Unimolecular reaction translational

The ratio of translational partition functions (Qjr/Qtr) is 1 here, and for all unimolecular reactions, because the mass and number of molecules of the reactants is the same as for the transition state. The rotational ratio (Q, /Q, ) is given by the ratio of the moments of inertia (/ //t/2/3)1/2- The moments of inertia are probably slightly higher in the... 

For these reactions the 0 K activation enthalpy and the room temperature activation enthalpies and free energies are almost the same, and so are the 0 K reaction enthalpy and the room temperature reaction enthalpies and free energies. This is presumably so because these are unimolecular reactions, in which the relative translational velocities of reacting molecules are not a factor. 

The center-of-mass translational motion can be separated out (as described in Section 1.1) and it plays no role in unimolecular or bimolecular reactions. Thus, the translational energy of the molecule is not included in the internal energy that is relevant to unimolecular reactions. 

For a unimolecular reaction like nitrogen inversion the translational, rotational and vibrational partition functions per degree of freedom may be assumed not to differ greatly in the initial and transition states. Then F /Fj may be reduced to l// where fv is the partition function for one vibrational degree of freedom. In (1 // ) is of the order of — 1 to 0 and should not change much with temperature 2.18). 

With this brief overview of classical theories of unimolecular reaction rate, one might wonder why classical mechanics is so useful in treating molecular systems that are microscopic, and one might question when a classical statistical theory should be replaced by a corresponding quantum theory. These general questions bring up the important issue of quantum-classical correspondence in general and the field of quantum chaos [27-29] (i.e., the quantum dynamics of classically chaotic systems) in particular. For example, is it possible to translate the above classical concepts (e.g., phase space separatrix, NHIM, reactive islands) into quantum mechanics, and if yes, how What is the consequence of... 

This minimally dynamic approach has been applied to both bimolecular and unimolecular reactions a typical result for the latter case is shown in Fig. 6. In this case we consider the dissociation of CCH on two different potential surfaces due to Wolf and Hase.36 These authors classified the first surface (their case IIC) as yielding RRKM dissociation, whereas their surface IIA yielded non-RRKM dynamics. The exact trajectory results for translational, vibrational, and rotational distributions for these two cases are shown as solid histograms in Fig. 6. The minimally dynamic construction, which requires only short-lived trajectory calculations, are shown as dashed histograms in the same figure and are seen to be in excellent agreement with the exact results. 

The differential rate constant for forming products with translational/rotational kinetic energy, E, is given by Eq. (7.57). This rate constant is proportional to the probability P,f( trk- E) of forming products with energy If the products of the unimolecular reaction are an atom and a polyatomic, the probability for vibrational energy, E, in the polyatomic is simply... 

This program calculates densities and sums of ro-vibrational states. It is a translation into BASIC of a program written in APL [Forst, W. (1973). Theory of Unimolecular Reactions. Academic Press, pp. 395-403], The density or sum is calculated simply by changing the variable R as defined below. In order to increase speed, frequencies can be combined by replacing a set of n frequencies by their geometric mean. This is especially useful for the high frequencies which do not contribute much to the density of states. It is best not to combine those frequencies below about 500 cm. All energies are expressed in cm. ... 

Microcanonical TST has found wide application in the case of unimolecular reactions at the limit of high pressure (see below). In this situation, the translational partition functions for the reactants and transition state species are identical, so that eqn (1.14) for the canonical rate constant simplifies to ... 

Evidence for strong non-equilibrium effects has first been obtained in the investigation of unimolecular reactions at low pressures. Here, the transition from first- to second-order kinetics is caused by perturbations of the equilibrium distribution of molecules over energies close to the activation energy (see Section V.17). Furthermore, it stimulated theoretical investigations on similar effects in bimole-cular reactions. However, the study of simple models has shown that non-equilibrium effects are not very marked and corresponding corrections to the equilibrium rate constants (i.e. rate constants calculated under the assumption of the Maxwell-Boltzmann distribution) are of the order of several per cent only [339]. Yet, this conclusion is based on the assumption that the reaction cross section depends solely on the translational energy which readily relaxes. 

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