Photodissociation of CH2: A test case for the light–heavy–light approximation

Abstract

The validity of the light–heavy–light (LHL) approximation for calculating absorption spectra and partial photodissociation cross sections has been assessed for photodissociation of H2O, CH2, and CD2 through their first absorption bands. For this purpose, results of full 3D (three-dimensional) calculations were compared with 3D LHL and 2D LHL results. The 3D LHL approximation works well for calculating absorption spectra and cross sections which are resolved with respect to the final rotational state of the fragment. However, the fragment vibrational distributions calculated using the 2D and 3D LHL approximations are too warm. For the v=0–3 partial cross sections, the LHL approximation gives good results for H2O and reasonable results for CH2, but breaks down when applied to CD2. Using time-independent perturbation theory, it is found that the colder vibrational fragment distributions obtained using full 3D dynamics arise mostly from the influence of one particular coupling term. This term acts to push the wave packet into the dissociation channel earlier, thereby decreasing the vibrational excitation which results from both oscillators being stretched simultaneously in the molecule’s motion towards the saddle point. The size of this term is proportional to the cosine of the bond angle divided by the mass of the central atom. Therefore, in assessing whether the LHL approximation will be valid for photodissociation of a particular molecule, both the mass of the heavy atom and the equilibrium bond angle should be considered, and CH2 is a ‘‘worse case LHL molecule’’ mostly because its ground state equilibrium bond angle (134°) is larger than that of H2O (104°).