Thermal equilibrium transitive character

The triplet dimer diradical DR2(Ti) finally will relax into thermal equilibrium (kT) with its singlet ground state DR2(So). As we have seen from the ESR spectra (see Fig, 10) the energy separation between the singlet and triplet diradical states is very low and thermally activated transitions occur even at low temperatures. Furthermore the ESR spectra have revealed an admixture of about 10% carbene character with the diradical intermediates. This carbene character may be important in determining the probability x of the side reactions (see Eq. (19)) for the DR -+ AC chain termination reaction. It surely is not, however, the only essential factor, otherwise there should be no difference in the optical and thermal termination reaction steps. Up to now a direct observation of the metastable triplet state Ti(M) has been possible only in two specific crystals where the polymerization reactions are very weak. 

The TST, as Eyring s theory is known, is a stadstical-mechanical theory to calculate the rate constants of chemical reactions. As a statistical theory it avoids the dynamics of colUsions. However, ultimately, TST addresses a dynamical problem the proper defmition of a transition state is essentially dynamic, because this state defines a condition of dynamical instability, with the movement on one side of the transition state having a different character from the movement on the other side. The statistical mechanics aspect of the theory comes from the assumption that thermal equilibrium is maintained all along the reaction coordinate. We will see how this assumption can be employed to simplify the dynamics problem. 

This re-derivation of the one-dimensional TST result emphasizes the effective character of the potential used in one-dimensional treatments of barrier crossing problems. The one-dimensional model, Eq. (14.11), will yield the correct TST result provided that the potential V (x) is taken as the effective potential of the reaction coordinate, that is, the potential of mean force along this coordinate where all other degrees of freedom are in thermal equilibrium at any given position of this coordinate." It should be stressed, however, that this choice of the one-dimensional effective potential assumes that such a coordinate can be identified and that a point along this coordinate can be identified as the transition point that separates reactants from products. 

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