James 0. Schreck University of Northern Colorado Greeley, Colorado 80631
Nonlinear Hammett Relationships
The Haminett equation is a well-known empirical relationship for correlating structure and reactivity. 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 compounds, respectively; u is the substituent constant, and p is the reaction constant. The substituent constant is a measure of the ability of the substitueut to change the electron density a t the reaction site and is independent of the reaction involved; whereas, the reaction constant is a measure of the sensitivity of the reaction series to changes in electron density a t the reaction site. In most cases the equation is valid only for substituents in the meta- or para-positions of the benzene ring. (In a recent article, however, the relative chemical shifts of OH in ortho-substituted phenols in DMSO are correlated excellently with ortho-substituents ( I ) . ) Hence, the substituent changes the electron density a t the reaction site by polar and/or resonance effects. 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 experimental errors, reactive or catalytic im~uritiesin the 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). A different type of deviation arises when the mechanism of a reaction changes because of the presence of certain suhstituents or when the measured rate constant is actually a composite quantity depending on the rate and equilibrium constant of several reaction steps. In these cases, curvature in the relationship occurs. Figure 1 shows several types of linear and nonlinear plots. Generally, a change in the rate determining step with otherwise constant mechanism causes the curve to be concave down, while a concave upward curve indicates a change in the mechanism or transition state of the reaction, as one proceeds from electron-donating to electron-withdrawing groups. A transition state diagram (Fig. 2) for a two-step
S!h$tttuent
Figure 1.
"
Cmrtant. 0
Types of lineor ond nonlinear Hammoll curves.
reaction such as
shows how changes in structure which affect principally the second step can result in a nonlinear structure-reactivity correlation (6). I n this case the rate controlling step of the reaction changes from the first step to the second step due to the greater effect of changes in structure on the second step of the reaction. The diagram (Fig. 2) is for a reaction with a metastable intermediate. The curve in Figure 2 is opposite in
--
.AG
....
rn
I
I
I
Reactlon Coord~nate Figure 2. A tmndtion r t a k diagram for a two-step reaction and ih corresponding nonlinear Hommell plot.
direction to that of (a) in Figure 1 because the structural parameter is being plotted against free energy rather than the logarithm of a rate or equilibrium oonstant. An example of such nonlinear structure-reactivity correlations is that reported by Crowell, et al. (7) who studied the reaction of aromatic aldehydes with nbutyl amine under acid catalyzed conditions and under neutral conditions. The products are substituted benzylidene n-butyl amines (eqn. (3)). Volume 48, Number 2, February 1971 / 103
xEb
CHO
+
+
n-BuNH,
A plot of sigma values for the substituted benzaldehydes versus the logarithms of the observed rate constants for the uncatalyzed reactions is shown in Figure 3. A maximum in the curve occurs near the point for henzaldehyde. This maximum is interpreted as the point where the rate controlling step changes from the reversible addition of amine to aldehyde, which is favored by electron-withdrawing suhstituents while the suhsequent dehydration step is accelerated by electrondonating suhstituents.
Figure 4. Log k versus #for the reoclion of bonmldehydes with semicarbarids of pH 1.75. See eqn. 14).
Figure 5. Log K., V e n u s olunbroken line), log kdrbrdiationvenvs# (evenly verrvr li (unevenly bmksn line) for the reocbroken line), and log ~,,...II tionr of benzaldehydes with remisarboride a t neutral pH. See eqn. (41.
'J -06
.
-01
Figure 3. Log k venur amine. See eqn. (31.
ir
I -02
0
.
02
.
64
US
aS
for the reaclion of bcnzaldehydes and n-butyl
More recently (8),Crowell, et al., have shown that this maximum is not due to solvent-substrate interaction by studying the reaction in two differentsolvents of different polarity: methanol and dioxane. It was found that the rate is much more sensitive to the substituent in dioxane than in methanol, but in each case a maximum appears with the unsubstituted compound. The effects of substituents on the equilibrium and rate of semicarhazone formation from substituted beuzaldehydes has also been studied (9). At pH 1.75the rate of
the addition reaction of semicarbazide to a series of substituted benzaldehydes in 25% ethanol is increased by electron-withdrawing substituents (Fig. 4) indicating that the addition step (kl) is rate determining. Electron-withdrawing substituents make the carhonyl carbon more positive. At neutral pH (Fig. 5) the equilibrium concentration (k,/k-,) of the addition compound is increased by electron-withdrawing suhstituents (unbroken line), hut the rate of acid-catalyzed 104
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Journal of Chemical Education
1.1'.. 0-YIO
-06 dl
-02
*
02
. :.
OI
06
08
Figure 6. Log kdehydration v e n u s o for the raaclion of benrddehyder with semicarbazide a t pH 3.9. See oqn. (41.
dehydration (kz) of the addition compound is increased 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 intermediate 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 decreasing rate of the dehydration step when electronwithdrawing 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 assume that the multistep nature of a reaction alone results in a nonlinear p~ plot as evidenced in Figure 5. Concave downward plots have also been observed in S c b 8 base hydrolysis ( l o ) ,the reaction of hydrazones of diary1 ketones, methyl ketones, and aldehydes (11), the rates of semicarbazone formation for benzaldehydes (179, the decomposition of benzene diazonium salts (I$), and the acid hydrolysis of substituted amides (14). Deviations from linearity in the Hammett plot in
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 ( 1 5 ) have reported a case illustrative of the concave upward type: the reaction of psubstituted benzyl chlorides with thiosulfate in solvents of differentdielectric constant.
+
IC,H&-X
S20,!--
PRODUCTS
(5)
I
.
.
a
.
i qa2
M
i l . 0 -a6
a
02
06
10
IA
1.8
Figure 8. Log l X ~ / X c lversus c for the rolubilitier of benrois acids in dioxane and cyclohexone. Xo is the mole fraction dubility in dioxane.
The results are shown in Figure 7.
%.a4
1.
M
@a
Figure 7. Log kvenusnfor the reaction of benryl chlorides with thiorulfate in ( I I ethanol, 12) diglyme, and (31 acetone. See eqn. (51.
The amount of energy required for desolvation of the thiosulfate ion is less in the less polar solvent diglymewater than in the more polar acetone-water, and less for the looser p-isopropyl transition state than for the tighter transition states. In addition, it appears that 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 pisopropyl 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 concave upward curve for the solubilities of substituted benzoic acids in dioxane and cyclohexane. From Figure 8 it can be seen that acids with electron-donating substituents fall on a curve of negative slope, while those acids with electron-withdrawing. substituents fall on a curve of positive slope when CJ is plotted versus the mole fraction solubilities in dioxane and cyclohexane. Concave upward Hammett plots are usually rationalized in terms of different mechanisms for the two groups of compounds defined by the different limes, but a similar analogy for the relationship shown in Figure 8 is difficultto make due to the complexity of the factors which affect the solution processes in the several solvents. Moreover, in considering solubilities, which are unlike a chemical reaction, there is not a localized
"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 sulfonium ions in water (17), in the reactivities of substituted styrenes toward the methacrylate radical ( I S ) , and in the hydrolysis of ethyl carboxylates in concentrated strong acids (19). Although the preceding examples dealt with the effect of abrupt changes in reaction mechanism, it is believed that for some reactions the mechanism varies 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 unsubstituted compound. But there are also cases in which the data fit a single curved trace. Swain and Langsdorf (20)studied the reactions of various benzyl chlorides and bromides with various nucleophiles in several solvents. Figure 9 shows the
-
Q#
*
0.
@a
U
16
Figure 9. Log kverrur -for the reaction of benryl chlorides with trimethylamine in benzene.
Hammett plot for substituted benzyl chlorides in benzene reacting with trimethylamine at 100°C. One of the assumptions of the Hammett equation is that the substituent constants are independent of the reaction. The results, however, show that lower rates are obtained with m-substituents. Electron-donating substituents stabilize, by resonance, a transition state having a high positive charge on the benzylic carbon. This facilitates the bond breaking process in the transition state. On the other hand, an electron-withdrawing substituent increases the capacity of the benzylic carbon for a more negative charge in the transition state relative to .a Volume 48, Number 2, February 1971
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105
positive charge on the same carbon in the ground state. This facilitates the bond making process in the transition state. If the type of curvature observed in Figure 9 is due to resonance in the transition state, the lower rates should be obtained with the m-substituents since it is these substituents which cannot interact through resonance with the reaction site in the transition state. This is exactly what is observed in Figure 9. The reaction between henzyl bromides with pyridine 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.
tosylates in acetone (88), and the reactions of parasubstituted beuzyl bromides with para-substituted thiophenols (29). A system (30) in which the data fit a single curve is the cleavage of substituted benzylmercuric chlorides by iodine and cadmiumiodide at 20°C CsH6CHzHgC1 '/EL I CsHsCHJ + HgICl ( 6 ) The study was carried out in both methanol and dimethylformamide and the data is shown in Figure l l .
I n the thiosulfate reactions of these compounds, it can be seen that points on the Hammett equation plot representing the Psubstituted-3-nitrobenzyl chlorides(I1) describe a U-shaped.line, and the rates are quite different from those of the 4-substituted henzyl chlorides(1). The 3-substituted henzyl chlorides(II1) fall on a U-shaped plot below the line for the 4-substituted compounds(1). The substituents decrease the rate for the thiosulfate reaction and as can be seen this decrease is additive in the 3,5-disubstituted henzyl chlorides(1V). Thus, the 3-suhstituents appear to have an intrinsic ability to decrease the rate of the thiosulfate reaction and this property is approximately additive in the 3,5-disubstituted benzyl chlorides(IV), which, as a series have the lowest order of reactivity.
Figure 11. Log k versus # f o r the reaction of benryl mercuric chlorides with iodine-cadmium iodide in methmnol and in DMF. See eqn. (6).
+
+
-
The reader will note the absence of the p-nitro compound whose rate of cleavage occurs too rapidly to me& sure. Thus, both electron-withdrawing and electrondonating groups (methyl, methoxy) cause a rate enhancement relative to benzylmercuric chloride. The authors found that the various substituents caused essentially no change in activation energy for the cleavage in dimethylformamide; but that the rate differences are associat,ed wibh changes in the entropy of activation. Perhaps differences in solvation in the ground and transition states may account for these 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
.
. O Z M M 0 8 1 0 1 2 U
r Figure 10. Log k venw r for the reactions of substituted benryl chlorides with thiosulfote: 4-substituted benryl chloridesll) 4-substituted-3-nitm benryl ~hloride~(il), 3-substituted benzyl chlorides(lll), and 3.5-diwbrtifuted benzylchbrider(lV1.
Other cases in which there is aseparation of the data into two curves, one for met,a-suhstituents (including the unsuhstituted compound), and one for para-substituents are the reactions of henzyl bromides with pyridine in 90% ethanol (23), the hydrolysis of benzyl chlorides in 50% ethanol (24) or 50% acetone (25), the reactions of benzyl chlorides with iodide ion (W), the reaction of 8-phenylethyl chlorides with iodide ion (27), the rates of solvolysis of meta- and para-substituted 106
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Journal o f Chemical Education
The previous examples of nonlinear structure-reactivity, Hammett correlations summarize most of the types of reactions in which deviations due to change in mechanism or rate-controlling step occur. A word regarding the interpretation of experimental data would be pertinent at this point. Deviations of experimental points from a straight line appear more striking when the line is flat (the slope approaches zero, and p is small), than when the line is steep ( p is large) and the data cover several logarithmic units (Fig. 12). A reaction with data covering four logarithmic units, that is, log k / k o = 4, means that one compound is lo4times more reactive than the unsubstituted compound. If p is small, then small negative deviations may be interpreted as evidence for a maximum, minimum, or curvature in the plot; whereas if p is large, these small negative deviations may not be taken too seriously. That is why it is important, if possible, in structure-reactivity studies that the experimenter use substituents which give the
Literature Cited (1) T n l a a m , M. T., w o T n * m n * ~ , J. G., J . Amer. Chem. Soe., 91, 379 ,>on",
(2) J m m , H. H., Chem. Reus., 53,191 (1953). R. W., Jn., J. Amer. Chem. Soe., 79, 1045 (1957). (3) TAFT, (4) BnowN, H. C., A N D OTAIOTO. Y., J . Amer. Chem. Soc., 80, 4979
~-"--,.
(IQS*,
(5) VANB~XKUM, H., VERKADB. P. E.,AND WEPBTER,B. M., Rec. T I O ~ ) . Chim. Phus.. 78,815 (1959). (6) Krnscn, J. F.. AND JENCKS, W . P..J . A m w . Chem. SOC.,86, 837 (1964). (7) S*n~~nnm. G. M.. H ~ B O T SC. , J.. JR., A N D C B O W ~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). ~ , P., J . Amer. Chcm. Soe., 82, 1773 (9) Awor;saow, B. M., *ND J E N C KW. [19601. ,~ ~ ~ , . (10) WIIII, A. V.. AND ROBBRTSON. R . E.. Con. J . C h m . , 31, 361 (1953): WILL&A. V.. Helu. Chim. Acto. 39,1193 (1956). H. H.. AND H*nun=~, C. M., J . Amer. Chcm. Soc.. . 86.. 29M) (11) Ss.unn~, (1964). (12) Norcr, D. 6.. BOTTINI, A. T., AND BMITA, 8. G., J . O w . C h m . , 23, 752 ,,"KQ,
Figure 12.
Interprdation of experimental dam.
(13) (14) (15) (16) (17) (18) (19) (20)
Bnnmn, J. F., AND Z*HLER, R. E.. Chcm. R N ~ .49,294 , (1951). LEIBTBN, J.A.. J . Cham. SOE..765 (1959). FDCHB, R., AWD NIBBET, A,, J . Amer. Chcm. Soe., 81,2371 (1959). Hmoooa, C. K.. nl*o Inoux, J. P., J . Oq. Chem., 32,1931 (1967). SWAIN, C. G., A l i D THOBNTON, E. R., J . O v . Chem., 26,4808 (1961). WILLINO,C., etol., J . Amrr. Chem. Soc., 70, 1537 (1948). KERNSHAW. D. N., AND LEI~TEN. J. A,. PIDC. ROY.SOC.,84 (1960). Sw*m, C. G., AND LAIIDSDORI., W. P.,JR.,J . Amm. Cham. Soc., 73,2813
\."".,. ,,OK,,
largest differences in reactivity for it is these substituents that give data that cover several logarithmic units. Acknowledgment
The author gratefully acknowledges the helpful suggestions and encouragement of Dm. Richard Fuohs and John Idoux.
(21) B*KER, J. W..A N D NATHAN. W. 8.. J . Chem. Soe.. 519, 1840 (1935); B*r~n, J. W.. Trans.Foradoy Soc.. 37,632 (1941). (22) FDOHB, R.. AND CARLTON, D. M.. J . Amer. Cham. Soc., 85, 104 (1963). (23) BAXER. J. W.. J . Chem. Soc.. 2631 (1932). , C. J.. Rec. Trou. Chim. Phvs., 41,646 (1922). (24) O f i l v ~ nS. (25) BENNETT. G. M..A N D JONEB, B., J . Chem. Soe.. 1815 (1935). W. T., AND BEAWBTEIN. V., J . Amel. Chem. Soe.. . 70.. 3600 (26) MILLER. (1948). (27) B*me=r. G.. nxo Bmasrr, G. M., J . Chcm. Soc., 1819 (1936). (28) FANG. F. T.. KOOAI.J. K., AND HA O M IN ID, 0. S..J . AmW. Chcm. Soo., 80,563 (1958): KOCHI,J. K., AND H*UIOWD,G. 8.. J . Amcr. Chcm. Soe., 75,3445 (1953). (29) Humow,R. F., A N D Km~snrr, G., J . Chcm. Soc., 1062 (1962). (30) BELETBI*Y*, I. P.. FETISOVA, T . P.. AND REOTOV, 0. A , , PIOC.Alod. Sci., USSR. Chem. Sset., 55,347 (1964).
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