Free-Energy Relations

Only few attempts have been made to apply free-energy relations to thiazole reactivity. 

These techniques are known as linear free energy relations, LFER. Imagine that one has determined the rate constants, or the Gibbs free energies of activation, for a series of reactions. The reactions are all the same, save for (for example) a different substituent on each reactant. The substituent is not a direct participant in the reaction. In an LFER, the values of log k or AG are correlated with some characteristic of the substituent as manifested in another reaction series. If the correlation is successful, then the two series of reactions have a common denominator. This technique has proved to be a powerful one for systematizing reactivity. We shall see a number of such correlations. 

Linear free energy relations (see LFER) Lineweaver-Burk treatment, 91 Long-chain approximation, 183... 

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. 

Zahradnik R. Correlation of the biological activity of organic compounds by means of the linear free energy relations. Experimentia 1962 18 534-6. 

If the free-energy-related parameters for electronic (a), hydrophobic (P), and steric ( ,) factors are defined, Eq. 2 gives the well known, free-energy relationship ... 

The same first-order replacements are seen when M is Mo or W, somewhat slower than in the case of Cr, but still much faster than for the hexacarbonyls. The rate increases with the pK of the inert ligand (N-N) and Fig. 9 shows the linear free-energy relation between log ki and pK . The relative orders would not have been expected on the basis of any 7t-bonding effects since increasing back-donation to CO would increase the M-C bond order. This increase in M-C bond order is supported by a decrease in Vco with increasing o-phenanthroline basicity. The same consideration applies for the pentacarbonyl halide anions where the first-order rates decrease (Cl > Br > I), unexpectedly as the halide polarizability increases. 

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. 

As an illustration of PLS regression (PLSl) we reconsider the inhibitory potencies of oxidative phosphorylation of 11 doubly substituted salicylanilides [ 17] in Table 37.1. An extended Hansch model is defined by the linear free energy relation ... 

Despite many papers over many years, there is still a serious shortage of information that allows linear free energy relation treatment of these reactions. The available linear free energy relations, some of them calculated for this chapter, are collected in Tables 1.4 and 1.5. There are definite indications that p is... 

By linear free energy relation arguments, Williams et al. concluded that in the case of a five-membered ring sultone the reaction with a phenoxide was either stepwise or, if concerted, had a transition state close to the pentacoordinated intermediate. ... 

Tetrahedral intermediates vary enormonsly in stability relative to the corresponding carbonyl componnds, from extremes like hexaflnoroacetone hydrate where it is difflcnlt to remove the nncleophile from the addnct, to amide hydrates where the obligatory intermediate in acyl transfer is present at nndetectably low concentrations. Linear free-energy relations provide a route to calculating the eqnilibrinm constant... 

From a comparison of Eqs. (9) and (22) we see that H = F(0 ). To elucidate the physical meaning of the exponent in Eq. (22), we consider first the case when 0 = 1 (barrierless reaction). In this case Eq. (20) determines the change of the free energy of the system F(l) when it is polarized by the electric field AEU = E -E (only the free energy related to the inertial polarization is considered). It may be easily seen that the absolute value of F(l) is equal to the energy of the reorganization of the medium Es (>0). 

Correlation Methods for Kinetic Date—Linear Free Energy Relations... 

CORRELATION METHODS FOR KINETIC DATA—LINEAR FREE ENERGY RELATIONS... 

The Hammett equation is the best-known and most widely studied of the various linear free energy relations for correlating reaction rate and equilibrium constant data. It was first proposed to correlate the rate constants and equilibrium constants for the side chain reactions of para and meta substituted benzene derivatives. Hammett (37-39) noted that for a large number of reactions of these compounds plots of log k (or log K) for one reaction versus log k (or log K) for a second reaction of the corresponding member of a series of such derivatives was reasonably linear. Figure 7.5 is a plot of this type involving the ionization constants for phenylacetic acid derivatives and for benzoic acid derivatives. The point labeled p-Cl has for its ordinate log Ka for p-chlorophenylacetic acid and for its abscissa log Ka for p-chloroben-zoic acid. The points approximate a straight line, which can be expressed as... 

Kiefer PM, Hynes JT (2002) Nonlinear free energy relations for adiabatic proton transfer reactions in a polar environment. I. Fixed proton donor—acceptor separation. J Phys Chem A... 

Expressed in terms of moduli, the Helmholtz elastic free energy relation is given by eq. 5. 

A8. The Helmholtz elastic free energy relation of the composite network contains a separate term for each of the two networks as in eq. 5. However, the precise mathematical form of the strain dependence is not critical at small deformations. Although all the assumptions seem to be reasonably fulfilled, a simpler method, which would require fewer assumptions, would obviously be desirable. A simpler method can be used if we just want to compare the equilibrium contribution from chain engangling in the cross-linked polymer to the stress-relaxation modulus of the uncross-linked polymer. The new method is described in Part 3. 

The two-network method has been carefully examined. All the previous two-network results were obtained in simple extension for which the Gaussian composite network theory was found to be inadequate. Results obtained on composite networks of 1,2-polybutadiene for three different types of strain, namely equibiaxial extension, pure shear, and simple extension, are discussed in the present paper. The Gaussian composite network elastic free energy relation is found to be adequate in equibiaxial extension and possibly pure shear. Extrapolation to zero strain gives the same result for all three types of strain The contribution from chain entangling at elastic equilibrium is found to be approximately equal to the pseudo-equilibrium rubber plateau modulus and about three times larger than the contribution from chemical cross-links. 

Linear free energy relations between the tendency to form solute complexes and corresponding surface complexes. 

The term F2/CsRT is obtained from the constant capacitance model (Chapter 3.7). Fig. 4.6 gives a plot of the linear free energy relation between the rate constants for water exchange and the intrinsic adsorption rate constant, kads. 

Using predictive models for measuring environmental chemodynamics of organic pollutants in complex mixtures requires literature data on partition coefficient values. In some cases the values cited are not strictly experimental, being derived from linear free energy relations, while in others wide variations are reported in experimental values. The main problem is how one should evaluate which values are correct. Thus, Table 2 provides some basis to discriminate between reported values of partition coefficients, as well as predictive equations for partition coefficient calculations [21,62,65-85]. 

This is based on the fact that the energetics of transferring a -CH3 group from one environment to another is relatively constant from compound to compound -hence the term linear free energy relations... 

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