Transition state, symmetric energy dependence

The correlation between bulky substituents and stereoselectivity is graphically shown in Figure 3, depicting the possible transition states in the dihydroxylation of a monosubstituted olefin by osmium tetroxide derivatives. This reaction is known to be selective [54], and the selectivity depends on whether the olefin substituent takes a position of type A or B in the transition state. The problem with calculations on a model system where the bulky base is replaced by NH3 is that the positions A and B are completely symmetrical, and thus, they yield the same energy. In other words, the reaction would not be selective with this model system. 

Neither of these vibrations corresponds to stretching vibrations of AH or BH. The antisymmetric vibrational mode represents translational motion in the transition state and has an imaginary force constant. The symmetric transition-state vibration has a real force constant but the vibration may or may not involve motion of the central H(D) atom2,12 13. If the motion is truly symmetric, the central atom will be motionless in the vibration and the frequency of the vibration will not depend on the mass of this atom, i.e. the vibrational frequency will be the same for both isotopically substituted transition states. It is apparent that under such circumstances there will be no zero-point energy difference... 

In instances where bond breaking and bond making at the transition state are not equal, bond breaking is either more or less advanced than bond formation, and the symmetric vibration will not be truly symmetric. In these cases, the frequency will have some dependence on the mass of the central atom, there will be a zero-point energy difference for the vibrations of the isotopically substituted molecules at the transition state and will have values smaller than seven. 

The expected changes in the zero-point energies of the H transferred are illustrated schematically in Fig. 6.6 for the degenerate case, as proposed by Westhei-mer [45]. The antisymmetric stretch in the initial state exhibits quite different ZPEs for H and for D as the force constants are large. This vibration becomes imaginary in the transition state, which is assumed here to be located in the minimum of q2, i.e. the ZPE of the antisymmetric stretch is lost in the transition state. The ZPE of the symmetric stretch in the transition state is small and exhibits little isotope dependence. We note that ZPE is built up in the bending vibration in the... 

Note that in the region of the observed structures the activation energy shows a sharp decrease (> 50%) associated with only a relatively modest shift in molecular structure towards the transition state. The fourth-order dependence between structure and energy follows if the symmetric, double-well reaction profiles for the molecules involved are assumed to have the following simple algebraic form... 

That such reaction path dependent density enhancements can have a significant effect on free energy of activation barriers in compressible SCFs is shown in Fig. 7. There we present the reaction-path-dependent free energy of solvation (zeroed to the reactant value) for the symmetric Cl + CH3CI S 2 exchange reaction in supercritical water at 1.0 and pr 0.5 as a function of the reaction coordinate (defined as the difference between the two Cl-C bond lengths) rc = 0 denotes the transition state, while = 8.0X is taken as the reactant (product). The squares represent the free energies of solvation computed from a standard incompressible continuum model. 

The table illustrates many of the points considered qualitatively above. There is a maximum isotope effect for a symmetrical transition state and the expected dependence of the force constants and vibration frequencies on activation energy and energy of reaction is found. Negative bond force constants have not been considered previously but they reflect encroachment of the energy barrier into the reactant or product valleys of the potential surface where the reaction path is nearly parallel to one of the bond axes cf. Figure 5). For a crude comparison with experiment, if it is assumed that A = AG the most exothermic reaction with AE = 33 kcal mol corresponds to aApK of 24. 

Since two enantiomeric substrates or products are physically equal in a symmetrical environment, their different reaction rates in a kinetic resolution process depend only on the free energy difference between their respective diastereomeric transition states during interaction with the chiral resolving agent. Under thermodynamic control, both enantiomers... 

---