Polarizability parameters, directional

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. 

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. 

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 ... 

Physically, the higher-order ( i.e., nonlinear) terms such as 6 relate to the potential well anharmonicity. Miller has suggested that to a first approximation the second-order polarizability is directly proportional to the linear polarizability (first-order) times a parameter defining the anharmonic potential (14,15). This relationship works best for inorganic materials. In organic molecules the relationship becomes complex because the linear polarizability and the anharmonicity are not necessarily independent variables (see tutorial by D. N. Beratan). 

Hehre, W. J., Pau, C. F., Headley, A. D., et al. (1986) A scale of directional substituent polarizability parameters from abinitio calculations of polarizability potentials. Journal of the American Chemical Society, 108(7), 1711-1712. 

The connectivity indices and the polarizability parameters, however, relate a solutes solubility directly to its molecular structure, and thus could be more useful in the design and evaluation of new chemicals. A particular drawback of the polarizability parameter used here is that, unlike the LSER descriptors, it is not universally applicable to all solute-solvent interactions. It has to be defined and optimized for each property being studied. The log p descriptor is purely empirical, and does not poru ay any direct mechanistic significance in relation to the solutes molecular structure. Further, since Model 1 is significantly improved by including melting point data, it can be noted that log p alone docs not encode sufficient information relating aqueous solubility. 

Parameters which encode certain structural features and properties are needed to correlate biological activities with chemical structures in a quantitative manner. Of special value are physicochemical properties which are directly related to the intermolecular forces involved in the drug-receptor interaction as well as to the transport and distribution properties of drugs. In this respect hydrophobic, polar, electronic, and steric properties are most important most often, polarizability parameters are considered as being closely related to steric parameters and are discussed together with these parameters, although they are definitely different (if structural variation is appropriate). 

There were two schools of thought concerning attempts to extend Hammett s treatment of substituent effects to electrophilic substitutions. It was felt by some that the effects of substituents in electrophilic aromatic substitutions were particularly susceptible to the specific demands of the reagent, and that the variability of the polarizibility effects, or direct resonance interactions, would render impossible any attempted correlation using a two-parameter equation. - o This view was not universally accepted, for Pearson, Baxter and Martin suggested that, by choosing a different model reaction, in which the direct resonance effects of substituents participated, an equation, formally similar to Hammett s equation, might be devised to correlate the rates of electrophilic aromatic and electrophilic side chain reactions. We shall now consider attempts which have been made to do this. 

The proton affinities (PA) of two restricted subsets of amines were correlated directly with inductive and polarizability effect parameters, respectively (Figs. 19 and 22). These can be combined with data on other hetero-substituted amines to give a set of 80 amines of different skeletal and substitution types (e.g. Fig. 24). In this and all other systems (below), a residual electronegativity value, %l2, (Eq. 5) derived from those of the atoms of the first, 1, and second, 2, sphere neighbors of the nitrogen atom is preferred as a measure of the inductive effect49). 

They cannot be directly measured because of the chemical reactions of the dissolved molecular components, but must be calculated theoretically or estimated by correlation. Electrostatic theory does not predict negative coefficients, which are characteristic of ammonia with some salts. To us, it appears that scaled particle theory(22) is probably the best method of calculation, but the required parameters (polarizability and ion size) are not available for the salts of interest. 

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