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H. H. JAFFB [COSTRIBUTION F R O M T H E DEPARTMENT O F C l l E M I S r R Y , U N I V E R S I T Y OR
1’01. 81 CISCISNA’I’I 1
The Difference between the Hammett Equation as Applied to meta and pura Substituted Compounds’ BY H. 11. J ~ F P E RECEIVED Kovmrmm 20, 1958 In 336 reaction series of m- and p-substituted benzene derivatives for which appropriate data were available, separate Haminett correlations for the two types of compounds have been performed. T h e number of series for which the p-values are signijcantly different is larger than expected purely by chance, although no significant differences appear for 75 to ,S570 of the series esatnined. Sirnilarly no major differences are deinonstrated in tlie prccisioii with ~vhichnt- aiid p-substituted coiiipounds are represented by the Haiumett equation.
In a recent paper, Hine2 has outlined a theo- either pp and pni or between thclir standard deviaretical analysis, suggesting that the Hammett tions, or more probably both. equation cannot possibly have general validity. TABLE I One of the major conclusions of Hine’s arguments OF REACTION SERIES SiiomrNc, I>II~PEREXCT was that, even within the range of approximate TIIEXLJMBCR BETIVIEEN Pm A S D p~ .. validity of the Hammett equation, reaction conDifference Percentage showing stants (p) cannot be expected to be the same for significant difference by Applicah-umber of significant Lle v series a t 1-Test I;-Test meta and para substituents. It appeared of in18 terest to test this conclusion. We have conY sequently run separate correlations on m- and p 11 substituted compounds3 for the 336 reaction series 5 for which we had available for at least 3 substituents ci in each of the two groups. In each series, normal 4 a-, u+- or c--values were used in accordance with 15 the standard criteria for choosing the appropriate ” I constants. In the few cases where there was serious doubt from chemical information as to The second test was a standard F-test4 The which type of u should be applicable, the choice sum ( S ) of the sum of squares of deviations from was made so as to obtain the best fit. Polysub- regression for the separate ?netuand para lines was stituted compounds, compounds in which the sub- subtracted from the corresponding value for the stituent is a fused ring system, a heteroatom or has total regression (combining all data), and the difionic character have been disregarded. ference, involving two degres of freedom, was Two tests of differences in the correlations were tested against S (with n - 4 degrees of freedom). made. The first test was a simple t - t ~ s tin , ~which This procedure tests whether the separate correlapp-pl,, was tested against the mean of their standard tions produce a sign$cant improvement over the tleviations. Xssurning that pp and pm are estimates single correlation. Such improvement could occur o f the same quantity, and that the same is true of because of differences between pp and pm, or because their standard deviations (sp) this test is valid and of differences between intercepts (log Kocatc), and would be expected to lead to differences significant does not distinguish between these alternatives. a t the 05‘% level iri about 5y0of the cases, to dif- The results, shown in Table I, again clearly indiference significant a t the 99% level in about 1% cate that significant differences occur for each of of the cases. The results of the application of this the 3 groups, far in excess of the number expected test are shown in Table I, where it is seen that the on the basis of chance. proportion of significant differelices encountered A further observation is worthy of note. If the greatly exceeds the nuniber expected to occur by number of significant differences observed occurred cha~icr. The saiiie table gives a breakdown into as a matter of chance alone, one would expect the the groups iri which the different types of u- figures at the 99Yo level to be approximately one\ d u e s are used, and the proportion of significant fifth of those a t the 95% level. This ratio is quit
