The effect of the large impact parameter near-elastic peak of collisional energy transfer for unimolecular dissociation/bimolecular recombination reactions is studied. To this end, the conventional single exponential model, a biexponential model that fits the literature classical trajectory data better, a model with a singularity at zero energy transfer, and the most realistic model, a model with a near-singularity, are fitted to the trajectory data in the literature. The typical effect of the energy transfer on the recombination rate constant is maximal at low pressures and this region is the one studied here. The distribution function for the limiting dissociation rate constant k 0 at low pressures is shown to obey a Wiener-Hopf integral equation and is solved analytically for the first two models and perturbatively for the other two. For the single exponential model, this method yields the trial solution of Troe. The results are applied to the dissociation of O 3 in the presence of argon, for which classical mechanical trajectory data are available. The k 0 's for various models are calculated and compared, the value for the near-singularity model being about ten times larger than that for the first two models. This trend reflects the contribution to the cross section from collisions with larger impact parameter. In the present study of the near-singularity model, it is found that k 0 is not sensitive to reasonable values for the lower bound. Energy transfer values ͗⌬E͘'s are also calculated and compared and can be similarly understood. However, unlike the k 0 values, they are sensitive to the lower bound, and so any comparison of a classical trajectory analysis for ͗⌬E͘'s with the kinetic experimental data needs particular care.

The power law quantum dot blinking, dependence of the exponential tail and the power on light intensity is explained.

A general maximum likelihood estimation (MLE) method is given to analyze experimental data with a power law form with any power exponent which does not break down for a power close to −1. It contrasts thereby with a standard procedure that does. It can be extended to a power law with an exponential tail and more generally to other distribution forms. Inasmuch as the theoretical value of the power for dye-sensitized charge recombination in semiconductors systems, and for certain charge injection, is −1 (Chen, W.; Marcus, R. A., J. Phys. Chem. C, accepted), the present correction to the current MLE method has immediate application to the data in these systems, but it is equally applicable to other systems, regardless of whether the power is −1.