Transition free energy difference

For analysing equilibrium solvent effects on reaction rates it is connnon to use the thennodynamic fomuilation of TST and to relate observed solvent-mduced changes in the rate coefficient to variations in Gibbs free-energy differences between solvated reactant and transition states with respect to some reference state. Starting from the simple one-dimensional expression for the TST rate coefficient of a unimolecular reaction a— r... 

The different phase behaviors are evidenced in the corresponding free energy diagrams, which have been estimated for both polymers [15]. These diagrams are shown in Fig. 10 (due to the different approximations used in the calculation of the free energy differences, these diagrams are only semiquantitative [15]). It can be seen that the monotropic transition of the crystal in... 

Reaction temperature is one of the parameters affecting the enantioselectivity of a reaction [16]. For the oxidation of an alcohol, the values of kcat/fQn were determined for the (R)- and (S)-stereodefining enantiomers E is the ratio between them. From the transition state theory, the free energy difference at the transition state between (R) and (S) enantiomers can be calculated from E (Equation 2), and AAG is in turn the function of temperature (Equation 3). The racemic temperature (% ) can be calculated as shown in (Equation 4). Using these equations, % for 2-butanol and 2-pentanol of the Thermoanaerobacter ethanolicus alcohol dehydrogenase were determined to be 26 and 77 °C, respectively. 

Since the transition state formulation of a reaction rate expression treats the activated complex as being in equilibrium with the reactants, the resultant expression for the reaction rate constant depends similarly on the free energy difference between reactants and the activated complex. In this case equation 4.3.34 can be rewritten as... 

This equation means that when there is a free energy difference of a few fcs T the probability P( ) is reduced considerably, that is, those conformations with large A( ) are sampled very rarely. This is a very important observation in terms of numerical efficiency. At the transition region for example, the free energy is maximum and typically very few sample points are obtained during the course of molecular dynamics simulation. In turn this results in very large statistical errors. Those errors can only be reduced by increasing the simulation time, sometimes beyond what is practically feasible. 

Fig. 24 For systems near equilibrium the rate-limiting free energy difference may be from an intermediate in cycle 1 to a transition state in cycle 2.

As a matter of fact, we are rather interested in free energy differences between dividing surfaces. Then, if S and SR stand for the dividing surfaces associated to the transition state and the reactants, respectively, taking into account that Q, is not dependent of the dividing surface, the free energy barrier (AF ) is written as... 

Therefore any flexible acetal will undergo conformational changes to permit 2p(0) <-> 2p(C+) stabilizing interaction to intervene in the transition state of its heterolysis. This is also true for pyranosides for which the free energy difference between chair, boat and sofa conformers rarely surpasses 10 kcal/mol. 

Application of the Kurz approach to CD-mediated reactions, whether they be accelerated or retarded, is straightforward (Tee, 1989), provided appropriate kinetic data are available. From the rate constants A u for the normal, uncatalysed reaction (2) and for the mediated ( catalysed ) reaction (k2 = kJKs) as in (3), application of simple transition state theory, in the manner shown above, leads to (9), where now Krs is the apparent dissociation constant of the transition state of the CD-mediated reaction (symbolized here as TS CD) into the transition state of the normal reaction (TS) and the CD. This constant and its logarithm, which is proportional to a free energy difference, is a valuable probe of the kinetic effects of CDs on reactions. 

Fig. 2 Relative Gibbs energies for the species involved in a reaction which is uncatalysed (S —> TS — P) and mediated by a catalyst (S + cat — TS cat — P). For a specified [cat] the free energy differences can be directly calculated from the measurable constants ku, kc and K, and the derived values k2 and Krs, as indicated. pKrs = -logKrs is a measure of the stabilization of the transition state by the...

It should come as no surprise that a chapter dealing with asymmetric catalysis should mention resolutions. Resolutions depend primarily on the solubility differences of disastereomers in the ground state. X-Ray analyses of diastereomeric salts (4,3) appear to point to a best-fit structure for the least soluble salt. Success in asymmetric catalysis depends on free-energy differences between disastereomeric transition states. When these energy differences approach 2 kcal/ mol, resulting in an e.e. of 93% at 23°C, the favored complex, although the result of a termolecular reaction, shows the best-fit characteristics typical of a diastereomeric salt. 

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