Multi-parameter approach

A multi-parameter approach is preferable and the re scale of Kamlet and Taft (Kamlet et al., 1977) deserves special recognition because it has been successfully applied to the positions or intensities of maximal absorption in IR, NMR, ESR and UV-visible absorption and fluorescence spectra, and many other physical or chemical parameters (reaction rate, equilibrium constant, etc.). Such observables are denoted XYZ and their variations as a function of solvent polarity can be expressed by the generalized equation 

The observable XYZ can be in particular the wavenumber v of an absorption or emission band and the preceding equation is rewritten as 

It is remarkable that the n scale has been established from the averaged spectral behavior of numerous solutes. It offers the distinct advantage of taking into account both non-specific and specific interactions. 

A good illustration is provided by 4-amino-7-methylcoumarin (Kamlet et al., 1981), which possesses both hydrogen bond donor and acceptor groups (see 

4) Equation (7.1) applies when only non-chlorinated aliphatic solvents or aromatic solvents are considered. When chlorinated and non-chlorinated aliphatic solvents and aromatic solvents need to be considered together, Eq. (7.1) must be rewritten as 

---

Clearly what is needed in SFC for samples with diverse, wide-ranging compounds is a systematic approach to optimization, applicable when two or more variables are changed simultaneously. The remainder of this chapter is therefore devoted to the description of some systematic, multi-parameter approaches, with a natural emphasis on those strategies for which experimental results are available. 

Because of the different effects of electrophilic solvation of the various negative charges (i.e. Cl- for Y, "OTs for Tots I" for Z, 0 for Ej), direct comparisons between the various scales should be done cautiously. A wide variety of correlations giving clear indications of trends, has been reported by Reichardt and Dimroth (1968), but the significance of a recent general survey of scales of solvent polarity is doubtful, because of the many parameters used in the correlations (Fowler et al., 1971). The multi-parameter approach has also been adopted and reviewed by Koppel and Palm (1972). 

This multi-parameter approach provides reliable information to drug discovery teams on the relative toxicity of new compounds in a class, toxicity relative to similar drugs already on the market, STRs, subcellular targets, identification of the mechanism of adverse effects, and plasma concentrations where toxicity would be expected to occur in vivo. 

Dilution ratio, DR, is used to express the tolerance of solvents to diluents, most frequently, toluene. DR is the volume of a solvent added to a given solution that causes precipitation of the dissolved resin. This ratio can characterize the compatibility of a diluent with a resin solution in primary solvent. When compatibility is high, more diluent can be added. Only a multi-parameter approach provides a satisfactory correlation with solubility parameters. DR depends on the polymer concentration. With polymer concentration increasing, DR increases as well. T emperature influences DR in a similar manner. Determination of DR must be performed at standard conditions. DR can be related to the solubility parameters but such correlation depends on concentration. 

Finally, we may wish to consider a multi-pass approach whereby the search region for each unknown parameter is determined by the maximum change of the parameter during the last pass (Luus, 1998). 

Another possible advantage with MolSurf descriptors (and also other multi parameter descriptors) is the fact that they describe the investigated compounds not only with a single value, as in the case of PSA and log P descriptors, but in a multivariate way. This approach provides a more balanced description of the requirements that a structure must have in order to be well absorbed and may, in turn, provide additional insight on how to develop compounds having favorable absorption properties. However, as will be described in Section 16.4.10, simpler -i.e., less computationally demanding - parameters carrying similar information content with equal interpretability may be used to derive models for intestinal absorption at the same level of statistical quality. 

Many different approaches have been reported in the last decade toward a better understanding of the medium factors that influence reaction rates. Fundamental studies have been devoted to probe the reaction at a microscopic level in order to obtain information on the nature of several specific solvent-solute interactions on S Ar and to attempt a description of these effects quantitatively. Recent works have shown the wide applicability of a single parameter scale such as the Ex(30) Dimroth and Reichardt37, as well as other multi-parameter equations. 

The success of these new multi-alignment approaches for the extraction of generalized order parameters from RDCs relies on a couple of fundamental assumptions. The first of these, as described in Section 2, is that the molecule is structured enough that the internal dynamics remain uncorrelated with the overall alignment. This corresponds to the assumption that the separation of averaging in Eq. (21) remains valid. If this does not hold, then overall alignment and internal motion will be convoluted in some nonlinear manner. The second assumption is that the structure and dynamics of the molecule is not influenced by change of medium. Provided that both of these assumptions are permissible, the acquisition of sufficient... 

It has been tried to overcome this drawback by the use of multi-parameter correlation equations. One approach involves the Gutmann donor number (DN) [81]. By this the absorption maximum (v ) observed for a dye in a certain liquid can be calculated from the absorption maximum of the dye in a reference medium (Vmax.o) according to [82-85]... 

Eq.(2-52) is a multi-parameter matrix which depends on time and other factors not easy to evaluate. This is because we deal with complicated states. Fig.2-20 presents results for S(0) = [0, 1, 0], i.e., the system (some country) is initially at a state of war. The following values were also assumed for the transition probabilities q = p = 0.1,r = 0.5, t = 0, u = 0.2 and v = 0.1. It is observed that after five steps the system approaches a steady state for which S(5) = [0.206, 0.091, 0.704]. The state vector indicates that the chances for peace are quite high, 70.4%, promising a bright future. 

---