Extrathermodynamic

Increasing attention has been paid to the generation of quantitative stmcture—activity relationships in which the effects of molecular substitution on pharmacologic activity can be interpreted in terms of the physicochemical properties of the substituents. These approaches are based on the extrathermodynamic analysis of substituent effects (36) ... 

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. 

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. 

Evaluation of the individual contributions requires extrathermodynamic assumptions and analysis of a body of data so as to achieve a self-consistent set of numbers. For this reason, there may be small differences between 8q of Eq. (8-52) and the 8 defined by Eq. (8-43). Table 8-7 gives value of 8, 80, 8j, 8p, 8h for the solvents of Table 8-2." ... 

Without some additional relationship it is impossible to resolve y into and "y. By introducing an extrathermodynamic assumption as this additional relationship, it becomes possible to estimate single ion transfer activity coefficients. A widely used assumption is that the transfer activity coefficients of the cation and anion of tetraphenylarsonium tetraphenylboride, Ph4As BPh4, are equal, i.e.,... 

By combining these ions with other counterions, single ion transfer activity coefficients are calculated. By these techniques transfer free energies or activity coefficients have been determined for many ions and nonelectrolytes in a wide variety of solvents.Parker has discussed the extrathermodynamic assumptions that lead to single ion quantities. 

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... 

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. 

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. 

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. 

The standard Gibbs energy of electrolyte transfer is then obtained as the difference AG° x ° = AG° ° - AG° x. To estabfish the absolute scale of the standard Gibbs energies of ion transfer or ion transfer potentials, an extrathermodynamic hypothesis must be introduced. For example, for the salt tetraphenylarsonium tetraphenyl-borate (TPAs TPB ) it is assumed that the standard Gibbs energies of transfer of its ions are equal. 

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 ... 

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 ... 

The second extrathermodynamic method that we discuss here differs from Hansch analysis by the fact that it does not involve experimentally derived substitution constants (such as o, log P, MR, etc.). The method was originally developed by Free and Wilson [29] and has been simplified by Fujita and Ban [30]. The subject has been extensively reviewed by Martin [7] and by Kubinyi [8]. The method is also called the de novo approach, as it is derived from first principles rather than from empirical observations. The underlying idea of Free-Wilson analysis is that a particular substituent group at a specific substitution site on the molecule contributes a fixed amount to the biological activity (log 1/C). This can be formulated in the form of the linear relationship ... 

Thermodynamics describes the behaviour of systems in terms of quantities and functions of state, but cannot express these quantities in terms of model concepts and assumptions on the structure of the system, inter-molecular forces, etc. This is also true of the activity coefficients thermodynamics defines these quantities and gives their dependence on the temperature, pressure and composition, but cannot interpret them from the point of view of intermolecular interactions. Every theoretical expression of the activity coefficients as a function of the composition of the solution is necessarily based on extrathermodynamic, mainly statistical concepts. This approach makes it possible to elaborate quantitatively the theory of individual activity coefficients. Their values are of paramount importance, for example, for operational definition of the pH and its potentiometric determination (Section 3.3.2), for potentiometric measurement with ion-selective electrodes (Section 6.3), in general for all the systems where liquid junctions appear (Section 2.5.3), etc. 

Two types of methods are used to measure activity coefficients. Potentiometric methods that measure the mean activity coefficient of the dissolved electrolyte directly will be described in Section 3.3.3. However, in galvanic cells with liquid junctions the electrodes respond to individual ion activities (Section 3.2). This is particularly true for pH measurement (Sections 3.3.2 and 6.3). In these cases, extrathermodynamical procedures defining individual ion activities must be employed. 

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. 

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]

Extrathermodynamic calculations of EM s 86 The question of the smallest rings in SN2 reactions 89... 

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... 

An alternative approach, which is usual among physical organic chemists, involves a comparison of changes of thermodynamic quantities for structurally-related reaction series. Such an approach, for which the term extrathermodynamic is widely used (Leffler and Grunwald, 1963), will be adapted here in an appropriate form to the interpretation of chain-length effects on cyclisation rates and equilibria. The experimental basis is provided by cyclisation reactions for which either 0AS+- or 0AS -data are available. 

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. 

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