Reaction path Hamiltonian applications

B. C. Garrett and D. G. Truhlar, WKB approximation for the reaction-path Hamiltonian Application to variational transition state theory, vibrationally adiabatic excited-state barrier heights, and resonance calculations,/. Chem. Phys. 81 309 (1984). 

S. Lee and J. T. Hynes,/. Chem. Phys., 88,6863 (1988). Solution Reaction Path Hamiltonian for Reactions in Polar Solvents. II. Applications. 

Application of the Reaction Path Hamiltonian Method to the Reaction H2 + OH —> H2O + H Acceptor-Donor (AD) Theory of Chemical Reactims (O 4)... 

Once a Hamiltonian is constructed in terms of these coordinates and their conjugate momenta—the reaction path Hamiltonian —one needs dynamical theories to describe the reaction dynamics. Section II first discusses the form of the reaction path Hamiltonian, and then Section III describes the variety of dynamical models that have been based on it. These range from the simplest, statistical models (i.e., transition state theory) all the way to rigorous path integral methods that are essentially exact. Various applications are discussed to illustrate the variety of dynamical treatments. 

Other aspects of the reaction path Hamiltonian and its application have been discussed in earlier papers to which the reader... 

I have attempted in this paper to illustrate the wide variety of dynamical treatments that can be usefully based on the reaction path Hamiltonian model, from simple "back of the envelope" statistical approximations (TST, RRKM, etc.) all the way to rigorous computational methods that can be practically applied to polyatomic systems. Given the necessary "input" which characterizes the model — i.e., the quantum chemistry calculations of the reaction path, and the energy and force constant matrix along it — the example applications that have been discussed show that it provides a quantitative ab initio approach to reaction dynamics in polyatomic molecular systems. 

Application of the reaction path Hamiltonian method to the reaction H2 + 0H H2O + H... 

REACTION PATH HAMILTONIAN FOR POLYATOMIC SYSTEMS FURTHER DEVELOPMENTS AND APPLICATIONS... 

This paper describes some new developments and applications based on the reaction path model. In section II the original form of the reaction path Hamiltonian [of. equation (1) below] is transformed to a new representation that has a more desirable structure for some applications. Section III shows how the reaction path model makes application of the unified statistical model for chemical reactions especially simple, and a generalized version of the unified statistical model is also developed there. Finally, in section IV the fact that the reaction path model consists of one special degree of freedom — i.e., the reaction coordinate — coupled to a number of harmonic oscillators is exploited to derive a generalized Langevin equation (GLE) for motion along the reaction path. This is a reduced equation of motion for only the reaction coordinate, but it experiences friction" and a "random force" because of coupling to the transverse vibrational modes. 

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