Parameters polarizability

Molar volume MV, molar refractivity MR, and parachor PA are theoretically and practically closely interrelated parameters (eqs. 33 — 35 MW = molecular weight, Q = density, n = refractive index y = surface tension) [285]. Another related parameter is the molar polarization P (dielectric constant 8 instead of the n term in eq. 34) [286]. 

Molar volume itself is not strictly additive, but the corrected volume parameters MR and PA are additive constitutive molecular properties, like log P and the Hammett a parameter. While molar refractivity has attracted much attention [50, 286 — 288], molar volume [55, 289] and parachor [50, 290] have only rarely been used in QSAR studies. 

MR still is the chameleon [91] amongst the physicochemical parameters, despite its broad application in QSAR studies. It has been correlated with lipophilicity, molar volume, and steric bulk. Of course, due to its MW/q component it is indeed related to volume and size of a substituent. But two recent statements that MR is only based on these properties [91, 291] cannot be accepted. The refractive index-related correction term in MR accounts for the polarizability and thus for the size and the polarity of a certain group [158, 173, 286]. The larger the polar part of a molecule is, the larger its MR value will be. Even hydrophobic substituents have a weak enthalpic interaction due to dispersion forces, in addition to their entropic 

In the above-mentioned parameter collection of 59 different substituents [158], MR is correlated with van der Waals volume (r = 0.97), parachor (r = 0.92), 

The different nature of MR, as compared to hydrophobic and steric properties, can only be detected in cases where a proper selection of substituents allows this. One sueh example is the inhibition of malate dehydrogenase by 4-hydroxyquinoline-3-carboxylic acids (5), where the interaction of the ligands with the enzyme is described better by MR (eq. 36) than by Jt (pljo vs. Ji n = 13 r = 0.604 s = 0.716), and the respiration inhibition of ascites tumor cells, where the transport into or the accumulation in the cells is more appropriately described by Jt (eq. 37 same set of compounds) than by MR (piso vs. MR n = 14 r = 0.699 s = 0.554) (Table 9) [293]. 

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The basic premise of Kamlet and Taft is that attractive solute—solvent interactions can be represented as a linear combination of a nonspecific dipolarity/polarizability effect and a specific H-bond formation effect, this latter being divisible into solute H-bond donor (HBD)-solvent H-bond acceptor (HB A) interactions and the converse possibility. To establish the dipolarity/polarizability scale, a solvent set was chosen with neither HBD nor HBA properties, and the spectral shifts of numerous solvatochromic dyes in these solvents were measured. These shifts, Av, were related to a dipolarity/polarizability parameter ir by Av = stt. The quantity ir was... 

IT is the dipolarity/polarizability parameter. a. is the solvent HBD (aeidity) parameter. 

Finally we mention the very recent development of a scale of directional substituent polarizability parameters from ab initio calculations of polarizability potentials135. It is expected that this scale of oa values will prove of considerable utility in correlation analysis, often in association with oF values. The o, value of S02Me is given as — 0.62 cf. H, 0.00 N02, - 0.26 COMe, - 0.55 SMe, - 0.68 t-Bu, - 0.75. 

Thole s polarizability parameters were selected to optimize the molecular polarizabilities for a set of 16 molecules. The method was later expanded to fit 52 molecules [146], It must be emphasized that this electric-field damping method is totally independent of the polarization scheme used. For the Drude and fluctuating charge methods only /i(r) is required, whereas for methods based on induced dipoles both /i(r) and /2(r) are necessary. In the context of the induced dipole model other models were proposed since the formula of Thole does not provide enough attenuation. For example, in Ref. [152] the field is evaluated using... 

A common feature of the various methods that we have developed for the calculation of electronic effects in organic molecules is that they start from fundamental atomic data such as atomic ionization potentials and electron affinities, or atomic polarizability parameters. These atomic data are combined according to specific physical models, to calculate molecular descriptors which take account of the network of bonds. In other words, the constitution of a molecule (the topology) determines the way the procedures (algorithms) walk through the molecule. Again, as previously mentioned, the calculations are performed on the entire molecule. 

From comparative molecular field analysis (COMFA)5. This method can be used for electrical, steric and polarizability parameters. 

From topological methods. This method is best restricted to steric effect and polarizability parameters. 

The polarizability parameter used in this work, a, is given by the expression ... 

The new treatment had its origins partly in ab initio molecular orbital calculations of substituent effects and partly in extensive studies of gas-phase proton transfer reactions from about 1980 (Section V.A). Various aspects of this work essentially drew attention to the importance of substituent polarizability. In 1986 Taft, Topsom and their colleagues252 developed a scale of directional substituent polarizability parameters , oa, by ab initio calculations of directional electrostatic polarization potentials at the 3-21G//3-31G level for a large set of CH3X molecules. The oa values were shown to be useful in the correlation analysis of gas-phase acidities of several series of substrates252, and such work has subsequently been extended by Taft and Topsom151. 

The solubility of C60 and C70 in a series of vegetable oils, namely olive, sunflower, peanut, soybean, linseed and castor oil, has been determined quantitatively spectrophotometrically. Additionally, the solubility of C60 and C70 has been determined quantitatively in the methyl esters of brassica oilseed and only qualitatively in molten cow butter, molten stearic acid and molten behenamide. The experimental results show that the solubility of fullerenes appears to be dependent on the unsaturation level of the fatty acids composing the vegetable oils being lower in oils with higher unsaturation level. The solubility has been found dependent also on the polarizability parameter of the vegetable oils. 

At first glance the relationship between fullerene solubility and fatty acids unsaturation may appear as a surprise. However, it should be noticed that the unsaturation level of vegetable oils correlates also with their refractive index (Martinenghi, 1963). Thus, following the approach of Sivaraman et al. (1994), it is possible to show the change in solubility as function of the polarizability parameter of the solvent defined as ... 

Thus, by plotting the log of the fullerene molar fraction x 107 (Log %) against the polarizability parameter of the various oils one obtains a reasonable linear correlation, which shows the same trend of the unsaturation level. Such a graph is shown in Fig. 13.2 and suggests that the fullerene molar fraction decreases by increasing the polarizability parameter. 

Fig. 13.2 Variation of Log (Mole Fraction x 107) with the polarizability parameter Pp = [(n2 - 1) /( 2 + 2)] for both Cm and C70 in various triglycerides of fatty acids. The triangles refer to C60 and...

The correlations with data on gas phase reactions have served to establish that the parameters calculated by our methods are indeed useful for the prediction of chemical reactivity data. Their application is, however, not restricted to data obtained in the gas phase. This has been shown through a correlation of pK values (in H O) of alcohols with residual electronegativity and polarizability parameters, by including a parameter that is interpreted to reflect steric hindrance of solvation ( ),... 

Figure 5, Experimental gas phase acidity data of alcohols plotted against values calculated from electronegativity and polarizability parameters. (Reprinted from Gasteiger, J. Hutchings, M.G. J. Am. Chem. Soc. 1984, 106, 6489).

Atomic polarizabilities Pm for atoms M may be used as polarizability parameters but they are not directly comparable to a values, thus a comparison of coefficients obtained from correlations with a are not directly comparable to those obtained with Pm - In order to obtain a values for some atoms we have first defined AP in equation 19 ... 

The rotational barrier increases with increasing ionic radius of the metal ion. We have noted above that rj is highly linear in the polarizability parameters a and Vm and are therefore unable to determine whether this dependence is due to ionic size or ionic polarizability. 

From topological algorithms . This method is best restricted to steric effects and polarizability parameters. The nature of topological parameters has been described. They are composite parameters and result from a count of structural features. ... 

For alkyl and cycloalkyl groups, the number of carbon atoms in the group is a good polarizability parameter when no other type of substituent is present in the data set. Improved results are obtained on using corrected values of wc for cycloalkyl groups . 

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. 

Ca represents the contribution of the polarizability parameter a to the regression equation r is the partial correlation coefficient of cri with a. 

Tab. 7 Values of the electron-richness ( s) and polarizability (/ ) parameters for 16-electron metal sites Ms ...

Taft Taagepera Abboud Wolf DeFrees Hehre Bartmess Mclver /. Am. Chem. Soc. 1978, 100, 7765. For a scale of polarizability parameters, see Hehre Pau Headley Taft Topsom /. Am. Chem. Soc. 1986,108, 1711. Bartmess Scott Mclver/. Am. Chem. Soc. 1979, 101, 6056. 

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