Free energy thermodynamic coupling

It also follows that, when three (or more) oxidation states lie approximately on a straight line in the volt-equivalent diagram, they tend to form an equilibrium mixture rather than a reaction going to completion (provided that the attainment of thermodynamic equilibrium is not hindered kinetically). This is because the slopes joining the several points are almost the same, so that E° for the various couples (and hence AG°) are the same there is consequently approximately zero change in free energy and a balanced... 

In this chapter the basic theory of the structurally coupled QM/MM is summarized. This is followed by some technical points important in the practical use of the method. In particular, details about the treatment of the QM/MM boundary are discussed. The thermodynamically coupled quantum mechanical/ free energy (QM/FE) method is then introduced. Some representative applications of QM/MM methods are then described. The examples are selected to provide a representative picture of the potential applications of QM/MM methods on studies of reaction mechanisms. Here there is special emphasis on recent advances in the computational methodologies and in the future developments needed to improve the applicability of the methods. 

To conclude, a related thermodynamic treatment has been extended to the calculation of the enthalpic variation for redox couples, AH°C = H°ed - if°x. Such a treatment is useful to understand how enthalpic or entropic factors may influence the magnitude and sign of the free energy, or the electrode potential, of a redox change.20 In fact, one must consider that ... 

If kepi, k-epi are much larger than the rates k, ki of substitution, the enantiomeric ratio Hepi-1 is similar to kxjk (path C, dynamic kinetic resolution . Both mechanisms are performing when the rates of the two steps are similar. Since rates and equilibrium are temperature-dependent, enhancement of stereoselectivities can be achieved by sophisticated protocols (see Section m.E). The equilibrium 6/epi-6 is determined by the difference of free energy A AG. This effective energy difference is enlarged if it can be coupled with a second order transformation such as the selective crystallization of one diastere-omer dynamic thermodynamic resolution ). In fact, this applies to the first successful (—)-sparteine-mediated deprotonation (Section FV.C.l). 

---