Extrathermodynamic approach

The great generality of thermodynamics is a consequence of its minimal use of specific and detailed models on the other hand, it is the absence of such models that prevents thermodynamics from providing insight into molecular mechanisms. The combination of detailed models with the concepts of thermodynamics is called the extrathermodynamic approach. Because it involves model building, the technique lacks the rigor of thermodynamics, but it can provide information not otherwise accessible. Extrathermodynamic relationships often take the form of correlations among rates and equilibria, and the models used to account for these... 

The discussion in Section 7.1 should prepare us to expect deviations from such a simple relationship as the Hammett equation if the reaction being correlated differs greatly from the standard reaction. When this happens we have two choices (within this extrathermodynamic approach) We can select a different standard reaction, or we can increase the number of parameters. 

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 benefit of such LFERs is that they establish patterns of regular behavior, isolating apparent simplicity and defining normal or expected reactivity. Against such patterns it becomes possible to detect widely deviant or unexpected behavior. As we saw in Chapter 7, we cannot expect great generality from the extrathermodynamic approach, so it may be necessary to define numerous model processes so as to fit a full range of situations. 

We have seen that physical properties fail to correlate rate data in any general way, although some limited relationships can be found. Many workers have, therefore, sought alternative measures of solvent behavior as means for correlating and understanding reactivity data. These alternative quantities are the empirical measures described in this section. The adjective empirical in this usage is synonymous with model dependent this is. therefore, an extrathermodynamic approach, entirely analogous to the LFER methods of Chapter 7 with which structure-reactivity relationships can be studied. 

Now, it can be postulated that solvolysis rate should be a function of two properties of the solvent one is its ionizing power, and the other is its nucleo-philicity. An SnI process should be promoted by high ionizing power, and an Sn2 process by high solvent nucleophilicity. At this point, we are ready to bring the extrathermodynamic approach to bear on this problem. This was initiated by Grun-wald and Winstein, who defined a solvent ionizing power parameter Y by... 

The next step in the development of the extrathermodynamic approach was to find a suitable expression for the equilibrium constant in terms of physicochemical and conformational (steric) properties of the drug. Use was made of a physicochemical interpretation of the dissociation constants of substituted aromatic acids in terms of the electronic properties of the substituents. This approach had already been introduced by Hammett in 1940 [14]. The Hammett equation relates the dissociation constant of a substituted benzoic acid (e.g. meta-chlorobenzoic acid) to the so-called Hammett electronic parameter a ... 

However, in contrast to the EMF of a galvanic cell, the resultant expressions contain the activities of the individual ions, which must be calculated by using the extrathermodynamic approach described in Section 1.3. 

A suitable extrathermodynamic approach is based on structural considerations. The oldest assumption of this type was based on the properties of the rubidium(I) ion, which has a large radius but low deformability. V. A. Pleskov assumed that its solvation energy is the same in all solvents, so that the Galvani potential difference for the rubidium electrode (cf. Eq. 3.1.21) is a constant independent of the solvent. A further assumption was the independence of the standard Galvani potential of the ferricinium-ferrocene redox system (H. Strehlow) or the bis-diphenyl chromium(II)-bis-diphenyl chromium(I) redox system (A. Rusina and G. Gritzner) of the medium. 

We conclude this section by a few general remarks about extrathermodynamic approaches. These quantitative methods involve empirical approaches that cannot be derived strictly from thermodynamic theory. They are widely used to predict and/ or to evaluate partition constants and/or partition coefficients (see Box 3.2 for nomenclature) of organic compounds. There are many situations in which some of the data required to assess the partitioning behavior of a compound in the environment are not available, and, therefore, have to be estimated. For example, we may need to know the water solubility of a given compound, its partition coefficient between natural organic matter and water, or its adsorption constant from air to a natural surface. In all these, and in many more cases, we have to find means to predict these unknown entities from one or several known quantities. 

The background supporting the versatility of the Hansch approach is that it is in fact an extrathermodynamic approach to drug action. The information on the structure-activity relationship of various kinds of drugs is expressed as equations which provide a convenient way for comparative studies with simpler and similar model reactions to elucidate the mechanism of overall drug action without microscopic knowledge of complex processes occurring in vivo. 

Tihe two methods of structure-activity correlation which have received the most application in the past decade are the Hansch multiple parameter method, or the so-called extrathermodynamic approach, and the Free-Wilson, or additive model. The basic differences and similarities of these methods are discussed in this presentation. 

This approach to separating the different types of interactions contributing to a net solvent effect has elicited much interest. Tests of the ir, a, and p scales on other solvatochromic or related processes have been made, an alternative ir scale based on chemically different solvatochromic dyes has been proposed, and the contribution of solvent polarizability to it has been studied. Opinion is not unanimous, however, that the Kamlet-Taft system constitutes the best or ultimate extrathermodynamic approach to the study of solvent effects. There are two objections One of these is to the averaging process by which many model phenomena are combined to yield a single best-fit value. We encountered this problem in Section 7.2 when we considered alternative definitions of the Hammett substituent constant, and similar comments apply here Reichardt has discussed this in the context of the Kamlet-Taft parameters. The second objection is to the claim of generality for the parameters and the correlation equation we will return to this controversy later. 

In relating structure and chromatographic retention the extrathermodynamic approach is applied which lacks the rigour of thermodynamics but provides otherwise inaccessible information. Extrathermodynamic approaches are combinations of detailed models with certain concepts of thermodynamics [5]. 

Sometimes used as a synonym of - Hansch analysis, the extrathermodynamic approach refers to models based on empirical relationships of - physico-chemical properties with thermodynamic parameters such as free energies, enthalpies and entropies for various reactions. 

Between 1961 and 1964, Hansch and co-workers used, for the first time, an extrathermodynamic approach to mathematically relate biological activity to the physicochemical properties of molecules. The basic assumption is that the introduction of different substituents into a reference compound modifies its biological activity, which can be expressed to a first-order approximation by the following relationship ... 

Fujita, T. (1990). The Extrathermodynamic Approach to Drug Design. In Quantitative Drug Design. Vol. 4 (Ramsden, C.A., ed.), Pergamon Press, Qxford (UK), pp. 497-560. 

In the early 1950s Taft (10) outlined a sound quantitative basis for the estimation of steric effects and for separating them from polar and resonance effects. This derivation follows the standard extrathermodynamic approach and is therefore empirical. The definition of steric substituent constants is closely related to polar substituent constants, for they are obtained from the same reference system (10). The polar substituent constants, however, have been shown to arise from electronic effects, and they strongly correlate with the inductive substituent constants (10, 43, 61). 

The reactivity of molecules represents their ability to undergo certain interactions. In the extrathermodynamic approach, the reactivity characteristics of molecules are described as changes in the reactivity of a reference molecule upon substitution. It is known from chemistry, however, that molecular interactions are determined by properties of the entire molecule. Quantum chemistry offers the means of obtaining molecular properties from first principles of physics and chemistry the quantum chemical computation methods are now able to predict good relative values of physicochemical properties that can be determined by experiment either with great difficulty or only by inference. 

Several attempts have been made (217, 218, 219, 220) to establish the relationship between the extrathermodynamic approach of Hansch (114) and the mathematical approaches (198, 212, 213, 215, 216). The numerical equivalence and the theoretical interrelation between the two approaches derives from the assumption that the contributions of the individual substituents to the biological activity is represented as a weighted sum of several physicochemical properties (e.g., the extrathermodynamic parameters in the Hansch equation) as expressed in equation 103... 

The Hansch-Fujita approach is also called the linear free-energy relationship (LFER) or extrathermodynamic approach, since most of the descriptors are derived from rate or equilibrium constants. 

Kubinyi, H. The Free-Wilson method and its relationship to the extrathermodynamic approach. In Comprehensive Medicinal... 

Between 1961-1964 Hansch and coworkers used, for the first time, an extrathermodynamic approach to mathematically relate biological activity to the physico-chemical properties of molecules. 

Linear Free Energy Relationships —> extrathermodynamic approach... 

Structure/Response Correlations, Hansch analysis, Hammett equation, Free-Wilson analysis. Linear Solvation Energy Relationships, Linear Free Energy Relationships, group contribution methods, substituent descriptors, extrathermodynamic approach, and biological activity indices. 

Kubinyi H. The Free-Wilson method and its relationship to the extrathermodynamic approach. In Ramsden CA, ed. Quantitative Drug DesignHansch C, Sammes PG, Taylor JB, eds. Comprehensive Medicinal Chemistry. The Rational Design, Mechanistic Study and Therapeutic Application of Chemical Compounds 1990 Vol. 4. Oxford Pergamon Press, 1990 589-643. 

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