Temperature dependence degeneracy factors

Using transition state theory, find the temperature dependence of the pre-exponential factor in the Arrhenius expression for the reaction NO + NO3 —> NO2 + NO2. In other words for A (X Tn, find n. Assume that both NO3 and the activated complex are nonlinear. Furthermore assume that hv << kgT and that the electronic degeneracies are all one. 

Here is the energy of state m, is the degeneracy, or multiplicity, of the state (the number of substates with the same energy), kg is the Boltzmann constant (1.3709 x 10 erg), and Z (the partition function) is a temperature-dependent factor that normalizes the sum of the probabilities over all the states ... 

Finally, we consider the situation at finite temperature. In this case, we will take the temperature-dependent occupation number of the single-particle state k to be k for each spin state. This leads to the assignment of (1 — 2 k) as the Cooper pair occupation number of the same wave-vector. Consequently, each occurrence of a Cooper pair will be accompanied by a factor (1 — 2 k). while the occurrence of an electronic state that is not part of a Cooper pair will be accompanied by a factor 2 k taking into account spin degeneracy. With these considerations, the total energy of the ground state at finite temperature will be given by... 

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