Reaction degeneracy

The symmetry number approach for evaluating the reaction degeneracy is based on the obvious requirement that the ratio of the reaction degeneracies for the forward and backward reactions must lead to the correct equilibrium constant. Consider first the equilibrium A B. The canonical equilibrium constant at some temperature, T, is given by... 

It follows that the symmetry factor for the equilibrium reaction, A fi, is given by the ratio of the forward and backward reaction degeneracy as crjub, which is correct. We see then that the reaction degeneracy has its roots in the molecular and transition-state symmetry. 

It is interesting to consider the relationship between the reaction degeneracy and the molecular symmetries in canonical transition state theories. In the latter, the rate constants are expressed in terms of the partition functions, including the rotational partition functions, so that the molecular symmetries are automatically included. On the other hand, in the microcanonical TST, the rotational density of states is often not part of the rate constant expression (see discussion of rotational effects in the following chapter). Thus, the reaction degeneracy must be included separately. 

Now consider the reaction of H2 loss from benzene, and suppose that the TS structure involves the loss of adjacent H atoms. If the TS structure is a planar benzene ring with two adjacent H atoms leaving in the benzene plane, the TS symmetry number will be 2. Thus the reaction degeneracy for the reaction... 

The benzene ion also loses the linear C3H3 moiety to form the cyclopropenium ion, C3H3+. The transition state clearly has no symmetry. Hence, the reaction degeneracy for this path is either 12 or 6 depending upon whether the two electronic states mix, or do not mix. 

We are now in a position to derive our first important result for evaporative ensembles of clusters. The logarithm of the RRKM molecular rate constant, k(E) (without the reaction degeneracy) is given by... 

At T < tunneling occurs not only in irreversible chemical reactions, but also in spectroscopic splittings. Tunneling eliminates degeneracy and gives rise to tunneling multiplets, which can be detected with various spectroscopic techniques, from inelastic neutron scattering to optical and microwave spectroscopy. The most illustrative examples of this sort are the inversion of the... 

To calculate AG = Gts - Greactant, we need and AS AHf is directly the difference in elecfi onic energy between the TS and the reactant. Except for complicated reactions involving several electronic states of different degeneracy (e.g. singlet molecules reacting via a triplet T, A5 g, is zero. 

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