Excess molar refraction

In this equation E (R2) is the excess molar refraction, S (tt ) is the solute dipolarity-polarizabiUty, A (2a ) and B(2 3 ) are the solute H-bond acidity and basicity, respectively, and Vis the McGowan characteristic volume (in cm mol /100). The solute size, V, (molecule favors octanol) together with solute H-bond basicity, B, (favors water) are the dominating parameters of this equation. The use of Bo(2P ) resulted in equation... 

In an excellent paper, Zhao et al. [29] assembled a carefully reviewed literature set of human absorption data on 241 drugs. They showed that a linear regression model built with 5 Abraham descriptors could fit percent human absorption data reasonably well (r2 = 0.83, RMSE = 14%). The descriptors are excess molar refraction (E), polarizability (S), hydrogen bond acidity (A), hydrogen bond basicity (B), and McGowan volume (V), all related to lipophilicity, hydrophilicity, and size. In a follow-on paper, data on rat absorption for 151 drugs was collected from the literature and modeled using the Abraham descriptors [30]. A model with only descriptors A and B had r2 = 0.66, RMSE = 15%. 

Abraham et at. [2], [3], [4] Solubility, excess molar refraction, polarizability, hydrogen-bond acidity/basicity, and McGowan volume... 

Zhao and coworkers [53] also constructed a linear model using the Abraham descriptors. The MLR model possesses good correlation and predictability for external data sets. In this equation, E is an excess molar refraction (cm3/mol/ 10.0) and S the dipolarity/polarizability, A and B are the hydrogen bond acidity and basicity, respectively, and V is the McGowan characteristic volume (cm3/ mol/100). The large coefficients of A and B indicate too polar molecules having poor absorption. 

Here E is the solute excess molar refractivity, S is the solute dipolarity/ polarizability A and B are the overall or summation hydrogen-bond acidity and basicity, respectively and V is the McGowan characteristic volume lower-case letters stand for respective coefficients which are characteristic of the solvent, c is the constant. By help of sfafisfical methods like the principal component analysis and nonlinear mapping, the authors determined the mathematical distance (i.e., measure of dissimilarify) from an IL fo seven conventional solvents immiscible with water. It appears that the closest to the IL conventional solvent is 1-octanol. Even more close to IL is an aqueous biphasic system based on PEG-200 and ammonium sulfate (and even closer are ethylene glycol and trifluoroethanol, as calculated for hypofhefical water-solvenf sysfems involving fhese solvenfs). 

In spite of claims to the contrary, to date no completely satisfactory method exists to calculate the polarity / polarizability parameter, n, as it applies to the equilibrium of solute between water and octanol. The excess molar refractivity of the solute (compared to an alkane of equal size) can be estimated separately from polarizability/dipolarity (Abraham, 1994) and seems an attractive approach to this problem, but it needs further verification. The dipole moment of the entire molecule has been used as a polarity parameter (Bodor, 1992), but there are good reasons to believe it has marginal value at best. The square of the dipole moment also has been used (Leahy, 1992), and it, at least, has some theoretical basis (Kirkwood, 1934). 

In Eq. [20], Ri is the excess molar refraction (MR), which is the MR of the solute less the MR of the alkane with the same characteristic volume, V 2, as the solute. The 7t symbol is the dipolarity/polarizability, and X) P2 3re the so-called overall LIB acidity and basicity descriptors, respectively. The summation sign is used to emphasize that these are overall HB properties designed to be appropriate to situations where the solute molecule is surrounded by an excess of solvent molecules. These descriptors are in contrast to the HB descriptors 0.2 and p2 employed in Eq. [19], which are derived from 1 1 complexation constants. Equation [20] has also been used with the Vx2 term replaced by a log (L ) term, where is the equilibrium constant... 

In this equation, R, is the excess molar refraction iTs is the dipolarity/polarizability 2 and E jSp. are the summation of hydrogen bond acidity and basicity values, respectively and Vx is McClowan s volume. 

EVtype descriptors -> van der Waals excluded volume method EVwhole descriptors - van der Waals excluded volume method excess electron polarizability -> electric polarization descriptors excess molar refractivity -> molar refractivity expanded distance Cluj matrices -> expanded distance matrices expanded distance indices -> expanded distance matrices expanded distance matrices... 

R2 = MRa - MR = MRa - (2.83195 Vx - 0.52553) where MRa is the molar refractivity of the considered compound and MR the molar refractivity of the n-alkane with the same characteristic volume Vx. The parameter R2 can be considered a polarizability descriptor and is called excess molar refractivity. By definition, / 2 = 0 for all n-alkanes, and the same holds for branched alkanes. 

This equation is based on Abraham s solvation equation which uses five molecular descriptors excess molar refraction (F), solute polarity/polarizability (S), McGowan characteristic volume (V), solute overall acidity (A) and basicity (B). The steric (size/shape) descriptors E, S and V have a positive effect on oral absorption, while the descriptors related to H-bonding, A and B, have a negative effect. The model accounts for 74% of the variance (r ) in the data and the predictions have a 14% standard error (i). This is nearly as good as it gets, since the experimental biological variance is ca. 15%. 

Abraham developed what is termed a general solvation equation. The main idea behind the model involves the creation of a cavity in the solvent, incorporation of the solvent in the cavity, and turning on solute-solvent interactions. These interactions require a relevant solute parameter, and the ones chosen were the excess molar refraction, ttf the solute dipolarity/polarizability, flf and Pf the hydrogen-bond acidity and basicity, respectively, and a characteristic volume. Applying this general equation to 132 solutes in aqueous SDS, Abraham et al. obtained the following equation for the partition coefQcient ... 

For the cationic surfactants studied, the excess molar refraction and solute hydrogen-bond acidity contribute positively to K although the effect is small. Solubilizate dipolarity exhibits a weakly negative contribution to and the solubilizate hydrogen-bond basicity a significant negative contribution to K. ... 

The solute excess molar refraction, R2 or E, models polarizability contributions from n- and 7t-electrons. The solute molar refraction is too closely related to solute size to be used in the same correlation equation as Vx. To avoid correlation between the molar refraction and Vx, an excess molar refraction, R2, was defined as the molar refraction for the given solute, less the molar refraction for an n-alkane of the same characteristic volume [61,62]. The excess molar refraction is simply calculated from the refractive index of the solute at 20°C for the sodium D-line, q, as indicated by Eq. (1.8)... 

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