Inductive parameter

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. 

Marriott and Topsom have recently developed theoretical scales of substituent field and resonance parameters. The former correspond to the traditional inductive parameters but these authors are firm believers in the field model of the so-called inductive effect and use the symbol The theoretical substituent field effect scale is based on ab initio molecular orbital calculations of energies or electron populations of simple molecular systems. The results of the calculations are well correlated with Op values for a small number of substituents whose Op values on the various experimental scales (gas-phase, non-polar solvents, polar solvents) are concordant, and the regression equations are the basis for theoretical Op values of about 50 substituents. These include SOMe and S02Me at 0.37 and 0.60 respectively, which agree well with inherent best values in the literature of 0.36 and 0.58. However, it should be noted that a, for SOMe is given as 0.50 by Ehrenson and coworkers . 

Taft and Topsom151 have fairly recently written an extensive review of the electronic effects of substituents in the gas phase. This article includes a tabulation of substituent inductive and resonance parameters. The inductive parameters (designated Op) are based on measured spectroscopic properties in either the gas phase or in hydrocarbon or similar solvents. The resonance parameters were arrived at through the treatment of 38 gas-phase reactivity series by iterative multiple regression, using the cr values of Bromilow and coworkers155 as the starting point. The of value for NO2 was found to be 0.65 (quoted... 

Inamoto and co-workers (97,98) introduced a new inductive parameter i (iota) based on atomic properties of X, namely the effective nuclear charge in the valence shell and the effective principal quantum number, as well as E(X) (97). They thereby established a reasonable correlation between the a-SCSs in substituted methanes and ethanes and the t. parameters for a series of substituents not including X = CN and I (97). 

The rates of H-D exchange at the a-positions have been determined for a series of N- substituted pyridinium salts and pyridine 1-oxides in D20 at 75 °C (Scheme 197) (70JA7547). The rates give a good correlation with the Taft inductive parameter <77 pi = 15). The positively charged nitrogen in a ring has been estimated to activate the a-position towards deprotonation and ylide formation by a factor of 1014 16. 

A systematic and intensive theoretical study of reactivity has been reported by Brown and his colleagues,8,115,139-142 who discussed the reactivity of pyridine, quinoline, and isoquinoline in terms of localization energies. They investigated the values of these indices, first of all for electrophilic substitution, with regard to the value of the Coulomb integral of the heteroatom orbital and the orbitals adjacent to it (auxiliary inductive parameters). They demonstrated that the course of electrophilic substitution can be estimated from theoretical reactivity indices if 77-electron densities are used for reactions that occur readily and localization energies for those occurring only reluctantly. 

In view of the highly reactive character of pyrrole, the controlling factor for electrophilic substitution is considered to be the v-electron densities. To obtain an agreement between Hiickel MO calculations and experimental observations of chemical reactivity, recourse has to be made to the use of the auxiliary inductive parameter. Satisfactory results are obtained when h = 2 and = 0.25. 

The somewhat arbitrary use of the auxiliary inductive parameter in the Hiickel MO calculations has been questioned and the effect of the nonuniform distribution of a-electron densities, particularly in the CN bond,90 upon the 77-electron distribution has been discussed.65 Variable electronegativity self-consistent field (VESCF) molecular orbital calculations, which are an elaboration of the conventional SCF method and allow for the variation in electronegativity of an... 

Taft separated the resonance from the inductive substituent effects and proposed Equation 2.15. The inductive parameter, ah is based on a obtained from aliphatic systems (see p. 68).14... 

Now that the steric parameter can be evaluated, the inductive parameter is available. Taft noted that the transition-state structures for acid- and base-catalyzed hydrolysis of esters (15 and 16, respectively) differ from each other by only tiny protons. Therefore the steric effect of a substituent should be approx-... 

The inductive parameter, aL, is the same in both the meta and para positions the resonance parameter, aR, is, of course, appreciably different in the two positions the inductive reaction constant is pv This three-parameter equation was employed to calculate reaction types of meta- and para-substituted benzene derivatives. It was shown that free radical processes yielded different values, and a common set of resonance parameters was not possible. The conclusion is, of course, identical to that of van Bekkum and his co-workers (1959). The utility of a unique set of resonance parameters for electrophilic reactions is obscured by the inclusion of both electrophilic side-chain and electrophilic substitution reactions in a single series. 

Roberts et al. (1993) have provided an in-depth analysis of QSARs for dehydrohalogenation reactions of polychlorinated and polybrominated alkanes. The QSARs were developed based on a dataset of 28 polychlorinated and polybrominated compounds in aqueous solution at 25° C. The QSARs are for the OH- and water-mediated second-order elimination reactions (E2), as Equation (25) shows. The first QSAR is for base-promoted dehydrochlorination and is based on the inductive parameter o, (Equations (26) and (27)) ... 

Sum of inductive parameters sigma (molecules atom) for all atoms within a molecule Sum of absolute values of group inductive parameters sigma (molecule- -atom) for all atoms within a molecule... 

Largest positive group inductive parameter sigma (molecules atom) for atoms in a molecule... 

Largest (by absolute value) negative group inductive parameter sigma (molecules atom) for atoms in a molecule Largest positive atomic inductive parameter sigma (atom molecule) for atoms in a molecule... 

The model requires one further definition in order to predict ignition. A curve of chemical induction time as a function of temperature must be included in order to define the induction parameter,... 

Figure 6. Calculated results from the similarity solution plotted as a function of time. Here R0 is the characteristic radius for energy deposition, A is the nonlinear amplitude of the temperature and density functions, T (R = 0) is the central temperature, and I is the induction parameter. The indicates the predicted induction time r0 = 1.0 x 10 4 sec E0 — 4.0 X 10 ergs R0 = 0.1 cm.

Additional problems in theoretical calculations are (1) selection of the coulomb and resonance integral parameters (2) whether an auxiliary inductive parameter be used for the a-carbons (3) whether d orbitals, etc., be taken into account for S, Se, and Te and (4) what type of calculations to use. 

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