Unified statistical model

Miller W H 1976 Unified statistical model for complex and direct reaction mechanisms J. Chem. Rhys. 65 2216-23... 

A unified statistical model for premixed turbulent combustion and its subsequent application to predict the speed of propagation and the stmcture of plane turbulent combustion waves is available (29—32). 

W. H. Miller For a reaction such as H + O2 — OH + O, or ketene isomerization CC O — OCC H2, which involve a metastable intermediate, one can certainly do better than simple TST by using a model with two transition states and the unified statistical model to approximate the net reactive flux. Such an approach, though often useful, is nevertheless an approximate model that can never be made into a rigorous description. Such a model, for example, cannot describe the resonance tunneling structure in the ketene isomerization that I described. 

B. C. Garrett, D. G. Truhlar, R. S. Grev, A. W. Magnuson, and J. N. L. Connor, Variational transition state theory, vibrationally adiabatic transmission coefficients, and the unified statistical model tested against accurate quantal rate constants for collinear F + H2, H + F2, and isotopic analogs, 7. Chem. Phys. 73 1721 (1980). 

E. PoUak, P. Pechukas, Unified statistical model for "complex" and "direct" reaction mechanisms A test on the collinear H + H2 exchange reaction, J. Chem. Phys. 70 (1) (1979) 325-333. 

K. N. C. Bray and J. B. Moss. A unified statistical model of the premixed turbulent flame. Acta Astronautica, 4 291-319, 1977. 

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. 

The "unified" statistical model was introduced originally in order to reconcile, or unify, two different kinds of statistical theories, transition state theory which is appropriate for reactions proceeding via a direct" reaction mechanism, and the phase space theory of Lightand Nikitin which is designed to describe reactions proceeding via a long-lived collision complex. It is particularly straightforward to apply this theory within the framework of the reaction path Hamiltonian. 

If two minima are found, at sj and say, separated by a relative maximum at S2, then the unified statistical model gives the following approximation to N(E) ... 

The unified statistical model and its generalizations discussed in section III and the generalized Langevin description developed in section IV may find utility as computational techniques and/or conceptual frameworks for understanding various aspects of reaction dynamics in polyatomic systems. 

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