Substituent constants errors

It is important to note that the fitting according to eq. (1) requires zero intercept behavior i.e., F =. 00 for H (for which Oj = Or =. 00). While we recognize that the data for the unsubstituted (H) member of a set may be as subject to experimental error as any other member, such error is generally relatively small for a set of reliable data. Any constant error from this source will be distributed among all of the substituents in such a manner as to achieve best fit. Any loss in precision of fitting of the set which may result by such a procedure we believe is a small price to pay compared to the violence done by introduction in eq. (I) of a completely variable constant parameter. The latter procedure has been utilized by other authors both in treatments by the simple Hammett equation and by the dual substituent parameter equation. 

These results explain the deviation of these values from the general observation that substituent constants for groups of the type M(ZAk) are usually constant within experimental error. 

The lack of fit of the CH2SnMe3 group is certainly due to an error in the value of era,. The poor fit of the SiBr3 and SiF3 groups is probably also due to errors in their substituent constants. The cause for the lack of fit of the N3 group is unknown. 

Group-contribution estimation techniques were developed for -it and a. The contributions were obtained by regressing the substituent constants tabulated by Hansch and Leo (1979). Overall the estimation techniques have considerable error and cannot be used for quantitative estimation. However, they provide correct overall trends and thus inform the designer of promising substitutions. 

Indeed, a plot of the AD [Eq. (9)] versus the cAD [Eq. (19)] values follows an excellent correlation (r2 > 0.999) with the expected slope of 0.1. A typical deviation amounts to 0.0001cm-1 and is, thus, within experimental error. Consequently, the initially defined AD parameter [Eq. (9)], like Arnold s values, serves as radical substituent constant. 

We now have available a small group of primary aj values (from set 01) which are as close to being properly scaled as is possible at the present time. This small set of primary constants is insufficient for the needs of those workers who are interested in applying correlation analysis to a very wide range of structural types. It is therefore necessary for us to make use of secondary sources. As was pointed out by McDaniel and Brown (28), the use of secondary sources may lead to large errors in the values of the (Tm and Op substituent constants. 

This method has three disadvantages (1) As more data accumulate, all substituent constants must be revised. Thus, the values of the constants are continually subject to change. (2) With a large body of data, the periodic revision of the substituent constants requires a large amount of time and effort even with the aid of a computer. (3) In treating the data statistically, the assumption is made that all the data can be represented by a common set of substituent constants, and that small deviations from this common set of substituent constants represent noise due to some combination of experimental error and of minor effects. In this averaging process, it is possible to submerge small, subtle, and important effects. 

In our search for a method for assigning errors to the substituent constants evaluated from various secondary sources, we have considered two possible approaches. In the first of these, we assume that the method normally used for compounding of errors (43) in experimental work may be applied to the evaluation of the standard error of substituent constants. For a quantity y which is obtained from the experimental measurements and X2 by the function... 

All ionic substituent constants are very variable, probably due to their dependence upon the type of solvent and the ionic strength of the solution. It is for this reason that we have labeled all substituent constants for these groups uncertain, no matter how small the error reported for the ionization constants from which they were determined. Use of these constants should be avoided when... 

The substituent constants presented here are the best obtainable from chemical reactivities at the present time. They are generally applicable in protonic solvents. The sparse data available suggests that they are probably applicable in dipolar aprotic and nonpolar solvents and in the gas phase. These statements do not apply to ionic substituents or to the OH group, all of which are strongly dependent on medium. The ff/ constants reported here are the best choice for any correlation of substituent effects of groups attached to sp hybridized carbon. The tr constant are inferior and should not be used. The evidence presented here clearly indicates that the use of Swain-Lupton constants or their modifications should be discontinued. The correction proposed by Exner for ct/ and or constants is in error. These corrected constants should not be used. 

These results demonstrate that, within experimental error, the corresponding reaction constants for the two reactions, solvolysis and rearrangement, are the same. In other words, the two reactions have the same dependence on substituent effects, which is consistent with Scheme 8-10 because the transition state for rearrangement is identical to the first transition state in the mechanism of solvolytic dediazoniation. 

The error in the isotope effect is l/ftplfAkn)2 + AhAd)2 x (A d)2]172 where Akn and A/. [, are the standard deviations for the rate constants for the reactions of the undeuterated and deuterated substrates, respectively. The Hammett p values were obtained by changing the para-substituent in the nucleophile. 

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