Polarizability descriptors

Polarizability-related parameters such as molar refractivity are mostly described as steric descriptors with the acknowledgement of some extra electronic information. Their dual character combines elements that account for the general steric bulk as well as for the polarizability, which refers to the displacement of charges within molecules influenced by an electric field (i.e. induced dipoles). Evidently, molar polarizability influences various global properties of compounds, such as their hydrophobicity, by contributing to the solvation energies in different solvents (Lewis, 1989 Schuiirmann, 1990b). The polarizability factor a corresponds to the dipole induced by the electric field E  

This formula represents the two components in this parameter the term - l)/ ri + 2) indicates the delocalizability of the electrons in the molecule (i.e. the aptness of the electron system to be polarized). The relation MW/d reveals MR to depend on the molar volume. The larger the polar part of a molecule, the larger is its MR value. Atomic molar refractivity contributions are assumed to be additive and can be retrieved from tabulations (e.g. Hansch, 1975 Seydel and Schaper, 1979). The closely related parachor, the product of the molar volume and a surface tension term, is of negligible relevance for QSAR studies and cannot be recommended for use, except for the empirical estimation of boiling points (section 4.5). 

The dual nature of these polarizability descriptors poses severe problems with regard to their use in QSAR analyses. Only when the test set is designed so that intercorrelations with, for example, steric or lipophilic parameters can 

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Some empirical polarity / polarizability descriptors which were proposed to measure the ability of the compound to influence a neighbouring charge or dipole by virtue of dielectric interactions are reported below. 

This term is a measure of the exoergic balance (i.e. release of energy) of solute-solvent and solute-solute dipolarity / polarizability interactions. This term, denoted by n, describes the ability of the compound to stabilize a neighbouring charge or dipole by virtue of nonspecific dielectric interactions and is in general given by -> electric polarization descriptors such as -> dipole moment or other empirical - polarity / polarizability descriptors [Abraham et al, 1988]. Other specific polarity parameters empirically derived for linear solvation energy relationships are reported below. 

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 model is highly empirical in nature and the two interrelated polarizability descriptors (section 1.2.2) can be only vaguely related to dispersive interactions in the liquid phase. The estimates for the respective monofunctional compounds are generally within 5-10% of the experimental data, but larger deviations occur for polyfunctional substances. For a set of heterogeneous compounds, a mean method error of 21% (°C) has been reported (Lynch et a/., 1991). Significant outliers comprise (lUCT, 1992) ... 

The HIV-1 inhibitory activity is triggered by a hydrophobic interaction followed by energetic stabilization of the ligand/substrate (pyrididone derivative/viral protein) interaction here modeled by the heat of molecular formation and eventually completed by the ionic field influence herein represented by the polarizability descriptor. 

Previous studies with a variety of datasets had shown the importance of charge distribution, of inductive effect), of r-electronegativity, resonance effect), and of effective polarizability, aeffi polarizability effect) for details on these methods see Section 7.1). All four of these descriptors on all three carbon atoms were calculated. However, in the final study, a reduced set of descriptors, shown in Table 3-4, was chosen that was obtained both by statistical methods and by chemical intuition. 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

Quantum chemical descriptors such as atomic charges, HOMO and LUMO energies, HOMO and LUMO orbital energy differences, atom-atom polarizabilities, super-delocalizabilities, molecular polarizabilities, dipole moments, and energies sucb as the beat of formation, ionization potential, electron affinity, and energy of protonation are applicable in QSAR/QSPR studies. A review is given by Karelson et al. [45]. 

The HYBOT descriptors were successfully applied to the prediction of the partition coefficient log P (>i--octanol/water) for small organic componnds with one acceptor group from their calculated polarizabilities and the free energy acceptor factor C, as well as properties like solubility log S, the permeability of drugs (Caco-2, human skin), and for the modeling of biological activities. 

These first components of the autocorrelation coefficient of the seven physicochemical properties were put together with the other 15 descriptors, providing 22 descriptors. Pairwise correlation analysis was then performed a descriptor was eliminated if the correlation coefficient was equal or higher than 0.90, and four descriptors (molecular weight, the number of carbon atoms, and the first component of the 2D autocorrelation coefficient for the atomic polarizability and n-charge) were removed. This left 18 descriptors. 

H-bonding is an important, but not the sole, interatomic interaction. Thus, total energy is usually calculated as the sum of steric, electrostatic, H-bonding and other components of interatomic interactions. A similar situation holds with QSAR studies of any property (activity) where H-bond parameters are used in combination with other descriptors. For example, five molecular descriptors are applied in the solvation equation of Kamlet-Taft-Abraham excess of molecular refraction (Rj), which models dispersion force interactions arising from the polarizability of n- and n-electrons the solute polarity/polarizability (ir ) due to solute-solvent interactions between bond dipoles and induced dipoles overall or summation H-bond acidity (2a ) overall or summation H-bond basicity (2(3 ) and McGowan volume (VJ [53] ... 

A volume-related term (expressed by polarizability) and electrostatics (expressed by partial atomic charge) made minor contributions to intestinal absorption in humans. Lipophilicity, expressed by logP or logD values, shows no correlation with the human absorphon data. Recently, similar results were obtained for 154 passively transported drugs on the basis of surface thermodynamics descriptors [39] ... 

Valko et al. [37] developed a fast-gradient RP-HPLC method for the determination of a chromatographic hydrophobicity index (CHI). An octadecylsilane (ODS) column and 50 mM aqueous ammonium acetate (pH 7.4) mobile phase with acetonitrile as an organic modifier (0-100%) were used. The system calibration and quality control were performed periodically by measuring retention for 10 standards unionized at pH 7.4. The CHI could then be used as an independent measure of hydrophobicity. In addition, its correlation with linear free-energy parameters explained some molecular descriptors, including H-bond basicity/ acidity and dipolarity/polarizability. It is noted [27] that there are significant differences between CHI values and octanol-water log D values. 

The retention depends on the nature of both the stationary phase and the organic modifier in the mobile phase. Therefore CHI values obtained using different systems show different sensitivities towards solute characteristics. This has been studied systematically and used for the quantitative calculation of solute molecular descriptors (H-bond donor capacity, H-bond acceptor capacity and dipolarity/polarizability) for application in a general solvation equation [21]. 

MolSurf parameters [33] are descriptors derived from quantum mechanical calculations. These descriptors are computed at a surface of constant electron density, with which a very fine description of the properties of a molecule at the Van der Waals surface can be obtained. They describe various electrostatic properties such as hydrogen-bonding strengths and polarizability, as well as Lewis base and acid strengths. MolSurf parameters are computed using the following protocol. 

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. 

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