Linear free energy relations definition

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... 

The concept of the similarity of molecules has important ramifications for physical, chemical, and biological systems. Grunwald (7) has recently pointed out the constraints of molecular similarity on linear free energy relations and observed that Their accuracy depends upon the quality of the molecular similarity. The use of quantitative structure-activity relationships (2-6) is based on the assumption that similar molecules have similar properties. Herein we present a general and rigorous definition of molecular structural similarity. Previous research in this field has usually been concerned with sequence comparisons of macromolecules, primarily proteins and nucleic acids (7-9). In addition, there have appeared a number of ad hoc definitions of molecular similarity (10-15), many of which are subsumed in the present work. Difficulties associated with attempting to obtain precise numerical indices for qualitative molecular structural concepts have already been extensively discussed in the literature and will not be reviewed here. 

Levine RD. Free energy of activation. Definition, properties, and dependent variables with special reference to linear free energy relations. J Phys Chem 1979 83(1) 159-170. 

The same relations (11) and (12) hold for the Gibbs free energy in the (N, p,T) ensemble. Equation (11) is also valid for a quanmm mechanical system. Note that for a linear coupling scheme such as Eq. (10), the first term on the right of Eq. (12) is zero the matrix of second derivatives can then be shown to be definite negative, so that the free energy is a concave function of the Xi. 

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

Physical organic chemists have tended to examine parameters based on shifts in the absorption peaks in the spectra of various dyes or indicator molecules. The a and P scales of Taft and Kamlet, the ET(30) scale of Dimroth and Reichardt, the 7t scale of Taft and co-workers and the Z value of Kosower are all examples of this type of parameter. The definitions and measurement means for these parameters, as well as important references, are shown in Table 5. An alternative definition of the Dimroth-Reichardt parameter is the dimensionless, ETN, which is now preferred by some organic chemists (for a discussion see Ref. 15). The Z value is important in that it led to the scale of Dimroth and Reichardt, which overcomes many of the limitations of the earlier scale. Several workers have shown that relationships exist, with good correlation coefficients, between similar parameters. Thus, DN is linearly related to p, both parameters being designed to measure the donor properties (or Lewis basicity) of solvent molecules. Also, Lr(30) is related to a as well as to AN all three parameters purport to measure the electron acceptor properties (or Lewis acidity) of solvent molecules. It has been found that different solvent types have different coefficients in linear relationships between n and the dipole moment. The Taft and Dimroth-Reichardt parameters, in particular, have been found to correlate with free energies and... 

The formation processes of metal-containing nanostructures in carbon or carbon-polymeric shells in nanoreactors can be related to one t) e of reaction series using the terminology of the theory of linear dependencies of free energies (LFE) [16]. Then it is useful to introduce definite critical values for the volume, surface energy of nanoreactor internal walls, as well as the temperature critical value. When the ration Ig k/k is proportional -AAF/RT, the ratio WAV can be transformed into the following expression ... 

---