rovibrational

Rovibrational refers to the combined rotational and vibrational motions of molecules and the quantum states that arise from this coupling. In molecular spectroscopy, rovibrational states result from the interaction of internal vibrational motion along bonds with the overall rotation of the molecule, and they play a central role in infrared and Raman spectroscopy.

In simple models, the total energy is treated as a sum of vibrational and rotational contributions. The vibrational energy for a mode with quantum number v is approximated by E_v ≈ ω_e (v + 1/2) minus anharmonic corrections, while the rotational energy for a given vibrational level is E_rot(J) ≈ B_v J(J+1) minus centrifugal distortion terms, where J is the rotational quantum number. The rotational constant B_v typically decreases with increasing v because bond lengths lengthen with vibrational excitation. More accurate treatments include couplings such as Coriolis interactions and other anharmonic or centrifugal effects.

Rovibrational transitions are probed by infrared and, to a lesser extent, Raman spectroscopy. Transitions are characterized by changes in both vibrational and rotational quanta, producing spectra with P- and R-branch features corresponding to ΔJ = −1 and ΔJ = +1, respectively (and typically Δv = ±1 for fundamental transitions). In polyatomic molecules, each vibrational mode can generate a band with a complex pattern of rovibrational lines, reflecting the molecule’s geometry and rotational constants.

Rovibrational analysis yields molecular constants, bond lengths, force constants, and temperature information, and it supports studies in atmospheric chemistry, combustion, astrochemistry, and reaction dynamics. It remains a foundational concept in molecular spectroscopy and quantum chemistry.