Polarizability index

In the work of Famini and Wilson,a molecular volume, Vmc, (units of 100 A ) is used to model the cavity term that measures the energy required to create a solute-molecule sized cavity in the solvent. The dipolarity/polarizability term, which attempts to account for dispersion-type interactions, is modeled by the polarizability index, tij, (unitless). This index is defined as the average molecular polarizability divided by the molecular volume, a/Vmc, and helps account for the correlation between polarizability and molecular volume. 

In this equation, Vmc represents the molecular van der Waals volume (in A ) and indicates the cavity size needed in the solvent matrix to accommodate the solute. The polarizability index, tii, is obtained by dividing the polarizability volume by the molecular volume, to give a alternatively size-independent quantity that indicates the ease with which electrons may move throughout the solvent molecule. The solvent HBD... 

Two of the hydrophihcity scales in Table 2 were derived from experimental measures of the behavior of amino acids in various solvents, namely partitioning coefficients [K-D index of Kyte and Doolittle (30)] or mobility in paper chromatography [Rf index of Zimmerman et al. (31)]. By contrast, the Hp index was obtained from quantum mechanics (QM) calculations of electron densities of side chain atoms in comparison with water (32). The Hp index is correlated highly with these two established hydrophobicity scales (Table 4). Therefore, like the polarizability index, it is possible to represent fundamental chemical properties of amino acids (hydrophUicity, Hp) with parameters derived from ab initio calculations of electronic properties. However, in contrast to polarizabihty (steric effects), hydrophihcity shows significant correlation with preference for secondary structure. Thus, hydrophobic amino acids prefer fi-strands (and fi-sheet conformations) and typically are buried in protein structures, whereas hydrophilic residues are found commonly in turns (coil structure) at the protein surface. 

Several scales presented in Table 3 show promise as measures of fundamental electronic properties of amino acids as does the Hp index of hydrophilicity. Nevertheless, additional improvements are desirable. The polarizability index of steric effects should include hyperconjugation as a component. Clearly, the movement of electrons into antibonding orbitals contributes to molecular deformation (24). The Hp index is based on PM3 calculations of electron densities for the component atoms of amino acid side chains. A more integrative approach with higher-order theory is likely to refine this measure additionally. 

TLSER polarizability index theoretical linear solvation energy relationships... 

The Inner Molecular Polarizability Index (IMPI) was defined as [Cao, Liu et al., 1999[ ... 

IMPI = inner molecular polarizability index electric polarization descriptors ( polarizability effect index)... 

TLSER polarizability index —> Theoretical Linear Solvation Energy Relationships... 

Increasing Kamlet-Taft polarity/polarizability index ir ... 

Kamlet-Taft polarity/polarizability index p Density (kg m ) a Diameter, molecular (nm)... 

Many attempts have been made to develop empirical measures of solvent polarity that reflect the interaction of polar molecules with solutes and that correlate well with chemical reactivity, and Katritzky and co-workers discussed 184 such parameters. For example, Kamlet, Taft, and co-workers proposed a general dipolarity/polarizability index, n, to measure the ability of a solvent to stabilize an ionic or polar species by means of its dielectric... 

The solvent index , (30) depends on both the polarity and the hydrogen bond donicity of the solvent or binary aqueous mixture with a cosolvent. In all the mixtures, except aqueous acetonitrile, this index is smaller than expected for ideal mixtures, as the negative < values indicate for the equimolar mixtures. The polarity/polarizability index % may be smaller (for most mixtures) or larger (for aqueous pyridine, form-amide, DMF, and DMSO) than expected for ideal mixtures, as the sign of shows for the equimolar mixtures. The latter option (p >0) occurs where the cosolvent is aromatic (pyridine) or has the =0 group (except acetone) that contributes to the polarizability. 

However, the quantities already include the interactions of the solutes with water, but properties foreign to such interactions are preferable for predictive purposes. Two such properties have been proposed and tested by Marcus [65] the Kamlet-Taft polarity/polarizability index a (Section 3.3.2.1) and the Hildebrand solubility parameter (Section 3.2.2). These as well as the intrinsic volumes of the solutes, expressed as their McGowan volumes are independent of interactions with water, hence true predictive parameters that are known or calculable from group contributions for a large number of solutes. The predictive expression (for ambient temperatures) is ... 

In equation (37) and in further equations it is understood that the moments and polarizabilities indexed with /a, k/. .. (Ib. b- -) refer to molecule A (B). For the induction and dispersion constants Cj, and the corresponding result... 

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