Reaction Hamiltonian approach

Fehrensen B, Luckhaus D and Quack M 1999 Inversion tunneling in aniline from high resolution infrared spectroscopy and an adiabatic reaction path Hamiltonian approach Z. Phys. Chem., NF 209 1-19... 

The effect of the solvent on our reaction Hamiltonian is obtained by using the approach formulated in eq. (2.21), writing... 

In the quantum mechanical continuum model, the solute is embedded in a cavity while the solvent, treated as a continuous medium having the same dielectric constant as the bulk liquid, is incorporated in the solute Hamiltonian as a perturbation. In this reaction field approach, which has its origin in Onsager s work, the bulk medium is polarized by the solute molecules and subsequently back-polarizes the solute, etc. The continuum approach has been criticized for its neglect of the molecular structure of the solvent. Also, the higher-order moments of the charge distribution, which in general are not included in the calculations, may have important effects on the results. Another important limitation of the early implementations of this method was the lack of a realistic representation of the cavity form and size in relation to the shape of the solute. 

In an effort to understand the intramolecular dynamics in unimolecular dissociation. Remade and Levine [87] used an effective Hamiltonian approach that can account for different time scales associated with unimolecular reaction. In doing so, they assumed that a dense set of energy levels lies above the dissociation barrier and that the barrier is sufficiently high that the number of states from which dissociation occurs is small compared to the number of bound states. 

The effective Hamiltonian approach clearly shows the important role of intramolecular energy flow in the quantum dynamics of unimolecular dissociation. It suggests that unless intramolecular energy flow is dominantly rapid, there exist two drastically different time scales in the reaction dynamics. This is consistent with the classical concept that nonstatistical behavior in intramolecular energy flow, such as bottleneck effects, can dramatically alter the kinetics of unimolecular reaction. 

Flexible RRKM theory and the reaction path Hamiltonian approach take two quite different perspectives in their evaluation of the transition state partition functions. In flexible RRKM theory the reaction coordinate is implicitly assumed to be that which is appropriate at infinite separation and one effectively considers perturbations from the energies of the separated fragments. In contrast, the reaction path Hamiltonian approach considers a perspective that is appropriate for the molecular complex. Furthermore, the reaction path Hamiltonian approach with normal mode vibrations emphasizes the local area of the potential along the minimum energy path, whereas flexible RRKM theory requires a global potential for the transitional modes. One might well imagine that each of these perspectives is more or less appropriate under various conditions. 

First, we would like to mention the reaction path Hamiltonian approach (RPH) proposed by Miller et al. (1980). In this approach the information enclosed in the RP is supplemented by some information about the shape of the PES on the 3N - 7 coordinates which are perpendicular to each point of 5, and are described in the harmonic approximation. The PES thus assumes the form ... 

During the past few years we have observed an intensive development of many-channel approaches to the collision problem. In particular, the coupled-channels method is based on an expansion of the total wave fmiction in internal states of reactants and products and a numerical solution of the coupled-channels equations.This method was applied in the usual way to the atom-diatom reaction A + BC by MOR-TENSBN and GUCWA /86/, MILLER /102/, WOLKEN and KARPLUS /103/, and EL-KOWITZ and WYATT /101b/. Operator techniques based on the Lippmann-Schwinger equation (46.II) or on the transition operator (38 II) has also been used, for instance, by BAER and KIJORI /104/ The effective Hamiltonian approach( opacity and optical-potential models) and the statistical approach (phase space models, transition state models, information theory) provide other relatively simple ways for a solution of the collision problem in the framework of the many-channel method /89/<. 

For the Li + HF reaction Dunning, Kraka Fades (7) showed that the features of the reaction valley can be readily understood in terms of the changes in the electronic structure of the system as it evolves during the reaction. For the OH + H2 reaction they showed that the terms in the reaction path Hamiltonian provide a rationale for many of the qualitative features of reaction dynamics, including such fine effects as the deposition of reactant vibrational excitation into product vibrational modes. The reaction valley approach thus provides a direct connection between the electronic structure of the system, the potential energy surface and the reaction dynamics. 

With respect to a more quantitative characterization of the PE function along the reaction coordinate, in terms of local minima and barriers between them, the minimum energy reaction (MER) path concept is more promising. The MER path approach, also called the intrinsic reaction path approach [39], is defined as the steepest descent path from the transition state (a saddle point on the PE surface) down to the local minima that are equilibrium geometries of reactant and product. It has been shown [40] how to express the Hamiltonian of an N atom molecular system in terms of the reaction coordinate, and this approach has been used successfully to describe a variety of processes in polyatomic reaction dynamics. It is also well known that for many reactions (PT process among them) the MER path is very sharply curved, so that the relevant dynamical motion deviates far from it. This is not a particularly important point for our present purpose of a qualitative characterization of the PE surfaces relevant for the PT reaction, as far as we do not consider the dynamics of... 

A different formulation of the rotation coordinate, the reaction-path approach, eludes the uniqueness problem by treating internal rotation as a reaction leading from one rotamer to another - encompassing all relevant minima and transition states. Coupling between the rotation and the remaining degrees of freedom is included by the reaction-path Hamiltonian in terms of a unique rotation coordinate.Although continuous torsional potentials in terms of the rotation variable are produced, even this approach is not free of difficulties, since the potential is not always well defined. ... 

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