Multiparameter Approaches

A more rigorous approach has been suggested by Koppel and Palm [6, 112], who argue that a complete description of all solute/solvent interactions must include both non-specific and specific effects. They proposed the general four-parameter equation (7-50), which relates the variation of a given property A to two non-specific (T and P) and two specific characteristics of the solvent E and B). 

A seale of Lewis aeidity, E, was based on the t(30) values diseussed in Seetion 7.4 cf. Table 7-3), but these were eorreeted for the influenee of non-speeifie effeets, and adjusted to an origin L = 0 for the gas phase by means of Eq. (7-51) [6, 112, 115], 

The subtraetion of the polarization (y-Y) and polarizability p P) eontribu-tions from the total solvent effeet allows an estimation of the eontribution from speeifie solute-solvent interactions. This correction of j(30) values was made using least-squares regression analysis by correlating the data for suitably selected non-specifically and specifically interacting solvents. values derived in this way from j(30) values are presented in references [6, 115] they range from zero (gas phase, saturated hydrocarbons) to about 22 kcal/mol for water. By definition, e = 1 in Eq. (7-50) for the reference process, i.e. the n n transition of the pyridinium A-phenolate betaine dye (44). The reason for assuming that x(30), and thus , largely relates to Lewis acidity in protic solvents has already been mentioned . 

A detailed analysis of solvent effects on various solvent-sensitive processes by means of Eq. (7-50) has been presented by Koppel and Palm [6, 112]. If Eq. (7-50) 

The rate of reaction between benzoic acid and diazo-diphenylmethane in 44 non-HBD solvents correlates significantly with all four Koppel-Palm parameters of Eq. (7-50), according to Eq. (7-52) with = 44, r = 0.976, and standard deviation s = 0.188 [15, 116] cf also [117]. 

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Quantitative stmcture—activity relationships have been estabUshed using the Hansch multiparameter approach (14). For rat antigoiter activities (AG), the following (eq. 1) was found, where, as in statistical regression equations, n = number of compounds, r = regression coefficient, and s = standard deviation... 

There are single- and multiparameter approaches for determining the polarity and separation of contribution of different interactions to the total effect of polarity on spectroscopic characteristics. They are based on different theories of solvatochromic shifts of absorption and fluorescence bands. 

Kennicutt II, M.C., and Comet, P.A. (1992) research of sediment hydrocarbon sources multiparameter approaches. In Organic Matter Productivity, Accumulation, and Preservation in Recent and Ancient Sediments (Whelan, J.K., and Farrington, I.K., eds.), pp. 308-338, Columbia University Press, New York. 

Many different solvent parameters and multiparameter equations have been introduced in this Chapter 7. Certainly, only a few of them will survive the test of applicabihty and aeeeptanee by organic chemists. Indeed, the preference for certain time-tested solvent seales and multiparameter treatments is already clearly discernible. Amongst the one-parameter seales, the t(30) or Ej seale and the DN scale have frequently been used, while the Kamlet-Abboud-Taft (KAT) LSER approach seems to be the most widely applied multiparameter approach. 

We conclude that a multiparameter approach including parameters related to different seismicity patterns is promising for the improvement of seismic hazard assessment. 

Again, attempts were made to correlate initiation rates to physical properties while a weak correlation with Ex(30) was obtained (Figure 2.11), the best correlation was observed with a multiparameter approach (Eqn (2.6)). Comparison with the data for G2 suggests that differences in behavior result from different dependencies on P and tt G2 depends strongly on both of these factors, while for GH2 the error bars encompass zero (or close to it). 

The tendency of a transition metal hydride to transfer H to a substrate is called hydricity [ 12]. It is possible to determine the Gibbs free energy of the splitting of the covalent polar M-H bond to afford a metal cation and the hydride ion in solution. The hydricity is not parallel to the polarity of the M-H IxMid, nor can it be predicted on the basis of the electronic structure of the metal atom. It is a complex property that can be modeled for transition metal hydrides using multiparameter approaches. The hydricity concept applies to the interaction of M-H bonds with CO2 as well [13]. The reactivity of M-H bonds toward CO2 is linked to reactions that may have industrial interest, such as the hydrogenation of CO2 to afford formic acid (4.2) and the electrochemical reduction of CO2 to other Cl or C1+ molecules (4.3). 

A similar equation can be derived for the enthalpy. It turned out that this modification to give the retardation time a free volume dependence, was successful in describing one-step isothermal recovery but unsuccessful in describing memory effects. Kovacs, Aklonis, Hutchinson and Ramos (1979) attributed the latter to the contributions of at least two independent relaxation mechanisms involving two or more retardation times. These authors proposed a multiparameter approach, the so-called KAHR (Kovacs-Aklonis-Hutchinson-Ramos) model. The recovery process is divided into N subprocesses, which in the case of volumetric recovery may be expressed as ... 

To establish more accurate fed estimations, Benin et developed a multiparameter approach, in which logfed is described using the Hammett constants corresponding to polar inductive/field (alkyl radical (eqns [15] and [16] for TEMPO- and SGl-based alkoxyamines, respectively) ... 

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