Chapter 9: Molecular Structure

The Born–Oppenheimer approximation provides the essential starting point by treating nuclei as stationary relative to the much faster-moving electrons, simplifying the mathematical treatment of molecular systems. Valence-bond theory explains bonding through the pairing of electrons between atoms, emphasizing the role of orbital hybridization, where atomic orbitals blend into new hybrid orbitals with specific geometries suited to molecular architecture, such as sp2 or sp3 configurations. Within this framework, sigma bonds form through direct orbital overlap along the internuclear axis, while pi bonds arise from lateral p-orbital overlap. Molecular orbital theory offers an alternative perspective by distributing electrons across the entire molecular framework rather than localizing them between atom pairs. This approach employs linear combinations of atomic orbitals to construct molecular orbitals and relies on the variation principle and secular equation solutions to determine orbital energies, introducing key parameters like the Coulomb integral and resonance integral. For diatomic molecules containing different elements, differences in atomic orbital energies dictate bond polarity, a property quantified through electronegativity scales. When extended to polyatomic systems, molecular orbitals delocalize across multiple atoms, and the Hückel method provides a practical simplified approach for analyzing pi-electron systems, calculating orbital energies and measuring delocalization energy. Modern computational chemistry builds upon these foundations through self-consistent field methods and Gaussian-type orbitals, enabling systematic investigation of complex molecular structures.