Where is the transition state

The classical picture, where following the transition state the two oxygen atoms are channelled downwards to the nearest available metal atoms, is... 

A common approach for the study of activated barrier crossing reactions is the transition state theory (TST), in which the transfer rate over the activation barrier V is given by (0)R/2jt)e where 0)r (the oscillation frequency of the reaction coordinate at the reactant well) is an attempt frequency to overcome the activation barrier. For reactions in solution a multi-dimensional version of TST is used, in which the transfer rate is given by... 

The second explanation for the solvent isotope effect arises from the dynamic medium effect . At 25 °C the rotational and translational diffusion of DjO molecules in D20 is some 20% slower than H20 molecules in H20 (Albery, 1975a) the viscosity of D20 is also 20% greater than H20. Hence any reaction which is diffusion controlled will be 20% slower in D20 than in H20. This effect would certainly apply to transition state D in Fig. 3 where in the transition state the leaving group is diffusing away. A similar effect may also apply to the classical SN1 and SN2 transition states, if the rotational diffusion of water molecules to form the solvation shell is part of the motion along the reaction co-ordinate in the transition state. Robertson (Laughton and Robertson, 1959 Heppolette and Robertson, 1961) has indeed correlated solvent isotope effects for both SN1 and SN2 reactions with the relative fluidities of H20 and D20. However, while the correlation shows that this is a possible explanation, it may also be that the temperature variation of the solvent isotope effect and of the relative fluidities just happen to be very similar (see below). 

Returning to the problem of aromatic substitution, we see that this is an example of the special case where R, S are odd AH s. Here R is the transition state, an odd AH, while 5 is methyl methyl can be regarded as the limiting case of an odd AH whose NBMO is a single carbon 2p AO. This of course has the same energy (zero on our scale) as a NBMO the corresponding "coefficient bM will be unity. If the NBMO coefficients of atoms r, s in the transition state are a , a0, respectively,... 

Fig. 8 shows the changes in the total occupation numbers of the CH and HH bond structures along the IRC. The crossing point is located after TS, 0.42 bohr(amu)1/2. The structure at this point is given in Fig. 9. Compared to the TS, the longer and shorter CH bonds have stretched by 0.14 and 0.06 A, respectively, and the HH bond has become shorter by 0.18 A. These bond lengths are 1.03, 1.62, and 1.80 times longer than the corresponding equilibrium CH and HH bond distances. That point is the structure where the bonds switch in other words, the point is the transition state of chemical bond between the CH bonds and HH bond.

The loose transition state is the transition state considered by phase space theory [164], where the transition state is described in terms of the vibrations and rotations of the products. Treatment of the loose transition state by QET demands that angular momentum be given proper consideration. It is in the case of the loose transition state that phase space theory and QET (with full consideration of the restrictions imposed... 

The cylinder leading to the transition state is very obvious in this figure. There are several points to observe first, at the bottom of the figure, where the r2 arc length is 0, is the transition state. All trajectories at the transition state lie within the boundary of the perimeter family at this point. Second, as the trajectories leave the transition state, they remain clustered as they were at the transition state, sweeping out a cylinder in the phase space. Third, the cylinder moves as it evolves, following a somewhat twisted path in the phase space, predictable from the path of the central trajectory. Viewed in terms of (r, p,), the trajectories of the perimeter family oscillate around the outside of the cylinder. As r2 propagates, the trajectories then wind around the outside of the cylinder. 

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