Linear free-energy approaches

In the linear free-energy approach developed by Hansch and his associates biological activity is treated as a free-energy related property. The model equation used in this approach may be generalized by the relation... 

In the first linear free energy approach (Model 2a. 1), the energy of the electron(s) transferred on anion adsorption is the only potential dependent term in the adsorption free energy. This approach assumes that the electric field caused by the applied potential (or excess surface charge) has no interaction with the adsorbate or influence on the adsorbate-metal interaction. Two methods to approximate the impact of the electric field effect on elementary surface processes that do not require explicitly charging the metal surface (Models 2a.2 and 2a.3) will be discussed. The dependence of a species energy within an electric field F) is... 

Applying the vacuum model linear free energy approach (Model 2a. 1) via eqn (3.44), we have... 

Hammett [7] was the first to develop an approach that was later subsumed under Linear Free Energy Relationships (LFER). He showed that the addity constants of a... 

Two approaches to quantify/fQ, i.e., to establish a quantitative relationship between the structural features of a compoimd and its properties, are described in this section quantitative structure-property relationships (QSPR) and linear free energy relationships (LFER) cf. Section 3.4.2.2). The LFER approach is important for historical reasons because it contributed the first attempt to predict the property of a compound from an analysis of its structure. LFERs can be established only for congeneric series of compounds, i.e., sets of compounds that share the same skeleton and only have variations in the substituents attached to this skeleton. As examples of a QSPR approach, currently available methods for the prediction of the octanol/water partition coefficient, log P, and of aqueous solubility, log S, of organic compoimds are described in Section 10.1.4 and Section 10.15, respectively. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

Brown developed the selectivity relationship before the introduction of aromatic reactivities following the Hammett model. The former, less direct approach to linear free-energy relationships was necessary because of lack of data at the time. 

Another method for studying solvent effects is the extrathermodynamic approach that we described in Chapter 7 for the study of structure-reactivity relationships. For example, we might seek a correlation between og(,kA/l ) for a reaction A carried out in a series of solvents and log(/ R/A R) for a reference or model reaction carried out in the same series of solvents. A linear plot of og(k/iJk ) against log(/ R/ linear free energy relationship (LFER). Such plots have in fact been made. As with structure-reactivity relationships, these solvent-reactivity relationships can be useful to us, but they have limitations. 

The second aspect is more fundamental. It is related to the very nature of chemistry (quantum chemistry is physics). Chemistry deals with fuzzy objects, like solvent or substituent effects, that are of paramount importance in tautomerism. These effects can be modeled using LFER (Linear Free Energy Relationships), like the famous Hammett and Taft equations, with considerable success. Quantum calculations apply to individual molecules and perturbations remain relatively difficult to consider (an exception is general solvation using an Onsager-type approach). However, preliminary attempts have been made to treat families of compounds in a variational way [81AQ(C)105]. 

Many researchers have applied similar approaches to develop or apply linear free energy relationships, when the substituent is directly attached to the double bond, with some success. Two of the more notable examples can be found in the Patterns of Reactivity Scheme (Section 7.3.4) and the works of Giese and coworkers.16 19... 

Transition state theory is presented with an emphasis on solution reactions and the Marcus approach. Indeed, to allow for this, I have largely eliminated the small amount of material on gas-phase reactions that appeared in the First Edition. Several treatments have been expanded, including linear free-energy relations, NMR line broadening, and pulse radiolytic and flash photolytic methods for picosecond and femtosecond transients. 

The application of the overpotential t] can be considered to be equivalent to the displacement of the potential energy curves by the amount 7]F with respect to each other. The high field is now applied across the double layer between the electrode and the ions at the plane of closest approach. It is apparent from Fig. 12 that the energy of activation in the favoured direction will be diminished by etrjF while that in the reverse direction will be increased by (1 — ac)r]F where the simplest interpretation of a is in terms of the slopes of the potential energy curves (a = mi/ mi+m )) at the points of intersection electrode processes indeed are the classical example of linear free energy relations. 

The necessity of the statistical approach has to be stressed once more. Any statement in this topic has a definitely statistical character and is valid only with a certain probability and in certain range of validity, limited as to the structural conditions and as to the temperature region. In fact, all chemical conceptions can break dovra when the temperature is changed too much. The isokinetic relationship, when significantly proved, can help in defining the term reaction series it can be considered a necessary but not sufficient condition of a common reaction mechanism and in any case is a necessary presumption for any linear free energy relationship. Hence, it does not at all detract from kinetic measurements at different temperatures on the contrary, it gives them still more importance. 

It should be emphasized that the above equations, which relate reaction temperatures to calculated reactant or product energies, are equivalent to the more conventional linear free energy relationships, which relate logarithms of rate constants to calculated energies. It was felt that reactant temperatures would be more convenient to potential users of the present approach -those seeking possible new free radical initiators for polymerizations. 

CPU time. In response to these slow and rigorous calculations, many fast heuristic approaches have been developed that are based on intuitive concepts such as docking [10], matching pharmacophores [19], or linear free energy relationships [20], A disadvantage of many simple heuristic approaches is their susceptibility to generalization error [17], where accuracy of the predictions is limited to the training data. 

Platts, J. A., Abraham, M. H., Butina, D., Hersey, A. Estimation of molecular linear free energy relationship descriptors by group contribution approach. 2. Prediction of partition coefficient. J. Chem. Inf. Comput. Sci. 2000, 40, 71-80. 

A quite different and complimentary approach is to assume that addition of a nucleophile to an acyl derivative (RCOX) would follow the linear free energy relationship for addition of the nucleophile to the corresponding ketone (RCOR, or aldehyde if R=H) if conjugation between X and the carbonyl could be turned off, while leaving its polar effects unchanged. This can be done if one knows or can estimate the barrier to rotation about the CO-X bond, because the transition state for this rotation is expected to be in a conformation with X rotated by 90° relative to RCO. In this conformation X is no longer conjugated, so one can treat it as a pure polar substituent. Various values determined by this approach are included in the tables in this chapter. 

Having said all that, it is equally important to remember that the number and variety of useful correlations to which Hammett plots have given rise is quite astonishing, particularly when we consider the simplicity and convenience of the approach. Indeed, linear free energy relationships in general constitute a testament to the theoretical utility of concepts that are purely empirical in their genesis ... 

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