Inductive Polar Constants

Assuming that resonance, steric and inductive effects are additive, an inductive polar substituent constant (qj) may be defined by employing standard reactions reasonably assumed to possess no resonance transmission or steric effect. 

Roberts and Moreland measured the dissociation constants for a series of 4-substituted bicyclo[2.2.2]octane-l-carboxylic acids (Equation 17) and defined an inductive polar substituent constant a by Equation (18).  

The factor, 1.65, is employed to scale the a values so that they approximate the Hammett a constants for the substituents in question. 

An inductive polar substituent constant (a, ) based on the dissociation of 4-substituted quinuclidines (Equations 19 and 20) was introduced by Grob no scaling factor is used in this analysis to relate the values to Hammett s a. 

While g parameters from the dissociation of 4-substituted bicyclo-[222]octane-l-carboxylic acids are excellent measures of the inductive polar effect they suffer from the problem that the carboxylic acids cannot be synthesised readily for a wide range of X-substituents. A more substantial (but not universal) range of Gj constants is known than for g parameters.  

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In this manner one can estimate the constants of other substituents. They seem to change in parallel with the inductive (polar) constants of the sub-stituents". ... 

Finally, in this account of multiparameter extensions of the Hammett equation, we comment briefly on the origins of the a, scale. This had its beginning around 1956 in the a scale of Roberts and Moreland for substituents X in the reactions of 4-X-bicyclo[2.2.2]octane-l derivatives. However, at that time few values of o were available. A more practical basis for a scale of inductive substituent constants lay in the o values for XCHj groups derived from Taft s analysis of the reactivities of aliphatic esters into polar, steric and resonance effects . For the few o values available it was shown that o for X was related to o for XCHj by the equation o = 0.45 <7. Thereafter the factor 0.45 was used to calculate c, values of X from o values of XCH2 . ... 

Separation of Electronic and Nuclear Motions. The polarizabilities of the ground state and the excited state can follow an electronic transition, and the same is true of the induced dipole moments in the solvent since these involve the motions of electrons only. However, the solvent dipoles cannot reorganize during such a transition and the electric field which acts on the solute remains unchanged. It is therefore necessary to separate the solvent polarity functions into an orientation polarization and an induction polarization. The total polarization depends on the static dielectric constant Z), the induction polarization depends on the square of the refractive index n2, and the orientation polarization depends on the difference between the relevant functions of D and of n2 this separation between electronic and nuclear motions will appear in the equations of solvation energies and solvatochromic shifts. 

Dipole-Dipole Interaction. The first of the four terms in the total electrostatic energy depends on the permanent dipole moment of the solute molecule of radius a (assuming a spherical shape) immersed in a liquid solvent of static dielectric constant D. The function f(D) = 2(D - l)/(2D + 1) is known as the Onsager polarity function. The function used here is [f(D) — f(n2)] so that it is restricted to the orientational polarity of the solvent molecules to the exclusion of the induction polarity which depends on the polarizability as of the solvent molecules, related to the slightly different Debye polarity function q>(n2) according to... 

The r value should be a measure of the positive charge stabilization through the TT-delocalization interaction with the aryl rr-system in the incipient carbocation or the carbocationic transition state and will vary significantly with the a-R-substituents. Mishima et al. (1990c) found that the r values for all these systems [IC" ], ArC R R, can be correlated using (32) in terms of both resonance Act r and inductive polar a° substituent constants of R and R, ... 

The Taft o constant (or o electronic constant, Taft polar constant) was proposed by Taft [Taft, 1956] to measure the inductive effect in the aliphatic series ... 

Taft polar constant Taft a constant -> electronic substituent constants (O inductive electronic constants)... 

Grob, C.A. and Schlageter, M.G. (1976). 31. The Derivation of Inductive Substituent Constants from pKa Values of 4-Substituted Quinuclidines. Polar Effects. Part I. Helv.Chim.Acta, 59, 264-276. 

In the early 1950s Taft (10) outlined a sound quantitative basis for the estimation of steric effects and for separating them from polar and resonance effects. This derivation follows the standard extrathermodynamic approach and is therefore empirical. The definition of steric substituent constants is closely related to polar substituent constants, for they are obtained from the same reference system (10). The polar substituent constants, however, have been shown to arise from electronic effects, and they strongly correlate with the inductive substituent constants (10, 43, 61). 

The Hiickel molecular orbital model and its applications in organic chemistry are discussed in a three-volume series of books. Heats of hydrogenation data have been collected and discussed in a useful short review Chemical Abstracts data retrieval has been covered through to the end of 1974. Allied to this is an extensive review of the nature of strain in organic molecules. Other major reviews deal with the biosynthesis of sesquiterpenes, the use of inductive substituent constants to assess the effect of polar substituents on organic reaction rates, and non-classical ions. ... 

The polarization of chemical bonds due ro shifts of their electron pairs in the diiection of an elecrooegative group. A quantitative assessment of the inductive erects of groups (substituents) is given by the Taft aliphatic compounds and the inductive cri-constants forromaticcompounds. 

Research on the nature of substituent constants continues, with results that can bewilder the nonspecialist. The dominant approach is a statistical one, and the main goal is to dissect substituent effects into separate electronic causes. This has led to a proliferation of terms, symbols, and conclusions. A central issue is (here we change terminology somewhat from our earlier usage) to determine the balance of field and inductive effects contributing to the observed polar electronic effect. In... 

As suggested by Roberts and Moreland many years ago (1953), the acidity constants of 4-substituted bicyclooctane-l-carboxylic acids provide a very suitable system for defining a field/induction parameter. In this rigid system the substituent X is held firmly in place and there is little possibility for mesomeric delocalization or polarization interactions between X and COOH (or COO-). Therefore, it can be assumed that X influences the deprotonation of COOH only through space (the field effect) and through intervening o-bonds. On this basis Taft (1956, p. 595) and Swain and Lupton (1968) were able to calculate values for o and crR. 

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