Parameterization electrical effects

The earliest successful parameterization of electrical effects is that of Hammett6-8. Burkhardt reported the existence of QSRR two years before Hammett but did not develop a general relationship9. Hammett defined the am and ap constants using the ionization constants (Kx) of 3- and 4-substituted benzoic acids in water at 25 °C as the reference set and hydrogen as the reference substituent (i.e. K ) to which all others are compared. For hydrogen the values of the am and ap constants were defined as zero. 

The choice of electrical effect parameterization depends on the number of data points in the data set to be modeled. When using linear regression analysis the number of degrees of freedom, Ndf, is equal to the number of data points, Ndp, minus the number of independent variables, Ai,v, minus one. When modeling physicochemical data Ndf/Nj, should be at least 2 and preferably 3 or more. As the experimental error in the data increases, tVof/iViv should also increase. 

Stewart" proposed a parallel between the rate of esterification of 2-substituted benzoic acids and the molecular weights of the substituents. The nitro group deviated strongly from this relationship. It is the first work to attempt to relate the steric effect of a group to some property that might at least in part be a measure of size. Kindler made the first attempt at defining a set of steric parameters. These parameters were later shown to be a function of electrical effects. The first successful parameterization of the steric effect is due to Taft, who defined the steric parameter Es for aliphatic systems by equation 27 ... 

On the condition that two subsets have a structural feature whose parameterization is essentially the same, they can be combined into a single data set. As an example consider set 0X13, anfi-Ak—iyw-X—C=NOH, where Ak is either Me or Et. The electrical effects of these groups for Me and Et, respectively, are a , —.01, —,Q ad, —.14, —.12 ae, —.030, —. 036 the values of the steric parameter v are. 52 and. 56. A significant difference is found only in the polarizability parameter a, where the values for Me and Et are. 046 and. 093, respectively. Combination of oxime pXa values for Ak = Me or Et results in set 0X13 the best correlation was with the LDR equation. As only three substituent types are present in this data set and is 0.33, this data set cannot be considered as proof of anything. The only acceptable conclusion is that it is in accord with the combination of the two subsets. 

The earliest successful parameterization of electrical effects is that of Hammett He... 

The underlying physics and analysis of Mossbauer spectra have been explained in detail in Chap. 4. In that chapter, the principles of how a spectrum is parameterized in terms of spin-Hamiltonian (SH) parameters and the physical origin of these SH parameters have been clarified. Many Mossbauer studies, mainly for Fe, have been performed and there is a large body of experimental data concerning electric-and magnetic-hyperfine interactions that is accessible through the Mossbauer Effect Database. 

The theory of bolometer operation was developed by Mather [73-75] and parameterized analyses of an ideal bolometer have been developed [76,77] and extended to include the effects of electrical non-linearities [78], For further developments of infrared bolometers... 

A large variety of continuum models have been proposed and many are available in popular quantum chemical modeling packages. They differ in the sophistication of the procedure used to determine the shape of the cavity. In the simplest case, this is just a sphere, but most models nowadays use more tailored cavities (as in Figure 10.3), generated, for example, from the combination of a set of spheres placed around individual solute atoms. In most cases, the models include a relaxation of the electronic structure in response to the electric held created by the solvent around it, and in most cases this is then treated fully self-consistently. This effect can be quite important in some cases, as a polar solute may become considerably more polar due to interactions with a polar solvent. Different models are also parameterized in different ways. 

---