Extrathermodynamic correlation

This expression makes possible the examination of extrathermodynamic correlation between the free energy changes for two dissociation equilibria, i.e. AGhet(R-R ) values of the hydrocarbons and AGhet(ROH + HsO" ) values of the alcohols. 

Thermodynamic Transition-State Theory and Extrathermodynamic Correlations for the Liquid-Phase Kinetics of Ethanol Derived Ethers... 

The thermodynamic transition-state theory (TTST) is utilized for the elementary steps within the Langmuir-Hinshelwood-Hougen-Watson (LHHW) framework to develop rate expressions for liquid-phase catalytic reactions in terms of activities for the family of tertiary alkyl ethyl ethers. The TTST formulation also provides a rationale for the extrathermodynamic correlations (ETC) observed. 

It is shown that rate expressions in terms of activities are appropriate for the liquid-phase tertiary alkyl ethyl ether synthesis system. The rate expressions are based upon the application of the thermodynamic transition-state theory to the elementary steps within the LHHW formalism. Extrathermodynamic correlations that relate the kinetics to the reaction thermodynamics can also be rationalized within this framework and are experimentally observed for this family of tertiary ethers. 

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 most common manifestation of extrathermodynamic relationships is a linear correlation between the logarithms of rate or equilibrium constants for one reaction series and the logarithms of rate or equilibrium constants of a second reaction series, both sets being subjected to the same variation, usually of structure. For illustration, suppose the logarithm of the rate constants for a reaction series B is linearly correlated with the logarithm of the equilibrium constants for a reaction series A, with substituent changes being made in both series. The empirical correlation is... 

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. 

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. 

A linear relationship of free energies is extrathermodynamic, and such a correlation is hardly a theoretical corollary which directly results from the axioms of thermodynamics alone. However, the slope of the straight line and departures from linearity can often suggest something physically meaningful concerning the chemical reactivity, as seen in Fig. 2. 

As experimentally demonstrated above, in the complexation thermodynamics involving cationic species as guests and ionophores as hosts, the entropic change TAAS, induced by altering cation, ligand, or solvent, is proportional to the enthalpic change AAH. This correlation immediately leads to an empirical Eq. 14 with a proportional coefficient a, integration of which affords an extrathermodynamic relationship between TAS and AH. Thus, Eq. 15 is the quantitative expression of the observed compensation effect ... 

Having a data bank which contains extrathermodynamic equations on both pure organic reactions as well as biochemical reactions is important in gaining insight into mechanism of action as Equation 42 illustrates. The type of a constant best suited to correlate the data is important as well as the value and the sign of p. Examples in which o-+ has proved to be a better parameter than o- are also known (36). 

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. 

The correlation of biological activity with physicochemical properties is often termed an extrathermodynamic relationship. Because it follows in the line of Hammett and Taft equations that correlate thermodynamic and related parameters, it is appropriately labeled. The Hammett equation represents relationships between the logarithms of rate or equilibrium constants and substituent constants. The linearity of many of these relationships led to their designation as linear free energy relationships. The Hansch approach represents an extension of the Hammett equation from physical organic systems to a biological milieu. It should be noted that the simplicity... 

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. 

The attempt to correlate biological activity with chemical structure in quantitative terms assumes that a functional dependence exists between the observed biological response and certain physicochemical properties of molecules. Without a mechanistic model one obtains it by an empirical correlation. A rational way to define such empirical relationships is within the extrathermo-dynamic approach (1). Although extrathermodynamic relationships... 

In principle, extrathermodynamic relationships that deviate from the simple Hammett equation (equation 8) can be treated by equation 14. The major problem is the determination of the different sets of o s, (e.g., set and 0 set) in a way that will indeed reflect their relation to independent properties. An example of such a procedure is the separation of polar and steric effects (10). The need for such a separation arose when a nearly complete lack of correlation was observed between substituent effects represented by the Hammet a constants and the rates for alkaline hydrolysis of aliphatic systems (12). Inspection of the structures indicated that the proximity of the substituents to the reaction site was a common feature. The steric interaction between R and X had to be considered separately from the electronic effects. Polar substituent constants were thus defined as the difference between the rate constants of base and acid catalyzed hydrolysis of esters. From the structural similarity of the transition states for these reactions (equation 15) it was assumed that the difference in their charge reflects only the polar effect of the substituent... 

Early in this century, Meyer (109) and Overton (110) showed that the relative potencies of drugs that affect the nervous system correlated with their oil/water partition coefficients. Fifty years later it was shown that partition coefficients in different solvent systems were correlated (111), thus establishing the basis for an extrathermodynamical treatment of partition coefficients. 

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 connectivity indices x and xv (102, 103), quantitatively characterize the size of the molecule and the degree of branching. In that sense, and also because they are derived from a theoretical procedure (104), they lack the usual extrathermodynamic meaning. The strong correlation of X with molar refractivity, MR,... 

It thus seems appropriate to use partition coefficients between aqueous and organic phases to represent molecular properties related to the hydrophobic interactions between small molecules and the biophase. This choice is well established at the level of a second order approximation in the extrathermodynamic derivation (see section A. 3). Numerous examples (137, 138) illustrate the utility of the partition coefficient in correlations of biological activity with chemical structure. 

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