Linear free energy-related approach

Due to the relationship between biological activity and the free energies of binding (or partitioning) also the terms extrathermodynaraic relationships or linear free energy-related approach are used for quantitative structure-activity relationships, especially Hansch analysis. 

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. 

Platts, J. A., Butina, D Abraham, M. H., Hersey, A. Estimation of molecular linear free energy relation descriptors using a group contribution approach. /. Chem. Inf. Comput. Sci. 1999, 39, 835-845. 

These efforts were guided by the study of quantitative structure-activity relationships (QSAR) following the Hansch approach. In this method linear free-energy related and other electronic, hydrophobic, and steric substituent constants are used for a quantitative analysis of the possible ways in which substituents may modulate bioactivity in a congeneric series. In the QSAR studies of benzoylphenyl ureas the electronic Hammett a-constants and the hydro-phobic Hansch n-constants were used. To measure the steric influences, steric substituent constants of a new type (B1,B2,B3,B4, and L) were applied which had recently been introduced by us and which give improved correlations in comparison with the steric Es constants used in the literature hitherto (21, 22). The constants B- toBj are measures of the widths of substituents in four rectangular directions. The L-constant accounts for the length of a substituent ... 

Platts, J.A., Butina, D., Abraham, M.H. and Hersey, A. (1999). Estimation of Molecular Linear Free Energy Relation Descriptors Using a Group Contribution Approach. J.Chem.Inf.Com-putScL, 39, 835-845. 

Linear Free Energy Related (LFER) Approaches 187... 

LINEAR FREE ENERGY RELATED (LFER) APPROACHES... 

RP-LC, multivariate analysis methods such as principle component analysis (PCA) and nonlinear mapping (NML), or comparative molecular field analysis (CoMFA) approaches and linear free energy-related (LFER) equations have been used to derive structure-retention relationships in chiral chromatography [16-18]. 

At the time that the basic formulation and testing of the mathematical models of quantitative structure-activity correlations were being made, another type of approach, the linear free-energy related model, was introduced (2). Using the basic Hammett equation (22, 36) for the chemical reactions of benzoic acid derivatives (Equation 12), several investigators attempted quantitative correlations between physicochemical properties... 

Another potential use of this linear free-energy related method in custom tailoring a drug is parameter optimization. Once a particular series of data has been analyzed, one may evaluate r0 for the series and make this the starting point in suggesting molecules for further synthesis and testing. Use of this approach also might indicate that a different series of compounds should be considered if optimum parameters have already been achieved in the compounds tested (1). 

In fact, the solvolysis of teri-butyl chloride is one of the cornerstones of physical organic chemistry. " Thus, some quantitative approaches to the kinetics of spontaneous reactions in various solvents - and, more interesting, solvent mixtures - are based on linear free-energy relations such as that of Grunwald and Winstein or its extensions. " " These equations allow one to interpolate or extrapolate rate constants that cannot be readily measured, and also to derive mechanistically significant information in the process. 

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]. 

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. 

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