Partition function atomic reaction systems

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]. 

We have seen how statistical thermodynamics can be applied to systems composed of particles that are more than just a single atom. By applying the partition function concept to electronic, nuclear, vibrational, and rotational energy levels, we were able to determine expressions for the thermodynamic properties of molecules in the gas phase. We were also able to see how statistical thermodynamics applies to chemical reactions, and we found that the concept of an equilibrium constant presents itself in a natural way. Finally, we saw how some statistical thermodynamics is applied to solid systems. Two similar applications of statistical thermodynamics to crystals were presented. Of the two, Einstein s might be easier to follow and introduced some new concepts (like the law of corresponding states), but Debye s agrees better with experimental data. 

Using eq. (6.13), together with eqs. (6.20), (6.21), (6.25) or (6.26), and knowing the ZPE difference between the transition state and the reactants, it is now possible to calculate absolute reaction rates, hi practice, TST can only be applied if the structure of the transition state and its vibrational levels are also known, because the former is required for the calculation of the rotational partition function of the transition state, and the latter enter the transition-state vibrational partition function. These data and AEP can be obtained from ab initio calculations or experimental information employed in the making of potential energy surfaces (PESs). The rapid development of computers and software has made it possible to carry out accurate ab initio calculations of transition-state properties for many tii-atomic and some tetra-atomic systems in the gas phase. The best-known system is the atom exchange in the H + system, and the properties of its linear transition state are shown in Table 6.1. 

One of the advantages of classical mechanics is that it allows one to calculate any property of interest, since quantum mechanical constraints are absent classically one may know everything about a system. One can examine, in as much detail as one wishes, the behavior of the system at the atomic level. It is possible to calculate reaction rates, lifetimes of excited molecules, rates and probabilities of energy transfer, scattering distributions, the partitioning of energy among reaction products, the behavior of all the atoms as a function of time, and, in fact, any other classical property of a system. 

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