The theory of chemical bond formation in molecules and extended crystals is outlined. We start from the Born–Oppenheimer approximation, which associates the forces experienced by nuclei to the quantum electronic state. The Schrödinger equation for diatomic molecules reveals the formation of stable molecules when electrons are occupying “bonding” molecular orbitals. These are linear combinations of atomic orbitals (LCAO), in which the nuclei “share” electrons that effectively mask the electrostatic repulsion between them. The formation of effective LCAOs relies on compatibility in symmetry and energy of the underlying atomic orbitals. This is ubiquitously found in covalently bounded molecules, including conjugated polyatomic molecules. In the absence of effective LCAO, ionic bonds can be formed by charge transfer between atomic orbitals. In periodic lattices, effective LCAOs result in broad energy bands, which increase electrical conductivity. Conductor-to-insulator transition in response to the type of LCAO in the underlying material is demonstrated for a model system.

Summarizes elementary building blocks of solid-state physics, including the Born–Oppenheimer approximation. It also reviews time-reversal symmetry and its implications.