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.

Molecular clouds contain gas at T ∼ 15 K and at densities of n ∼ 100 cm^-−3 and upward. Although ${\mathrm{H}}_2$ provides the overwhelming majority of molecules in a molecular cloud, the absence of an electric dipole in the symmetric ${\mathrm{H}}_2$ molecule means it is difficult to observe. The 2.6 mm emission from the $J=1\to 0$ rotational transition in ${}^{12}\mathrm{CO}$ is among the most useful ways to observe molecular gas. Most molecular clouds, however, are optically thick to the 2.6 mm emission from ${}^{12}\mathrm{CO}$; seeing to their centers requires observing the scarcer isotopologue ${}^{13}\mathrm{CO}$ rather than the more abundant ${}^{12}\mathrm{CO}$. Within dusty, optically thick molecular clouds, molecules are made by dust grain catalysis. In the surface layers of molecular clouds, molecules are destroyed through photodissociation by ultraviolet light. However, molecular clouds are self-shielded from UV outside the cloud.