New insights into the semiclassical Wigner treatment of photodissociation dynamics

TL;DR

This paper extends the semiclassical Wigner treatment to full-dimensional triatomic photodissociation, introducing a new rotational Wigner distribution and a backward trajectory approach for improved efficiency and accuracy in predicting state distributions.

Contribution

It presents the first full-dimensional semiclassical Wigner treatment for triatomic photodissociation, including a novel rotational Wigner distribution and a backward trajectory method for enhanced efficiency.

Findings

High accuracy in predicting final state distributions compared to quantum results.

Introduction of rotational Wigner distributions revealing classical-quantum correspondence.

Backward trajectory approach improves computational efficiency and state selectivity.

Abstract

The \emph{semiclassical Wigner treatment} of Brown and Heller [J. Chem. Phys. 75, 186 (1981)] is applied to triatomic direct photodissociations with the aim of accurately predicting final state distributions at relatively low computational cost, and having available a powerful interpretative tool. For the first time, the treatment is full-dimensional. The proposed formulation closely parallels the quantum description as far as possible. An approximate version is proposed, which is still accurate while numerically much more efficient. In addition to be weighted by usual vibrational Wigner distributions, final phase space states appear to be weighted by new \emph{rotational Wigner distributions}. These densities have remarkable structures clearly showing that classical trajectories most contributing to rotational state $j$ are those reaching the products with a rotational angular momentum close to $[j(j+1)]^{1/2}$ (in $\hbar$ unit). The previous methods involve running trajectories from the reagent molecule onto the products. The alternative \emph{backward approach} [L. Bonnet, J. Chem. Phys. 133, 174108 (2010)], in which trajectories are run in the reverse direction, is shown to strongly improve the numerical efficiency of the most rigorous method in addition to be \emph{state-selective}, and thus, ideally suited to the description of state-correlated distributions measured in velocity imaging experiments. The results obtained by means of the previous methods are compared with rigorous quantum results in the case of Guo's triatomic-like model of methyl iodide photodissociation [J. Chem. Phys. 96, 6629 (1992)] and an astonishing agreement is found. In comparison, the standard method of Goursaud \emph{et al.} [J. Chem. Phys. 65, 5453 (1976)] is only semi-quantitative.