Partition function, potential energy surfaces rate constants

In this approach properties of potential energy surfaces are investigated from the point of view of all possible monomolecular transformations of the given reactants. A plausible suggestion concerning the mechanism of the reaction under study is usually made on the basis of reaction barriers or activation energies. Moreover, in some studies, partition functions are evaluated and rate constants are obtained within the framework of the absolute rate theory. 

Early in the development of VTST calculations on simple three atom systems compared rates obtained by exact classical dynamics with conventional TST and VTST, the same potential energy surface and classical partition functions being used throughout. These calculations confirmed the importance of eliminating the recrossing phenomenon in VTST. While TST yielded very much larger rate constants than the exact classical calculations, the VTST calculations yielded smaller rate constants, but never smaller than the exact classical values. 

The initial assumption is made — xa. This assumption will be discussed further subsequently. The problems of calculating ratios of rate constants become then a matter of calculation of ratios of isotopic partition functions. The latter is simplified by the fact that the potential energy surfaces for isotopic molecules are the same to a very high degree of approximation. 

This relation indicates that the rate constant can be determined from a knowledge of the partition functions of the activated complex and the reactant species. For stable molecules or atoms the partition functions can be calculated from experimental data that do not require kinetic measurements. However, they do require that molecular constants such as the vibrational frequencies and moments of inertia be evaluated from spectroscopic data. Evaluation of the partition function for the activated complex Gxyz presents a more difficult problem, since the moments of inertia and vibrational frequencies required cannot be determined experimentally. However, theoretical calculations permit one to determine moments of inertia from the various internuclear distances and vibrational frequencies from the curvature of the potential energy surface in directions normal to the reaction coordinate. In practice, one seldom has available a sufficiently accurate potential energy surface for the reaction whose rate constant is to be determined. 

The "adiabatic rate equations (106.Ill) and (124.Ill) both contain two corresponding factors, including the partition functions and the corrections to the activated complex theory. For an exact calculation of the rate constant using either of these equivalent expressions, we also need a complete potential energy surface, the main problem being again the evaluation of the factors and. There-... 

Thus, for a calculation of the rate constant it is necessary to compute, aside from the dynamical factor K, the partition function of reactants only for motion along the reaction coordinate, provided the potential energy surface is known. 

Calculation of the reaction rate constant by the transition-state method requires knowledge of the activation energy Ea and of the activated complex partition function F". The accuracy of the theoretical potential energy surfaces is inadequate for the determination of Ea. The only exceptions are the diatomic molecules for which accurate theoretical potential curves are available and also some three-atom systems, especially H3. Therefore, either semiempirical methods or independent experimental information have to be used to obtain Ea [37, 236]. 

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