Microcanonical ensemble, potential energy surfaces

The basic assumption in statistical theories is that the initially prepared state, in an indirect (true or apparent) unimolecular reaction A (E) —> products, prior to reaction has relaxed (via IVR) such that any distribution of the energy E over the internal degrees of freedom occurs with the same probability. This is illustrated in Fig. 7.3.1, where we have shown a constant energy surface in the phase space of a molecule. Note that the assumption is equivalent to the basic equal a priori probabilities postulate of statistical mechanics, for a microcanonical ensemble where every state within a narrow energy range is populated with the same probability. This uniform population of states describes the system regardless of where it is on the potential energy surface associated with the reaction. 

Chemical dynamics simulations were performed to study the unimolecular decomposition of microcanonical ensembles versus energy of the Cl — CH Br ion lipole complex.An analytic potential energy surface was used for the simulations. The complex has two unimolecular reaction paths, i.e. dissociation to C/ + CHjBr or isomerization to the CICH —Br ion iipole complex. The simulations were performed for energies of 30-80 kcal mol and the resulting non-exponential N t)IN 0) were lit by a sum of three exponentials, i.e. eqn (20.18). The resulting// and ki fitting parameters are listed in Table 20.2. 

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