Rotationsniveauer

Rotationsniveauer, or rotational energy levels, are the quantized energy states associated with the rotational motion of molecules. In quantum mechanics, a molecule rotating about its axes can only possess certain discrete energies, leading to characteristic spectra in the microwave and far-infrared regions.

For a linear or diatomic molecule modeled as a rigid rotor with moment of inertia I, the energy levels are E_J = (ħ^2/2I) J(J+1), where J = 0,1,2,... . The spacing between adjacent levels increases with J. In spectroscopy, it is common to express the levels in wavenumbers using the rotational constant B̃ = h/(8π^2 I c), so that E_J/hc = B̃ J(J+1).

Transitions between levels follow the selection rule ΔJ = ±1 for a dipole-allowed transition, producing microwave lines at frequencies approximately 2B, 4B, 6B, etc., modulated by thermal populations given by the Boltzmann distribution and the rotational temperature.

Non-rigid rotor effects, described by centrifugal distortion constants (e.g., D_J), cause deviations from the simple E_J formula at high J, making spectra increasingly complex.

For symmetric top molecules, rotational levels depend on J and K, and more complex selection rules apply. In practice, rotational spectroscopy provides molecular moments of inertia and thus structural information, aiding determination of bond lengths and molecular geometry. Rotational spectra also enable detection of molecules in interstellar space and tracking of atmospheric species.