2091
THE TRANSMISSION AND ADDITIVITY OF POLAR EFFECTS BY C. D. RITCHIE Department of Chemistry, The William M . Rice University, Houston, Texas Received J u n e SO, 1961
Several recent developments in the field of structure-reactivity relationships made it appear advisable to re-examine the basis of the linear-polar-energy equation which has been proposed by Taft. A test for the self-consistency of the u* parameters is derived from sim le symmetry considerations similar to those used by Hine for the Hammett equation. I t is found that U * values for alkyfgroups are not consistent with those for other groups. The implications of the inconsistency are examined, and new U * values are proposed. The discussion then is extended to the additivity of substituent effects. I t is shown that a "saturation effect" is observable even in cases where linear-free-energy equations are obeyed. Some conclusions regarding the transmission properties of groups are also possible from these arguments.
Introduction Taftl has recently suggest'ed a relationship, I = u * p * , for the purpose of separating polar effects from others in chemical rates and equilibria. Examples of the use of this relationship for the evaluation of steric,2resonance,3 hyperc~njugative,~ and solvations effects have been offered. Although the existence of linear-free-energy equations may be justified on fairly sound theoretical bases,8#7the evaluat'ion of the u* parameters is an empirical process. Ideally, the evaluation should be carried out using reaction series in which one can be certain that only polar effects are operative.* In practice, it becomes difficult to find series with enough substituents in which this ideal may be approached. Working on a suggestion by I n g ~ l dTaft'O ,~ used t'he difference in the rates of acid- and base-catalyzed ester hydrolyses as the standard series for the evaluation of u*. Although the assumption that only polar effects influence these differences seemed reasonable, it could be checked only by comparing u* values obtained with ot'her independent observations. Taftll has presented several lines of evidence which appear to verify individual constants, however, all of the values have not been verified. Hine's recent work with t'he symmetry properties of the Hammet't equation12 suggested that the analogous argument's applied to the Taft equation would provide a t'est for the self-consistency of the u* values. I t also appeared t'hat' hJiller's13 recent work on multiple variations in structure-reactivity correlations might provide a method of gaining information concerning the additivity of substituent effects. (1) R. W. Taft, Jr. in "Steric Effects in Organic Chemistry," edited by M. S. Newman, John Wiley and Sons, Inc., New York, N. Y., 1956, pp. 622 ff. ( 2 ) Ref. 1, pp. 633-636, 642-645. ( 3 ) Ref. 1, pp. 636-642; R. IT. Taft, Jr., and I. C. Lewis, J. Am. Chem. Sac., 81, 5343 (1959). (4) M. M . Kreevoy and R. W. Taft, Jr., i b i d . , 7 7 , 5690 (1955). (5) H. K. Hall, Jr., ibid., 79, 5439 (1957). (6) J. Hine, ibid., 82, 4877 (1960). (7) W. F. Sager and C . D. Ritchie, ibid., 89, 3498 (1961). (8) For efforts toward this ideal, see: J. D. Roberts and W. T'. Moreland, ibid., 76, 2167 (1953); S. Siege1 and J. M . Koniorny, ibid., 82, 2547 (1960). (9) C. K. Ingold, J . Chem. Soc., 1032 (1930). (10) R. W.. l'aft, Jr., J . Am. C h e m . Sac., 74, 3120 (1952)d (11) Cj.ref. 1, pp. 613-618. (12) J. Hine, J . Am. Chem. Soc., 81, 1126 (19591; (13) S. I. Miller, ibid., 81, 101 (1959).
Development of Equations Consider the reaction A-CH2-X
+ B-CH2-Y
=
-4-CH2-Y
+ B-CHz-X
(1)
where the equilibrium constant14 for the reaction is correlated by log K =
(U*A
-
(2)
U*B)P*XY
For the Taft equation to have general applicability, also log K = (u*x
-
(3)
U*Y)P*AB
Combining equations 2 and 3, and rearranging gives P *.4B (u*xP*XY - u *y ) - (U*A - U * B )
(4)
Since p*xy must be independent of g * . ~and U*B, and P*AB independent of u * X and u*y, these ratios must both equal a constant which we denote by T ( C H ~ ) . Thus, we find P*XY =
d C H z ) ( ~ * x-
(5)
U*Y)
Kom consider the reaction A-CH2CHz-X
+ B-CH2CH2-Y
=
+
A-CHZCH1-Y B-CHzCH2-X
(6)
Again for the Taft equation to apply log K
(U*ACH~
-
U*BCH~)P*XY= ( U * X C H ~
-
U*YCHJP*AB
(7)
Substituting in (7) the expression for and rearranging
p*
from ( 5 ) ,
Since the u* values of the A's, B's, X's, and Y's are independent of one another, these ratios must be equal to a constant which we denote T(CH~)/7(CH2CH2).I5 The relationship 8 then requires that
By considering reactions in which methylene groups are successively interposed between the substituent and the reaction site, equation 9 may be generalized to the statement that there is a constant fall-off factor for each methylene group between a substituent and reaction site. The derivation of equation 9, and its generalization, requires no other assumptions than the gener(14) The "inductive energy" (cf. ref. 2), I , may be substituted in place of log K in any of the equations presented without affecting the arguments. (15) As can be seen from inspection, r (CHnCHz) is the constant in the expression for p* of equation 6 if we were t o use u* of A, B, X and Y. That is +-*XCB~.YCH~= v(CHpCHz)(u*x @*y)for equation (6).
-
C. D. RITCHIE
2092
Yol. 65
Xow, combining equations 5 , 14 and 15 q=
IT(CHA) - T(C&)I(U*XU*A
O*Y)
(16)
But q must be independent of A and B, therefore q
u*x
-0.4
0.0
0.8
0.4
1.2
1.6
U*=.
of data for eouation 9:
Fitr. I.-Plot
1. CHXC):
2.
-
.
.
T(CH2)= constant (17)
U *A
Thus, we find the interesting result that the transmission constant is a function of the groups attached to the transmitting atom. This effect is the same as that which has been called a "saturation effect."" As Miller has pointed the general equatior for symmetric dual substitution is log KAB =
t-CIH9. (Values taken from ref. I, p. 619).
-
=____'('HA) u*y
(u*A
+
+ log KEA
+
U*B)~~XY ~ * A u * B ~
(18)
For triple substitution on a single carbon, a rather lengthy algebraic process gives18 log KABC= (U*A U*B U*C)P~XY (C*AU*B 4-
+
+ +
U*AU*C
++ log KHEH (19)
U*BU*C)~
Discussion
A plot of the
a* values to which equation 9
should be applicable is shown in Fig. 1. It is seen that alkyl groups fall on a separate line from that defined by other substituents. ?.O } Since most of the arguments which have been 1 presented by Taft'l tend to substantiate the u* 1.o , \ values for groups other than alkyl, our conclusion 0.0 0.5 1.0 1.5 2.0 must be that the u* values for alkyl groups are not U*. consistent with the generality of the Taft equation. Fig. 2.-Taft plot of ionization of aliphatic acids: 0, If we assume that the o* value of zero for the values for alkyl groups from ref. ;E e, values for alkyl methyl group is correct, equation 9 requires that groups from this paper; 9, group? other than alkyl; 1, CHs; u* values for all n-alkyl groups are zero. Branched 2 , CzH6;3, n-C3H;; 4,iGH7; 5, sec-C4Hg;.6, t-C4Hg;7 , H. alkyl groups cannot strictly be considered in the (Primary references for the data are given in ref. 1.) simple equation 3, since these involve multiple ality of the linear-polar-energy equation, and the substitution. Equations 18 and 19, however, give possibility of assigning u* values to groups A and log Kdkyl = log K m e t h v l , since u* values for the nACH, in the same reaction series. I n short, equa- alkyl groups are zero. Thus, branched alkyl groups tion 9 is a necessary condition for the existence of may be considered to have u* equal to zero. Several plots of the Taft equation, using these rethe linear-polar-energy equation. Another informative manipulation of the Taft quired values, are shown in Figs. 2-4. It is seen equation results from the consideration of multiple that the data are correlated as well with these new values as with those previously assigned. I n some variations in structure. l3 cases, notably with the basicity of primary and Consider the reaction secondary amines, the new values give better fits ABCH-X = ABCH-Y (10) than do the old ones. Applica,tion of the Taft equation gives It should be noted that the points for the hydrolog KAB= U * A P ~ X Y log KBH= U * B ' ~ X Y log KAH gen substituted compounds deviate seriously from (11) the plots for the acidity of aliphatic acids and for the hydrolysis of acetals and ketals. N o single subAlso by the Taft equation stituent constant for hydrogen will improve the log KBE = u*gpHxy + log KHH,and, log KAH = correlations shown. ~ * A P ~ X Y log KHH (12) Thus, if the linear-polar-energy equation exists, Combination of (11) and (12) gives the assumptions made in the original evaluation of u* constants must be in error. This is not hard to U*IP~XY @ * B P ~ X Y = ~ * B P ~ X Y U*AP"XY (13) Calling upon the necessary independence of the understand in terms of Miller's arguments. If other effects are operative in ester hydrolyses, it various u* and p * , and rearranging, gives would be expected that they interact with the P B X Y -- P H X Y - P A X Y - PHXY - constant = qI6 (14) polar effect. Assuming that the other effect could U*B U*A be expressed analytically, this interaction would By the same arguments used earlier lead to a cross term in the equation for log K . From the above arguments concerning p, this cross p A x y = r(CHA)(u*x - u * y ) , and , P X y = I
\9
\
+
+
+
+
~-
+
'(CHB)(u*x
- U*Y)
(15)
(18) An analogous equation has been derived by: C. D. Ritohie, J. D. Saltiel and E. 8. Lewis, J . Ana. Chem. Soc., 88, 4601 (1981).
(17) Ref. 1, pp. 823-825. (IS) The straightforward process analogous t o t h a t above givee three Q'S. It is easy t o show, using t h e symmetry of tire substltution, that these three Q'S are equal.
Sov., 1961
TR-4NSMISsION AND
ADDITIVITY O F POLAR
term should be a function of p * . Since p* for the acid- and base-catalyzed ester hydrolyses are not the same, it would not be expected that this cross term would cancel in the difference of the log K values for the two reactions. The possihle misinterpretations which have resulted from the use of u* values for alkyl groups in the past are obvious and need not be dwelled upon. Equations 14 through 19, of course, become trivial if q is zero. Past data have dealt with such narrow ranges of structures,13 or with cases in which substituents were so far separated,I6 that it has been difficult to assess the significance of the q terms in equations such as (18). From the derivation of equation 18, it is seen that if the linear-free-energy equations are to be applicable a t all to multiple substitution, the evaluation of u* for multiply substituted methyl groups will give q. That is, if o w for an X2CH group is twice u* for the XCHz group, q is zero; if not, then p is not zero. TaftIy recently has pointed out that u* for an X?CH group is generally 1.7 u* for the XCHz group, and that u* for an X3C group is 2.2 u* for the XCHz group. Siiice the data used deals necessarily with halogen substitution, for which u* of XCHz is nearly the same in each case, with u* equal 1.0, equations 18 and 19 require that q is equal to -0.30 p * x y . Equation 17 then requires that electron withdrawing substituents decrease the transmission properties of the carbon to which they are bonded
Conclusions The results presented above point out the difficulties in the disentanglement of various effects on reactivity. It would appear that the only safe way of proceeding in the separation of polar effects from others is t,o study series in which all other effects are carefully controlled. Acknowledgments.-Grateful acknowledgment is made to the Robert A. Welch Foundation for the (19) (a) R. W. Taft, Jr., Paper presented before the Hydrocarbon S>niposiiiin, Hoiiston, Texas January 1961; (b) R. W. Taft, Jr., perbonal coniruunic&tion, April 1!161.
2093
EFFECTS
12.0 10.0
6 Q.
8.0 6.0
4.0
0.0
0.5
1.o
U*.
Fig. 3.-Taft
plot of the ionization of aliphatic amines:
0, values for alkyl groups from ref. 1; 0 , values for alkyl
groups from this paper; 9, groups other than alkyl. p K , for primary amines uspd to establish line for all amines. pK. 2.00 is shown for secondary amines; p k ' , - 1.00 shown for tertiary amines. 1, CHn; 2, C2H,; 3, n-CZH7; 4,n-C4Hs; 5, i-C3H7; 6, t-C,Hg; 7, sec-C4Hg; 8, neo-CgHll; 9, i-CaHg; 10, H. (Data taken from ref. 5 . )
+
1.o
iz --. +.o
- 7.0
i.I_ i
0.0
0.4 U
\
0.8
*.
Fig. 4.-Taft plot for the hydrolysis of acetals and ketnls: 0, values for alkyl groups from ref. 1; 0, values for alkyl groups from this paper; a, groups other than alkyl; 1, CH::; 2, CZHS; 3, i-C3H7; 4, t-CaHg; 5, 'L'-CdH@;6, (CzHg)&H; 7, H ; 8, neo-CbHil. (Data taken from ref. 4.)
support of this work, and to Prof. E. S. Lewis for many helpful discussions and suggestions.
