A rigid rotor models rotational motion with fixed internal separations. Its use in the synthetic Stark effect figure omits vibrational motion and additional interactions in real molecules.
Rigidity fixes the molecular geometry, not the orientation, and does not require a spherical mass distribution. Remove motion of the centre of mass, choose principal axes of the inertia tensor, and write the classical rotational kinetic energy asHere are the principal moments of inertia, components of angular velocity, and components of angular momentum. Quantization replaces these last components by angular momentum operators. Different principal moments of inertia produce different spectra: the single-constant linear rigid rotor is a special case, not a formula for every molecule.[ref]
Lecture 24 Supplement: Energy levels of a Rigid Rotor by Dudley Herschbach. printed p. 1: principal-axis energy and classification; pp. 4–5: asymmetric rotors
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A **rigid rotor** is a model used in molecular dynamics and quantum mechanics to describe the behavior of a rotating molecule where it is assumed that the bond lengths and angles between atoms do not change during rotation. This simplification means that the molecular structure is considered to be fixed and rigid, which allows for the analysis of the rotational motion of the entire molecule as a solid object.