Rotational-angular-momentum relaxation mechanisms in the energy-corrected-sudden scaling theory

In calculating the infrared (IR) band shape for bending modes, the angular-momentum coupling between vibration, rotation, and radiation must be taken into account. The accuracy of the energy-corrected-sudden (ECS) model has been proved through many recent applications in isotropic Raman Q-branch profiles. Furthermore, this model is based on the physical infinite-order-sudden (IOS) approximation, which allows inclusion of the other relaxation mechanisms required when considering other spectroscopic branches, such as IR Q-bending bands. To include, in a consistent way, the role of the vibrational angular momentum in the rovibrational relaxation matrix, the relaxation of the rotational angular momentum J and of its associated higher-order tensors [J ${]}^{\mathrm{}\left(2\right)\mathrm{}}$,. . . (basically absent in the IOS approximation) is enforced in the present ECS model. Application to the 2076.86 ${\mathrm{cm}}^{\mathrm{-}1}$ infrared rovibrational band of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{}^{16}{}_{}{}^{}$ ${\mathrm{O}}_2$ leads to the determination of the [J ${]}^{\mathrm{}\left(2\right)\mathrm{}}$ relaxation time in agreement with previous values obtained from different measurements. The present theory may be applied to other spectroscopic bands, such as the anisotropic Raman ones.