On collisional energy transfer in recombination and dissociation reactions: A Wiener–Hopf problem and the effect of a near elastic peak

Zhu, Zhaoyan; Marcus, R. A.

doi:doi:10.1063/1.3026605

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Localized orbital corrections applied to thermochemical errors in density functional theory: The role of basis set and application to molecular reactions

This paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [ R. A. Friesner et al., J. Chem. Phys. 125, 124107 (2006) ; E. H. Knoll and R. A. Friesner, J. Phys. Chem. B 110, 18787 (2006) .] This methodology allows one to redress systematic density functional theory (DFT) errors, rooted in DFT’s inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3L...

Molecular dynamics with time dependent quantum Monte Carlo

In this paper we propose an ab initio method to solve quantum many-body problems of molecular dynamics where both electronic and nuclear degrees are represented by ensembles of trajectories and guiding waves in physical space. Both electrons and nuclei can be treated quantum mechanically where the guiding waves obey a set of coupled Schrödinger equations (quantum-quantum description) or, alternatively, coupled Schrödinger–Newtonian equations are solved for the quantum-classical approximation. T...

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 k₀ 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 O₃ in the presence of argon, for which classical mechanical trajectory data are available. The k₀’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 k₀ is not sensitive to reasonable values for the lower bound. Energy transfer values 〈ΔE〉’s are also calculated and compared and can be similarly understood. However, unlike the k₀ values, they are sensitive to the lower bound, and so any comparison of a classical trajectory analysis for 〈ΔE〉’s with the kinetic experimental data needs particular care.

Article Outline

INTRODUCTION
THEORY
1. General aspects
2. Single exponential model
3. Biexponential model
4. Singularity model
5. Near-singularity model
APPLICATION TO Ar+O₃
1. Comparison of single exponential and biexponential models
2. Comparison of single exponential and singularity models
3. Comparison of single exponential and near-singularity models
DISCUSSION
CONCLUDING REMARKS

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KEYWORDS and PACS

Keywords

association, dissociation, ozone, reaction kinetics theory, reaction rate constants

PACS

82.30.Lp

Decomposition reactions (pyrolysis, dissociation, and fragmentation)
82.30.Fi

Ion-molecule, ion-ion, and charge-transfer reactions
82.20.Nk

Classical theories of reactions and/or energy transfer
82.20.Pm

Rate constants, reaction cross sections, and activation energies
82.30.Nr

Association, addition, insertion, cluster formation

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http://link.aip.org/link/doi/10.1063/1.3026605

PUBLICATION DATA

ISSN:

0021-9606 (print)

1089-7690 (online)

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American Institute of Physics

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