RigideRotorModell

RigideRotorModell, or the rigid rotor model, is a simplified quantum-mechanical description used to characterize the rotational energy levels of linear molecules, especially diatomic ones. It treats the bond length as fixed and models the molecule as two masses connected by a rigid rod rotating about its center of mass. The rotational kinetic energy is given by H = L^2 / (2I), where L is the angular momentum and I is the moment of inertia, I = μ r^2, with μ the reduced mass and r the internuclear distance.

The energy levels are quantized as E_J = ħ^2 J(J+1) / (2I) = B J(J+1), where J is the rotational quantum number and B = ħ^2 / (2I) is the rotational constant. In spectroscopic terms, E_J / (hc) = B̃ J(J+1), with B̃ expressed in wavenumbers (cm^-1). Each level with quantum number J has degeneracy 2J+1. Allowed transitions in pure rotational spectroscopy follow ΔJ = ±1, producing P- and R- branches in the spectrum. The line positions scale approximately with 2B(J+1) for the R-branch and with 2BJ for the P-branch.

Limitations of the model include the assumption of a fixed bond length; in reality, centrifugal distortion causes bond stretching at higher J, and rovibrational coupling can shift line positions. The rigid rotor is best suited as a first approximation for low-to-moderate rotational excitations and for linear molecules; deviations are addressed by non-rigid rotor corrections and by more advanced rovibrational models.

Applications include interpreting microwave and far-infrared rotational spectra, extracting rotational constants B and higher-order distortion constants, and estimating bond lengths from experimental spectra.