Combination of Atomic Orbitals (LCAO) mathematically describes molecular orbitals by adding or subtracting atomic orbital wave functions
• Constructive interference yields bonding molecular orbitals with lower energy than constituent atomic orbitals
• Destructive interference produces antibonding molecular orbitals with higher energy than constituent atomic orbitals
• Symmetry considerations require orbitals to have proper symmetry for effective combination (σ and π bonds)

Molecular orbital diagrams

• Visual representations of molecular orbital energy levels show electron occupancy in bonding and antibonding orbitals
• Energy level ordering generally places $\sigma$ orbitals lower than $\pi$ orbitals with antibonding orbitals higher than bonding orbitals
• Bond order calculation: (bonding electrons - antibonding electrons) / 2 indicates bond strength and length (O₂, N₂)
• Stability determination considers bond order > 0 generally stable and even electron numbers typically more stable than odd
• Magnetic properties reveal paramagnetic molecules with unpaired electrons and diamagnetic molecules with all paired electrons (O₂ vs N₂)