The interaction of electromagnetic radiation with single-photon resonances in diatomic molecules is discussed in this chapter. The properties of the electric dipole moment of the molecule are determined primarily by the electron cloud that binds the two nuclei together, and these properties can be understood by considering a reference frame fixed to the molecule. However, the response of the molecule must be averaged over all possible orientations of the molecule in the laboratory frame. Using irreducible spherical tensors greatly simplifies the orientation averaging of the molecular response. The Born–Oppenheimer approximation is invoked to initially account for the effect of the electronic, vibrational, and rotational modes of the molecule. Corrections are applied to account for the coupling and interactions of the different modes, including Herman–Wallis effects. Tables of rotational line strengths are presented for singlet, doublet, and triplet electronic transitions. These tables incorporate the use of Hund’s case (a) basis state wavefunctions for increased insight into radiative interactions for levels intermediate between Hund’s cases (a) and (b).

The structure of diatomic molecules is discussed in this chapter. The electronic structure of diatomic molecules is then discussed in detail. The coupling of the orbital and spin angular momenta of electrons and the angular momentum associated with nuclear rotation are discussed, with an emphasis on Hund’s cases (a) and (b). The rotational wavefunctions for diatomic molecules in the limits of Hund’s cases (a) and (b) and in the case intermediate between Hund’s cases (a) and (b) are then discussed in detail. For molecules that are of importance in combustion diagnostics, such as OH, CH, CN, and NO, the electronic levels are intermediate between Hund’s cases (a) and (b). We use Hund’s case (a) as the basis wavefunctions, and linear combinations of these wavefunctions are used to represent wavefunctions for electronic levels intermediate between cases (a) and (b). The choice of case (a) wavefunctions as the basis set is typical in the literature although case (b) wavefunctions can also be used as a basis set.

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.