Polarizability effects

In Section 7.1.2 a method for the calculation of mean molecular polarizability was presented. Mean molecular polarizability can be calculated from additive contributions of the atoms in their various hybridization states in a molecule (see Eq. (6)). Mean molecular polarizability, a, expresses the magnitude of the dipole moment, fi, induced into a molecule imder the influence of an external field, E (Eq. (15)) 

In many chemical applications, however, it would be more interesting to know how polarizability can stabilize a charge introduced into a molecule. Thus, rather than the global molecular property, mean molecular polarizability, a local, site-specific value for polarizability is needed. 

An effective polarizability, reflecting the stabilization of a positive charge on the protonated nitrogen atom through polarizability, is calculated by Eq, (16). 

The contribution of an atomj to the polarizability effect is attenuated by the number of bonds, H , between this atom and the site of protonation, i. 

The method for calculating effective polarizabilitie.s wa.s developed primarily to obtain values that reflect the stabilizing effect of polarizability on introduction of a charge into a molecule. That this goal was reached was proven by a variety of correlations of data on chemical reactivity in the gas phase with effective polarizability values. We have intentionally chosen reactions in the gas phase as these show the predominant effect of polarizability, uncorrupted by solvent effects. 

The significance of the values calculated for the effective polarizability was first established with physical data, among them relaxation energies derived from a combination of X-ray photoelectron and Auger spectroscopy, as well as N-ls ESCA data 

From our point of view, however, the most important applications of effective polarizability are to be found in correlating chemical reactivity data. Thus, the proton affinity (PA) of 49 unsubstituted alkylamines comprising primary, secondary and tertiary amines of a variety of skeletal types correlate directly with effective polarizability values (Fig. 22). 

In solution, stabilization due to polarizability is of less importance, as the solvent will provide other charge stabilization mechanisms. However, recent work shows that polarizability is still of influence in solution 5 ss.ss) 

Following Wilson and Madden s approach [1], Tangney and Scandolo (TS) used a more flexible form for the potential which incorporates the effects of dipole polarization of the oxygen ions including the effective dipoles induced by the short-range 

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Figure 3-6. a) The charge distribution, b) the inductive effect, and c) the resonance effect, d) the polarizability effect, e) the steric effect, and f) the stereoelectronic effect,... 

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. 

To follow a simple scheme for calculating the polarizability effect... 

The polarizability effect can be calculated by a simple attenuation model. 

Fundamental enthalpies of gas-phase reactions such as proton affinities or gas-phase acidities can be correlated with the values of the Inductive and the polarizability effect. 

The knowledge base is essentially two-fold on one hand it consists of a series of procedures for calculating all-important physicochemical effects such as heats of reaction, bond dissociation energies, charge distribution, inductive, resonance, and polarizability effects (.see Section 7.1). The other part of the knowledge base defines the reaction types on which the EROS system can work. 

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 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... 

The n values were high for all of the ionic liquids investigated (0.97-1.28) when compared to molecular solvents. The n values result from measuring the ability of the solvent to induce a dipole in a variety of solute species, and they will incorporate the Coulombic interactions from the ions as well as dipole-dipole and polarizability effects. This explains the consistently high values for all of the salts in the studies. The values for quaternary ammonium salts are lower than those for the monoalkylammonium salts. This probably arises from the ability of the charge center on the cation to approach the solute more closely for the monoalkylammonium salts. The values for the imidazolium salts are lower still, probably reflecting the delocalization of the charge in the cation. 

Analogous DSP treatments, but with differences with regard to the basis of the calculations, were proposed by Charton (1981) and by Swain s group (Swain and Lupton, 1968 Swain et al., 1983). The potential significance of polarizability effects resulted in a triple substituent parameter treatment (Taft, 1983). A slightly different... 

Meyers and coworkers141 measured the pKa values of a number of arylthio-, arylsulfinyl-and arylsulfonyl-phenols. From their few results relating to the effects of 4 - R on 4-OH, Hogeveen138 inferred that relative influence of substituents was about the same in the three series, contrasting with what he had found in his various series of acrylic acids. He attributed this to the compensation of the polarizability effect (see above) by the influence of a(pd) conjugation in the anions of the sulfinyl and sulfonyl series. Meyers and coworkers141 were more interested in the effect of moving the OH from the 4- to the 2-position (see Section III.D). 

However, there is evidence against d-orbital overlap and the stabilizing effects have been attributed to other causes. In the case of a PhS substituent, carbanion stabilization is thought to be due to a combination of the inductive and polarizability effects of the group, and d-pn resonance and... 

CMR represents the overall calculated molar refractivity. Its negative sign bring out a steric effect. It is interesting to note here that there is a high mutual correlation between ClogF and CMR (r= 0.966). Thus, it is very hard to predict for this data set if it is a negative hydrophobic or a polarizability effect. 

Mahoney, M. W. Jorgensen, W. L., Quantum, intramolecular flexibility, and polarizability effects on the reproduction of the density anomaly of liquid water by simple potential functions, 7. Chem. Phys. 2001,115, 10758-10768... 

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). 

An extensive study132 has been presented on the polarizability effects of alkyl groups in RX moieties (R = Me, Et, i-Pr and i-Bu X = CH2, S, SO2, O and N) in families of weak acids and on the stabilities of adjacent anions and radicals in DMSO solution. Some of the results related to the 9-(dialkylamino)fluorenes are given in Table 12. The increases in acidity are believed to be caused by the progressive increases in anion stabilizing... 

Taft and Topsom s article151 and also Topsom s171 should be consulted for details of the setting up of the scales of substituent parameters. The equation has been applied to a wide range of gas-phase reactivities. (In the multiple regressions an intercept term is often permitted, but usually this turns out to be indistinguishable from zero, as it should be if equation 20 is valid.) For aliphatic and alicyclic saturated systems the resonance term is duly negligible. The roles of field, resonance and polarizability effects are discussed and the interpretat of the various p values is attempted. 

When the equation is applied to reactions in solution, it is found that polarizability effects tend to be much smaller than in the gas phase, but the PSP equation has to be adapted to include Substituent Solvation Assisted Resonance (SSAR). (See Section III.D.) The PSP equation then assumes the form of equation 21 ... 

Polarizability Effects. The next model demonstrates that an additivity scheme can be combined with other forms of mathematical relations to extract the fundamental parameters of a model from primary information. And furthermore, it shows than an additivity scheme useful for the estimation of a global molecular proparty can be modified to obtain a local, site specific property. 

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