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. The a carbon becomes "more negative" as the transition state is formed from the p-nitro and p-chloro compounds, and "more positive" with the p- isopropyl compounds. One needs to look further at the solvation of various benzyl chlorides, thiosulfate ion and the transition states in the different solvents. Since the rate differences are rather small, small variations in solvation could be an important factor. Hancock and Idoux (16) have observed what appears to be the only report of a physical property that gives a nonlinear Hammett plot. These workers observed a - Q# * 0. @a U 16 concave upward curve for the solubilities of substituted Figure 9. Log kverrur -for the reaction of benryl chlorides with trimethyl- benzoic acids in dioxane and cyclohexane. From Fig- amine in benzene. ure 8 it can be seen that acids with electron-donating substituents fall on a curve of negative slope, while Hammett plot for substituted benzyl chlorides in ben- those acids with electron-withdrawing. substituents zene reacting with trimethylamine at 100°C. One of the fall on a curve of positive slope when CJ is plotted versus assumptions of the Hammett equation is that the sub- the mole fraction solubilities in dioxane and cyclo- stituent constants are independent of the reaction. hexane. Concave upward Hammett plots are usually The results, however, show that lower rates are obtained rationalized in terms of different mechanisms for the with m-substituents. Electron-donating substituents two groups of compounds defined by the different limes, stabilize, by resonance, a transition state having a high but a similar analogy for the relationship shown in positive charge on the benzylic carbon. This facili- Figure 8 is difficultto make due to the complexity of the tates the bond breaking process in the transition state. factors which affect the solution processes in the several On the other hand, an electron-withdrawing substituent solvents. Moreover, in considering solubilities, which increases the capacity of the benzylic carbon for a more are unlike a chemical reaction, there is not a localized negative charge in the transition state relative to .a

Volume 48, Number 2, February 1971 / 105 positive charge on the same carbon in the ground state. tosylates in acetone (88), and the reactions of para- This facilitates the bond making process in the transi- substituted beuzyl bromides with para-substituted tion state. thiophenols (29). If the type of curvature observed in Figure 9 is due A system (30) in which the data fit a single curve is to resonance in the transition state, the lower rates the cleavage of substituted benzylmercuric chlorides by should be obtained with the m-substituents since it is iodine and cadmiumiodide at 20°C these substituents which cannot interact through CsH6CHzHgC1 '/EL I- CsHsCHJ + HgICl resonance with the reaction site in the transition state. + + - (6) This is exactly what is observed in Figure 9. The study was carried out in both methanol and di- The reaction between henzyl bromides with pyridine methylformamide and the data is shown in Figure ll. in dry acetone exhibits a similar behavior (21). More recently, Fuchs and Carlton (22) reported that the thiosulfate reactions of 3-, 4-, and 3,bsubstituted benzyl chlorides resulted in a series of concave upward curves as shown in Figure 10.

In the thiosulfate reactions of these compounds, it can Figure 11. Log k versus #for the reaction of benryl mercuric chlorides with iodine-cadmium iodide in methmnol and in DMF. See eqn. (6). be seen that points on the Hammett equation plot repre- senting the Psubstituted-3-nitrobenzyl chlorides(I1) de- scribe a U-shaped.line, and the rates are quite different The reader will note the absence of the p-nitro com- from those of the 4-substituted henzyl chlorides(1). The pound whose rate of cleavage occurs too rapidly to me& 3-substituted henzyl chlorides(II1) fall on a U-shaped sure. Thus, both electron-withdrawing and electron- plot below the line for the 4-substituted compounds(1). donating groups (methyl, methoxy) cause a rate en- The substituents decrease the rate for the thiosulfate hancement relative to benzylmercuric chloride. The reaction and as can be seen this decrease is additive in authors found that the various substituents caused the 3,5-disubstituted henzyl chlorides(1V). Thus, the essentially no change in activation energy for the 3-suhstituents appear to have an intrinsic ability to cleavage in dimethylformamide; but that the rate dif- decrease the rate of the thiosulfate reaction and this ferences are associat,ed wibh changes in the entropy of property is approximately additive in the 3,5-disub- activation. Perhaps differences in solvation in the stituted benzyl chlorides(IV), which, as a series have ground and transition states may account for these the lowest order of reactivity. effects. A gradual mechanistic change is probably involved (rale enhancement caused by the p-nitro compound) with more carbanionic character in the transition states substituted in such a manner to best disperse this charge. The rate of this reaction probably depends on the concentration of iodide and perhaps the reactive species is the triiodide ion. Summary The previous examples of nonlinear structure-reactiv- ity, Hammett correlations summarize most of the types of reactions in which deviations due to change in mech- anism or rate-controlling step occur. A word regarding . .OZMM081012U the interpretation of experimental data would be perti- r Figure 10. Log k venw r for the reactions of substituted benryl chlorides nent at this point. Deviations of experimental points with thiosulfote: 4-substituted benryl chloridesll) 4-substituted-3-nitm from a straight line appear more striking when the line benryl ~hloride~(il),3-substituted benzyl chlorides(lll), and 3.5-diwbrti- is flat (the slope approaches zero, and p is small), than futed benzylchbrider(lV1. when the line is steep (p is large) and the data cover several logarithmic units (Fig. 12). A reaction with Other cases in which there is aseparation of the data data covering four logarithmic units, that is, log k/ko = into two curves, one for met,a-suhstituents (including 4, means that one compound is lo4times more reactive the unsuhstituted compound), and one for para-sub- than the unsubstituted compound. If p is small, then stituents are the reactions of henzyl bromides with small negative deviations may be interpreted as evidence pyridine in 90% ethanol (23), the hydrolysis of benzyl for a maximum, minimum, or curvature in the plot; chlorides in 50% ethanol (24) or 50% acetone (25), the whereas if p is large, these small negative deviations reactions of benzyl chlorides with iodide ion (W), the may not be taken too seriously. That is why it is im- reaction of 8-phenylethyl chlorides with iodide ion (27), portant, if possible, in structure-reactivity studies that the rates of solvolysis of meta- and para-substituted the experimenter use substituents which give the

106 / Journal of Chemical Education Literature Cited

(1) Tnlaam, M. T., woTn*mn*~, J. G., J. Amer. Chem. Soe., 91, 379 ,>on", (2) Jmm, H. H., Chem. Reus., 53,191 (1953). (3) TAFT,R. W., Jn., J. Amer. Chem. Soe., 79, 1045 (1957). (4) BnowN, H. C., AND OTAIOTO. Y., J. Amer. Chem. Soc., 80, 4979 (IQS*,~-"--,. (5) VANB~XKUM, H., VERKADB.P. E., AND WEPBTER,B. M., Rec. TIO~). Chim. Phus.. 78,815 (1959). (6) Krnscn, J. F.. AND JENCKS, W.P.. J. Amw. Chem. SOC.,86, 837 (1964). (7) S*n~~nnm.G. M.. H~BOTS,C. J.. JR., AND CBOW~~.T. I., J. Amer. Chcm. Soc., 80,1254 (1958). (8) CROWELL.T. I., BELL,C. E.. JR., AND O'BAIEN,D. H.. J. Arne?. Chem. Soe.. 86,4973 (1964). (9) Awor;saow, B. M., *ND JENCK~,W. P., J. Amer. Chcm. Soe., 82, 1773 [19601., ~~~,. (10) WIIII, A. V.. AND ROBBRTSON.R. E.. Con. J. Chm., 31, 361 (1953): WILL&A. V.. Helu. Chim. Acto. 39,1193 (1956). (11) Ss.unn~,H. H.. AND H*nun=~,C. M., J. Amer. Chcm. Soc.. . 86.. 29M) (1964). (12) Norcr, D. 6.. BOTTINI,A. T., AND BMITA, 8. G., J. Ow. Chm., 23, 752 ,,"KQ, (13) Bnnmn, J. F., AND Z*HLER,R. E.. Chcm. RN~.,49,294 (1951). (14) LEIBTBN,J.A.. J. Cham. SOE.. 765 (1959). (15) FDCHB,R., AWD NIBBET,A,, J. Amer. Chcm. Soe., 81,2371 (1959). (16) Hmoooa, C. K.. nl*o Inoux, J. P., J. Oq. Chem., 32,1931 (1967). Figure 12. Interprdation of experimental dam. (17) SWAIN,C. G., AliD THOBNTON,E. R., J. Ov. Chem., 26,4808 (1961). (18) WILLINO,C., etol., J. Amrr. Chem. Soc., 70, 1537 (1948). (19) KERNSHAW.D. N., AND LEI~TEN.J. A,. PIDC.ROY. SOC., 84 (1960). (20) Sw*m, C. G., AND LAIIDSDORI.,W. P., JR.,J. Amm. Cham. Soc., 73,2813 \."".,.,,OK,, (21) B*KER,J. W.. AND NATHAN.W. 8.. J. Chem. Soe.. 519, 1840 (1935); B*r~n,J. W.. Trans. Foradoy Soc.. 37,632 (1941). largest differences in reactivity for it is these substitu- (22) FDOHB,R.. AND CARLTON,D. M.. J. Amer. Cham. Soc., 85, 104 (1963). (23) BAXER.J. W.. J. Chem. Soc.. 2631 (1932). ents that give data that cover several logarithmic units. (24) Ofilv~n,S. C. J.. Rec. Trou. Chim. Phvs., 41,646 (1922). (25) BENNETT.G. M..AND JONEB, B., J. Chem. Soe.. 1815 (1935). (26) MILLER.W. T., AND BEAWBTEIN.V., J. Amel. Chem. Soe.. . 70.. 3600 (1948). Acknowledgment (27) B*me=r. G.. nxo Bmasrr,G. M., J. Chcm. Soc., 1819 (1936). (28) FANG.F. T.. KOOAI.J. K., AND HAMIIOND, 0. S.. J. AmW. Chcm. Soo., 80,563 (1958): KOCHI,J. K., AND H*UIOWD,G. 8.. J. Amcr. Chcm. The author gratefully acknowledges the helpful sug- Soe., 75,3445 (1953). gestions and encouragement of Dm. Richard Fuohs and (29) Humow, R. F., AND Km~snrr,G., J. Chcm. Soc., 1062 (1962). (30) BELETBI*Y*,I. P.. FETISOVA,T. P.. AND REOTOV,0. A,, PIOC.Alod. John Idoux. Sci., USSR. Chem. Sset., 55,347 (1964).

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