The semiclassical Wigner treatment of bimolecular collisions, proposed by Lee and Scully on a partly intuitive basis [J. Chem. Phys. 73, 2238 (1980)], is derived here from first principles. The derivation combines E. J. Hellers ideas [J. Chem. Phys.
62, 1544 (1975); 65, 1289 (1976); 75, 186 (1981)], the backward picture of molecular collisions [L. Bonnet, J. Chem. Phys. 133, 174108 (2010)] and the microreversibility principle.
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 h
aving 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 Guos 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.
Elementary gas-phase reactions of the bimolecular type A + B -> Products are characterized by the second order kinetic law -d[A]/dt=k[A][B], where [A] and [B] are the concentrations of A and B species, t is time and k is the rate constant, usually es
timated by means of Eyring equation. Here, we show that its standard derivation, as such, is not consistent with the second order law. This contradiction is however removed by introducing a correlation between what we call potentially reactive pairs. A new derivation of Eyring equation is finally proposed on the basis of the previous findings.
The transformation from angle-action variables to Cartesian coordinates is a crucial step of the (semi) classical description of bimolecular collisions and photo-fragmentations. The basic reason is that dynamical conditions corresponding to experimen
ts are ideally generated in angle-action variables whereas the classical equations of motion are ideally solved in Cartesian coordinates by standard numerical approaches. To our knowledge, the previous transformation is available in the literature only for triatomic systems. The goal of the present work is to derive it for polyatomic ones.
