Extrathermodynamic relationship

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 

As seen earlier, these logarithmic terms are linearly related to free energy changes  

Such correlations are therefore called linear free energy relationships (LFERs). Often it is convenient to express the correlation in terms of ratios of constants by referring all members of the series to a reference member of the series thus the correlation in Eq. (7-1) can be expressed 

Though LFERs are not a necessary consequence of thermodynamics, their occurrence suggests the presence of a real connection between the correlated quantities, and the nature of this connection can be explored. This treatment follows Leffler and Grunwald. - PP Standard free energy changes AG° will pertain to either 

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Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

It follows that for a special value of one parameter, the observed value of y is independent of the second parameter. This happens at Ii= a2/ai2 or I2 = -ai/ai2 any of these values determines y= a -aia2/ai2, the so called isoparametrical point. The argument can evidently be extended to more than two independently variable parameters. Experimental evidence is scarce. In the field of extrathermodynamic relationships, i.e., when j and 2 are kinds of a constants, eq. (84) was derived by Miller (237) and the isoparametrical point was called the isokinetic point (170). Most of the available examples originate from this area (9), but it is difficult to attribute to the isoparametrical point a definite value and even to obtain a significant proof that a is different from zero (9, 170). It can happen—probably still more frequently than with the isokinetic temperature—that it is merely a product of extrapolation without any immediate physical meaning. 

On the analogy of the physicochemical relation, one was led to define a biological Hammett equation which related the equilibrium constant of the drug-receptor complex to the electronic a parameters of the substituents (e.g. chlorine, bromine, methyl, ethyl, hydroxyl, carboxyl, acetyl, etc.) of the drug molecule. Since the equilibrium constant of a drug-receptor complex is reflected by the biological activity, this led to the first extrathermodynamic relationship in QS AR ... 

An indication of the nature of the transition state in aromatic substitution is provided by the existence of some extrathermodynamic relationships among rate and acid-base equilibrium constants. Thus a simple linear relationship exists between the logarithms of the relative rates of halogenation of the methylbenzenes and the logarithms of the relative basicities of the hydrocarbons toward HF-BFS (or-complex equilibrium).288 270 A similar relationship with the basicities toward HC1 ( -complex equilibrium) is much less precise. The jr-complex is therefore a poorer model for the substitution transition state than is the [Pg.150]

It is well known that such quantities as the standard free energy, enthalpy and entropy display a remarkable tendency to be additive functions of independent contributions of part-structures of the molecule. This property, on which the mathematical simplicity of many extrathermodynamic relationships is largely based, is well illustrated, for example, by the enthalpies of formation at 298°K of several homologous series of gaseous hydrocarbons Y(CH2)mH, which are expressed by the relation (28) (Stull et al., 1969). In... 

One of the major objectives of physical organic chemistry is the detailed description of transition states in terms of nuclear positions, charge distributions, and solvation requirements. A considerable aid to this task is provided for many reaction series by the existence of extrathermodynamic relationships, whose mathematical simplicity largely arises from extensive cancellation of the contribution to the free-energy change from the part of the molecule outside the reaction zone. 

Bamford, H.A. Poster, D.L. Huie, R.E. Baker, J.E. 2002, Using extrathermodynamic relationships to model the temperature dependence of Henry s law constants of 209 PCB congeners. Environ. Sci. Technol. 36 4395 402. 

Enthalpy—Entropy Compensation Effect as Extrathermodynamic Relationship. 64... 

ENTHALPY-ENTROPY COMPENSATION EFFECT AS EXTRATHERMODYNAMIC RELATIONSHIP... 

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 ... 

We now proceed to more complicated ionophores in order to testify the validity of this extrathermodynamic relationship and its hypothetical interpretation as an attempt to understand the nature of supramolecular interactions more generally and deeply. The thermodynamic parameters are plotted in Figures 16-19 for long glymes, (pseudo)cyclic ionophore antibiotics, lariat ethers with donating side-arm(s), and bis(crown ethers), whose structural changes upon complexation are schematically illustrated in Figure 20. 

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... 

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... 

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