Temperature dependence microcanonical states

The most sophisticated and computationally demanding of the variational models is microcanonical VTST. In this approach one allows the optimum location of the transition state to be energy dependent. So for each k(E) one finds the position of the transition state that makes dk(E)/dq = 0. Then one Boltzmann weights each of these microcanonical rate constants and sums the result to find fc ni- There is general agreement that this is the most reliable of the statistical kinetic models, but it is also the one that is most computationally intensive. It is most frequently necessary for calculations on reactions with small barriers occurring at very high temperatures, for example, in combustion reactions. 

The radial dependence of the microcanonical number of states for the H CeH CeH reaction over a range of energies is illustrated in Fig. 4.12. At the lowest energy plotted, 0.2 kcal/mol, an inner transition state, at R sA, and an outer transition state, at R 8 A, are clearly visible. At E = 0.2 kcal/mol these bottlenecks are essentially identical, while the inner bottleneck becomes dominant (i.e., has the smaller number of states) as the energy increases. For this reaction, the inner transition state would clearly play a significant role in the low temperature kinetics. 

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