Activation free energy definition

Since the Es value is determined by the relative activation free energy from the unsaturated initial state to the saturated tetrahedral intermediate state of the ester hydrolysis, Hancock and his coworkers considered that a hyperconjugation effect of a-hydrogen may contribute to the estimate of Es values 19). To separate the hyperconjugation effect from the true steric effect , they defined the parameter E° (corrected steric) as Eq. 20, assuming that the hyperconjugation effect is proportional to the number of a-hydrogen atoms, nH. By definition, E (Me) = 0. 

Then, by use of the chain rule of partial differentiation on p,g we get (2.460), and thereafter eliminating the partial derivatives therein by (2.461) and (2.462), introducing the activity through (2.468), and eliminating the standard state potential by (2.471) as well as the Gibbs free energy definition ... 

A. Definitions and Interrelations of Activation Free Energy, Activation Heat, and Activation Entropy of Steady Reaction... 

The problem at hand is the evaluation of the activity coefficient defined in Eq. (76). It will be assumed that only pairwise interactions between the defects need be considered at the low defect concentrations we have in mind. (The theory can be extended to include non-pairwise forces.23) Then the cluster function R(n) previously defined in Eq. (78) is the sum of all multiply connected diagrams, in which each bond represents an /-function, which can be drawn among the set of n vertices, the /-function being defined by Eqs. (66), (56), and (43). The Helmholtz free energy of interaction of two defects appearing in this definition can be written as... 

As far as the definition of a as a measure of the symmetry of the activation barrier is concerned, as shown in Figure 15, let us focus on the apical region of the intersection between the free energy curves illustrated in Figure 14. 

The concept of the similarity of molecules has important ramifications for physical, chemical, and biological systems. Grunwald (7) has recently pointed out the constraints of molecular similarity on linear free energy relations and observed that Their accuracy depends upon the quality of the molecular similarity. The use of quantitative structure-activity relationships (2-6) is based on the assumption that similar molecules have similar properties. Herein we present a general and rigorous definition of molecular structural similarity. Previous research in this field has usually been concerned with sequence comparisons of macromolecules, primarily proteins and nucleic acids (7-9). In addition, there have appeared a number of ad hoc definitions of molecular similarity (10-15), many of which are subsumed in the present work. Difficulties associated with attempting to obtain precise numerical indices for qualitative molecular structural concepts have already been extensively discussed in the literature and will not be reviewed here. 

However, the choice of standard states makes no difference in the value of AG for the transfer of solute between two solutions of different concentrations in the same solvent. We can observe this by applying the definition of activity to the equation for the free energy change in a transfer process ... 

It is not possible at present to evaluate this function theoretically. The system is too complicated. The complexity of theoretical calculations can best be explained by considering the definition of AGg and processes involved in the activation process. AGf is defined in Figure 6.1. Free energy of activation for the forward reaction is the free-energy difference between the free energy of the activated state, G, and the free energy of the initial state, G ... 

---