rigidrotorModells

The rigid rotor model is a simplified quantum mechanical description of molecular rotation. It treats a molecule as a rigid body with fixed internuclear distances, so the only degrees of freedom are rotational motions. The model is widely used for interpreting microwave and far-infrared rotational spectra and provides a first estimate of molecular structure through moments of inertia. In some sources, especially German-language ones, the term rigidrotorModells is used to denote this concept.

In the simplest case of a linear diatomic molecule, the rotational motion is described by a single moment of inertia I = μ r^2, where μ is the reduced mass and r is the bond length. The Hamiltonian is H = L^2/(2I). The energy levels are E_J = ħ^2 J(J+1)/(2I) = h c B J(J+1) with B = h/(8π^2 I c). Transitions follow the selection rule ΔJ = ±1, producing lines separated roughly by 2B.

For nonlinear molecules the rigid rotor concept extends to three principal moments of inertia, yielding more complex level structures. Symmetric tops use quantum numbers J and K with rotational constants A, B, and C. In practice, observed spectra are fitted to these constants to infer geometry; asymmetric tops require more elaborate treatments. The rigid rotor framework provides a practical starting point for modeling rotational spectra and extracting structural information.

Limitations include the neglect of vibrational-rotational coupling and centrifugal distortion, which means bond lengths are assumed fixed. At high rotational excitation, non-rigid rotor effects appear, requiring corrections or more advanced Hamiltonians.

Applications include extracting bond lengths from rotational spectra, characterizing molecules in interstellar space, and providing inputs for thermodynamic and kinetic models in chemistry and astrophysics.