James 0. Schreck University of Northern Colorado Nonlinear Hammett Relationships Greeley, Colorado 80631 The Haminett equation is a well-known empirical relationship for correlating structure and re- activity. Specifically, it relates structure to both equilibrium and reaction rate constants for reactions of met* and para-substituted benzene derivatives. When the Hammett equation is written in the form log (k/ko) = .P (1) k and ko are the rate (or equilibrium) constants for the " reaction of the substituted and unsubstituted com- S!h$tttuent Cmrtant. 0 pounds, respectively; u is the substituent constant, and Figure 1. Types of lineor ond nonlinear Hammoll curves. p is the reaction constant. The substituent constant is a measure of the ability of the substitueut to change reaction such as the electron density at the reaction site and is indepen- dent of the reaction involved; whereas, the reaction con- stant is a measure of the sensitivity of the reaction series to changes in electron density at the reaction site. In shows how changes in structure which affect principally most cases the equation is valid only for substituents the second step can result in a nonlinear structure-re- in the meta- or para-positions of the benzene ring. (In activity correlation (6). In this case the rate control- a recent article, however, the relative chemical shifts ling step of the reaction changes from the first step to of OH in ortho-substituted phenols in DMSO are the second step due to the greater effect of changes in correlated excellently with ortho-substituents (I).) structure on the second step of the reaction. The Hence, the substituent changes the electron density at diagram (Fig. 2) is for a reaction with a metastable the reaction site by polar and/or resonance effects. intermediate. The curve in Figure 2 is opposite in That the Hammett equation is useful for predictive purposes has been amply demonstrated (2). In all these cases the members of a series of com~oundsare linearly related to the respective a values. However, in contrast to the large number of reactions which give .- linear relations, there are a number of reactions which - show deviations from linearity. In some cases these -- deviations can be explained as being due to experi- mental errors, reactive or catalytic im~uritiesin the AG rn .... compounds used, failure to isolate a single reaction, or complications arising from side reactions. Other types of deviations from Hammett plots can sometimes be removed by using a different substituent constant which takes into account varying polar and/or resonance effects(3-5). I I I A different type of deviation arises when the mecha- Reactlon Coord~nate nism of a reaction changes because of the presence of Figure 2. A tmndtion rtak diagram for a two-step reaction and ih cor- certain suhstituents or when the measured rate constant responding nonlinear Hommell plot. is actually a composite quantity depending on the rate and equilibrium constant of several reaction steps. In direction to that of (a) in Figure 1 because the struc- these cases, curvature in the relationship occurs. Fig- tural parameter is being plotted against free energy ure 1 shows several types of linear and nonlinear plots. rather than the logarithm of a rate or equilibrium oon- Generally, a change in the rate determining step with stant. otherwise constant mechanism causes the curve to be An example of such nonlinear structure-reactivity concave down, while a concave upward curve indicates correlations is that reported by Crowell, et al. (7) who a change in the mechanism or transition state of the studied the reaction of aromatic aldehydes with n- reaction, as one proceeds from electron-donating to butyl amine under acid catalyzed conditions and under electron-withdrawing groups. neutral conditions. The products are substituted A transition state diagram (Fig. 2) for a two-step benzylidene n-butyl amines (eqn. (3)). Volume 48, Number 2, February 1971 / 103 xEbCHO + n-BuNH, + A plot of sigma values for the substituted benzaldehydes versus the logarithms of the observed rate constants Figure 4. Log k versus #for the reoclion of bonmldehydes with semicar- for the uncatalyzed reactions is shown in Figure 3. A barids of pH 1.75. See eqn. 14). maximum in the curve occurs near the point for henz- aldehyde. This maximum is interpreted as the point where the rate controlling step changes from the revers- ible addition of amine to aldehyde, which is favored by electron-withdrawing suhstituents while the suhse- quent dehydration step is accelerated by electron- donating suhstituents. Figure 5. Log K., Venus olunbroken line), log kdrbrdiationvenvs# (evenly broken line), and log ~,,...II verrvr li (unevenly bmksn line) for the reoc- tionr of benzaldehydes with remisarboride at neutral pH. See eqn. (41. J.I.. ' -06 -01 -02 0 02 64 US aS Figure 3. Log k venur ir for the reaclion of bcnzaldehydes and n-butyl amine. See eqn. (31. More recently (8),Crowell, et al., have shown that this maximum is not due to solvent-substrate inter- action by studying the reaction in two differentsolvents of different polarity: methanol and dioxane. It was 0-YIO . :. found that the rate is much more sensitive to the sub- 1.1'.-06 dl -02 * 02 OI 06 08 stituent in dioxane than in methanol, but in each case Figure 6. Log kdehydration venus o for the raaclion of benrddehyder with a maximum appears with the unsubstituted compound. semicarbazide at pH 3.9. See oqn. (41. The effects of substituents on the equilibrium and rate of semicarhazone formation from substituted beuzalde- dehydration (kz) of the addition compound is increased hydes has also been studied (9). At pH 1.75 the rate of by electron-donating substituents (evenly broken line), so that the observed rate (unevenly broken line) in dilute solution, which is a resultant of these two effects, shows very little sensitivity to substituents. At inter- mediate pH (3.9) the rate determining step (kz)changes as the substituents change and a sharp break is found in the pu plot (Fig. 6). This is attributed to the de- creasing rate of the dehydration step when electron- withdrawing suhstituents are present. The phenomenon of nonlinear concave downward plots appears to be common in reactions involving the carhonyl group. Even though these reactions are commonly multistep reactions, it is not correct to as- the addition reaction of semicarbazide to a series of sume that the multistep nature of a reaction alone re- substituted benzaldehydes in 25% ethanol is increased sults in a nonlinear p~ plot as evidenced in Figure 5. by electron-withdrawing substituents (Fig. 4) indi- Concave downward plots have also been observed in cating that the addition step (kl) is rate determining. Scb8 base hydrolysis (lo),the reaction of hydrazones Electron-withdrawing substituents make the carhonyl of diary1 ketones, methyl ketones, and aldehydes (11), carbon more positive. At neutral pH (Fig. 5) the the rates of semicarbazone formation for benzaldehydes equilibrium concentration (k,/k-,) of the addition (179, the decomposition of benzene diazonium salts (I$), compound is increased by electron-withdrawing suh- and the acid hydrolysis of substituted amides (14). stituents (unbroken line), hut the rate of acid-catalyzed Deviations from linearity in the Hammett plot in 104 / Journal of Chemical Education which the curve tends to be concave upward are thought to be caused by a change in mechanism or transition state brought about by differing effects of electron donors or withdrawers on the course of the reaction. Effects of this type are most often encountered in the reactions of alkyl and acyl halides with nucleophilic reagents. In some cases, the Hammett plot is smoothly curved; whereas in others, a definite break occurs in the plot with a rate minimum. Fuchs and Nisbet (15) have reported a case illustra- tive of the concave upward type: the reaction of p- substituted benzyl chlorides with thiosulfate in solvents of differentdielectric constant. X-&H,CI X-&H,CI S20,!-- PRODUCTS (5) 1. + il.0 -a6 a 02 06 10 IA 1.8 Figure 8. Log lX~/Xclversus c for the rolubilitier of benrois acids in di- The results are shown in Figure 7. oxane and cyclohexone. Xo is the mole fraction dubility in dioxane. "reaction" site, but rather the gross structuie of the entire molecule plays an important role in the solution process. Hammett relationships of this type have also been obsefved in the hydroxide displacement of benzyl sul- fonium ions in water (17), in the reactivities of substi- tuted styrenes toward the methacrylate radical (IS), and in the hydrolysis of ethyl carboxylates in concentrated strong acids (19). Although the preceding examples dealt with the I... effect of abrupt changes in reaction mechanism, it is %.a4 a i qa2 M M @a believed that for some reactions the mechanism varies Figure 7. Log kvenusnfor the reaction of benryl chlorides with thiorulfate in (I I ethanol, 12) diglyme, and (31 acetone. See eqn. (51. continuously. In some cases, the data is separable into two distinct curves: one for the p-substituents and another for the m-substituents including the un- The amount of energy required for desolvation of the substituted compound. But there are also cases in thiosulfate ion is less in the less polar solvent diglyme- which the data fit a single curved trace. water than in the more polar acetone-water, and less Swain and Langsdorf (20) studied the reactions of for the looser p-isopropyl transition state than for the various benzyl chlorides and bromides with various tighter transition states. In addition, it appears that nucleophiles in several solvents. Figure 9 shows the these reactions have different amounts of carbonium ion character.