The zero-order rotational Hamiltonian of a molecule is the rigid-rotor Hamiltonian and it describes the molecule as rotating in space with its geometry fixed at equilibrium. Nonlinear molecules are categorized as being either symmetric tops, spherical tops or asymmetric tops and, in section 5.3, we discuss the rigid-rotor Schrodinger equation for each of these types of molecule. The derivation of the rigid-rotor Hamiltonian and an account of the detailed form of the wavefunctions are given at the end of the chapter in section 5.5. In section 11.5, the effects of rotation–vibration coupling, which produce centrifugal distortion and Coriolis coupling corrections to the rigid-rotor Hamiltonian, will be discussed. The rigid-rotor Hamiltonian involves the principal moments of inertia of the molecule and its eigenfunctions are functions of the Euler angle; so we begin by defining the Euler angles and by explaining what the principal moments of inertia are.