Inductive effect models

Attempts to distinguish inductive and field effects have been frustrated by the lack of a molecule that provides an unambiguous answer. Such a molecule would require that the low dielectric cavity of the field effect model 2 be occupied by the chemical bonds important to the inductive effect model. If a small attenuation factor is adopted for through-bond transmission of the polar effect, both models predict similar results. 2 For example, o-chlorophenylpropionic acid is weaker than expected by the inductive model 3 and is unsuitable. 

The underlying principle of the PEOE method is that the electronic polarization within the tr-bond skeleton as measured by the inductive effect is attenuated with each intervening o -bond. The electronic polarization within /r-bond systems as measured by the resonance or mesomeric effect, on the other hand, extends across an entire nr-system without any attenuation. The simple model of an electron in a box expresses this fact. Thus, in calculating the charge distribution in conjugated i -systems an approach different from the PEOE method has to be taken. 

The model adopted by Ri and Eyring is not now acceptable, but some of the more recent treatments of electrostatic effects are quite close to their method in principle. In dealing with polar substituents some authors have concentrated on the interaction of the substituent with the electrophile whilst others have considered the interaction of the substituent with the charge on the ring in the transition state. An example of the latter method was mentioned above ( 7.2.1), and both will be encountered later ( 9.1.2). They are really attempts to explain the nature of the inductive effect, and an important question which they raise is that of the relative importance of localisation and electrostatic phenomena in determining orientation and state of activation in electrophilic substitutions. 

Hiickel models of molecular electronic structure enjoyed many years of popularity, particularly the r-electron variants. Authors sought to extract the last possible amount of information from these models, perhaps because nothing more refined was technically feasible at the time. Thus, for example, the inductive effect was studied. The inductive effect is a key concept in organic chemistry a group R should show a - -1 or a —I effect (according to the nature of the group R) when it is substituted into a benzene ring. 

Wheland and Pauling (1959) tried to explain the inductive effect in terms of ar-electron theory by varying the ax and ySxY parameters for nearest-neighbour atoms, then for next-nearest-neighbour atoms and so on. But, as many authors have also pointed out, it is always easy to introduce yet more parameters into a simple model, obtain agreement with an experimental finding and then claim that the model represents some kind of absolute truth. 

Although in the above work the rate spread for detritiation was greater than for dedeuteration, surprisingly, in the reaction of lithium cyclohexylamide at 25 °C with fluorobenzenes and benzotrifluorides, the relative rates for dedeuteration and detritiation were595, respectively 2-F, 6.3 xlO5 and 3.4 x10s 3-F, 107 and 86 4-F, 11.2 and 9.1 3-CF3, 580 and 390, which therefore shows the reverse. The rate enhancement for these substituents were found to correlate reasonably with a field effect model for the inductive effect. 

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 . 

For S vl attack, considerable charge separation has taken place in the T.S. (cf. p. 81), and the ion pair intermediate to which it gives rise is therefore often taken as a model for it. As the above halide series is traversed, there is increasing stabilisation of the carbocation moiety of the ion pair, i.e. increasing rate of formation of the T.S. This increasing stabilisation arises from the operation of both an inductive effect,... 

Taft and his coworkers14-16 developed a diparametric model which separated the electrical effect into contributions from the inductive (actually the field) and resonance effects. This separation depends on the difference in the extent of electron delocalization when a substituent is bonded to an sp3 -hybridized carbon atom in one reference system and to an sp2-hybridized carbon atom in another. As the first case represents minimal delocalization and the second extensive delocalization, we have referred to the two effects as the localized and delocalized electrical effects. This diparametric electrical effect model can be written in the form ... 

Deprotonation provides the necessary electron push to kick out the electron pair joining C(6) with the nitrobenzene oxygen. If, however, N(l) is alkylated (as with the nucleosides and nucleotides), OH catalysis is much less efficient since it now proceeds by deprotonation from N(3) (with the uracils) or from the amino group at C(4) (with the cytosines). In these cases the area of deprotonation is separated from the reaction site by a (hydroxy)methylene group which means that the increase in electron density that results from deprotonation at N(3) is transferable to the reaction site only through the carbon skeleton (inductive effect), which is of course inefficient as compared to the electron-pair donation from N(l) (mesomeric effect) [26]. Reaction 15 is a 1 1 model for the catalytic effect of OH on the heterolysis of peroxyl radicals from pyrimidine-6-yl radicals (see Sect. 2.4). 

An inductive effect which involves the successive polarization of the bonds between X and Y. The decrease in the effect with increasing number of bonds is due to a falloff factor /, which decreases the effect for each successive polarization. The value of / is 0.33-0.36 . This is the classical inductive effect (CIE) model. 

Exner and Fiedler have proposed a modified inductive effect (MIE). The MIE model represents transmission through two or more paths by an expression analogous to Kirch-hoff s Law for the resistance of parallel resistors. 

Bayesian statistics are applicable to analyzing uncertainty in all phases of a risk assessment. Bayesian or probabilistic induction provides a quantitative way to estimate the plausibility of a proposed causality model (Howson and Urbach 1989), including the causal (conceptual) models central to chemical risk assessment (Newman and Evans 2002). Bayesian inductive methods quantify the plausibility of a conceptual model based on existing data and can accommodate a process of data augmentation (or pooling) until sufficient belief (or disbelief) has been accumulated about the proposed cause-effect model. Once a plausible conceptual model is defined, Bayesian methods can quantify uncertainties in parameter estimation or model predictions (predictive inferences). Relevant methods can be found in numerous textbooks, e.g., Carlin and Louis (2000) and Gelman et al. (1997). 

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