6999 to eliminate excess lithium, (36) The accuracy of this method was verified from a standard solution containing the very same products as the reaction. For each product the average of the values found is & O S % of the theoretical value. (37) R. Kaiser, "Gas Chromatography", Vol. 1, Butterworths, London, 1963, p 182.
shall show in this article, the reversibility of step V VI can be discarded. (33) J. E. Dubois, M. Boussu, and C. Lion, Tetrahedron Left., 829 (1971). (34) D. Zook, W. E. Smith, and J. L. Greene, J. Am. Chem. Soc., 79, 4436 (1957). (35) Before use the organolithiumcompoundwas decanted under argon pressure +
Metathetical Transposition of Bis-tert- alkyl Ketones. 2. Structural Effects on Alkyl Migration. Existence of Linear Relationship Networks P. Bauer and J. E. Dubois* Contribution from the Laboratoire de Chimie Organique Physique de I'UnicersitC de Paris VII, associe au C . N . R . S . ,75005 Paris, France. Receiued July 1 , 1975
Abstract: Structure-migrating group interactions which are present during 1,2 migrations of alkyl groups Rm (Rm = Me or Et) have been studied as a function of the influence of a variable environment e,, of the origin carbon C, for a fixed environment Ect of the terminal carbon C,, and vice versa, on the partial rate constant (kPRm)for migration in IV. The constants k p R m were determined from a study, in 96% HzS04, of the metathetical transposition of 11 n,d-bis-tert-alkyl ketones (RIRLRmCCORt (I)) leading to 24 rearrangement pathways of the following type: I F= R I R 2 R m C o C , + O H R t(IV) + R I R > C + C O H R m R t(V) RIRZRtCC+OHRm (VI). In a first approximation values kpRmwere calculated while considering the return of step IV + V, during which group R m migrates, as being negligible. This hypothesis was ultimately verified by measuring the return of this step by a study of the pinacol rearrangement of 16 glycols (RIRZCOHCOHRmRt (11) V IV VI) chosen as constituting the structural limits for the studied environments Gco and Gc,. Our results show that the return of step IV + V is too small to be the cause of the observed structural effects. The measured values of kpRmcover a range of about three powers of ten. Linear relationships have been observed between log kpRmand the number of carbon atoms, no and n,,comprising the environments &coand &ct: log kpRm(Gco,Ec,) = log kopRm an,, and log kpRm(Eco, Gc,) = log kopRm bn,, in which u = 0.017 ( R m = Me) and 0.26 (Rm = Et) for Ec, = t-Bu; and b = -0.63 (Rm = Me) and -0.66 (Rm = Et) for Eco = Me, Me. Thus, the environment &ct opposes migration, whereas the environment &coassists it. Moreover, the effect of &ct is more important than that of &c0,but it is less sensitive to the nature of Rrn. Among the structures studied two types Get) = log of behavior are observed: a strict additivity of environmental effects as shown by the relationship log kpRm(&co, kopRm uno bn, i (in which i = 0) and a partial additivity (i # 0). Each migrating group is characterized by a network of linear relationships. A comparison of the theoretical network ( i = 0) with the experimental one shows that "i" is most often independent of the nature of R m . It is likely that conformational effects and unbonded steric interactions will explain "i".
-
--
+
+
+
+
+
+
The migratory aptitude' of a group is a complex phenomenon which depends not only on the nature of the group, but also on the interactions between the group and the structure in which it migrates (group-structure interactions).* The lack of systematic information regarding these interactions is certainly one of the main reasons for the absence of quantitative data concerning the migratory aptitudes of alkyl g r o ~ p s . ~ I n the preceding article4 we have shown that the metathetical transposition of a,a'-bis-tert-alkyl ketones (Scheme I) was a reaction particularly suited to the obtainment of this kind of information. Reasoning that it is not possible to consider the notion of migratory aptitude without considering these interactions, we propose in this article to use this reaction for a systematic study of group-structure interactions in order to
measure their importance and to attempt to specify the nature of the structural parameters responsible for this effect. The complexity of this kind of interaction has led us to begin by separating arbitrarily the influence of the environments Ec, and Ect of the origin and terminal carbons, C, and C,, of the migration5 Thus, we have studied how the rate constant k p R m varies as a function of Gc, when the environment of the ter-
minal carbon is held constant a t Ect and conversely, as a function of Gct with Ec, constant. Every variable environment
Scheme I
bis-t-alkyl ketones
K,
' ;[
ECo
R
Rm
Rm
+
C - C - R o
1
1
t
E
+Ct ".Rm
/
.
1
It
I
1 7 Rt C o - C - R t I ;Co-C-Rm I I *
I
Q ,
OH
OH Rearrangement produc ts
Bauer, Dubois
/ Structural Effects an A l k y l Migration
7000 shall be expressed by & and every constant environment by E.
eleven a&-bis-tert-alkyl ketones, ten of which are obtained by the progressive substitution of the methyl groups in Ia by ethyl groups, in such a fashion that Ia and Ib constitute, with the exception of Ik, the structural limits of the studied series. The migration constants kpRm of the methyl and ethyl groups for ketones Ia and Ib, calculated starting from eq 1, were: kpMe= 775 X and kpEt= 8 X lo-* s-l. The determined values of G were equal to 0.96 for Ia and 0.70 for Ib, i.e., approaching unity. Calculation of these two constants, from the following simplified equation
Results The study of the metathetical transposition of hexameth-
La, R,= &
Ib, R,
=
= R2 =
R, R,
= R,’= R i = R j / = M e = R,’= = R,’ = Et
R,’
ylacetone (Ia) and hexaethylacetone (Ib) in 96% HzS04 a t 25 O C 4 indicates that the partial rate constant for migration (kpRm)of a group R or R’ may be calculated from hpRm =
-_ B
kexpt
(1-“(100/A))P
B
= -kexpt
100
GP
100
in which G = 1, respectively, yields kpMela= 742 X and kpEtlb= 5.5 X lo-* s-l, thus showing that the deviation introduced by this approximation on the values of log kpRmis 0.02 for Ia and 0.16 for Ib. This result shows that, insofar as these latter values constitute maximum deviations, the values of kpRmcan be calculated from eq 2 as a first approximation for the ketones included between Ia and Ib and for Ik structurally like Id. All values of kpRmthus calculated are shown in Table I. This approximation can, however, be questioned if, instead of comparing the structures related to ketones Ia, IC, Id . . . Ib, one compares for each path of the metathetical transposition the nature of the migrating group, Eco, and Ect. For Ia, R m = Me, Eco = Me,Me and Ect = t-Bu; for Ib, R m = Et, Eco = Et,Et and Ect = Et$: thus, for both compounds, the three structural parameters (Rm, Eco, and Ect) are different. Under these conditions, nothing proves that the approximation of G in eq 2 can be extrapolated from the migration of a given group, Rm, migrating in variable Gco and Gct environments. This leads us, so as to verify the validity of this approximation, to determine the values of G for the structures characterized by &co= Me,Me and Et,Et and by Gct = t-Bu and Et$ which, for each migrating group, constitute the structural limits of
(1)
in which kpRmis the partial rate migration constant of a migrating group Rm; kexptis the disappearance constant of ketones I in the medium; P is the statistical factor equal to the number of R or R’ groups in I whose migration leads to the same product; B is the percentage of the different reaction pathways of the metathetical transposition of I; the term G = 1 H ( 100/A) takes into account the return of step IV V, during which the group R m migrates (Scheme 11), and is measurable by H ( 100/A), in which H is the molar ratio of I in the sum of products I 111 X formed in 30 s by the pinacol rearrangement of glycols 11; and A is the percentage of the pathway passing via ion V in the pinacol rearrangement of I1 leading to these same products. For a nil return H ( 100/A) = 0 and G = 1; G < 1 for a non-nil return. In order to study the nature and importance of the interactions existing between a migrating group and the structure where the migration takes place, we present herein the constants kDRmobtained from the metathetical transpositions of
-
-
+ +
Scheme I1 Metathetical
F ragme n t a t i on
Pinacol rearrangement
transposition
.
Rm Rm
L
Rt
L
.
kl
C ,I
O
-
Rm
-
RIP
111
k- I
%
7C -
Rl
-
Rt
OH
R2
v
IV
F r a g m e n t a t i o n p r o d u c t s where X :
Rl-
R-
’CH - C - R n 11 0
Rt
4 .-
p1
Rt
if
f o r I 1 L : VII-+VI i f
2 5
R1 or
-u
R2 b e c a u s e R 1
= R2 = Rm
R:
f o r I1 M : V I I W V I b e c a u s e R I = R2 f Rm
Journal of the American Chemical Society
/
98:22
/ October 27,1976
+
C
1
1
Rp
OH
+
RC 1:
= C I R m
OH
RE
I?t = C
-’ \
R 1 b e c a u s e R I # R2 = Rm
-C-
VI
VI11
f o r I 1 K : VII-VI
-
I
R2
Rm
.!I *
C
\
I1
I
-
R‘ R
i
2
”;
IX
700 1 Table I. Experimental Rate Constants ke t of Ketones I and Partial Constants kpRm, Calculated by Equation 2, in Rearrangements of Bis-rerr-alkvl Ketones. in 96 Wekht % HeS8&at 25 "C. R, \
R,-C-C-C-R,
d
R,/
7) 'R,
1oskexpt f
1os-
kpRm,c
R,
R,
R',
R',
R',
s-l
Rm
&c0
Ia IC
Me Me
Me Me
Me Me
Me Me
Me Me
Me Et
4450 3080
R,
Id
Me
Me
Me
Me
Et
Et
4330
Me,Me Me,Me Me,Et Me,Me Me,Me Et,Et Me,Et Me,Me Et,Et Me,Et Me,Me Me,Et Me,Me Et,Et Me,Et Me,Et Me,Me Et,Et Et,Et Me,Et Et,Et Me,Et Et,Et Et,Et Et,n-Pr Me,n-Pr Me,Et Me,Me
Ketones R ,
Ie
Me
Me
Me
Et
Et
Et
9000
If
Me
Me
Et
Me
Me
Et
1180
Ig
Me
Me
Et
Me
Et
Et
1400
Ih
Me
Me
Et
Et
Et
Et
2775
Ii
Me
Et
Et
Me
Et
Et
333
Ij
Me
Et
Et
Et
Et
Et
277
Ib Ik
Et Me
Et Et
Et nPr
Et Me
Et Me
Et Me
33 5250
R, R', R', R, R', R', R, R', R, R, R, R, R', R', R, R, R', R, R, R, R, R', R, R, R, R, R',
g Ct
t-Bu t-Am t-Bu t-Bu t-Hex t-Bu t-Bu Et,C t-Bu f-Am r-Am t-Hex t-Hex t-Am t-Am Et,C Et,C t-Am r-Hex t-Hex Et,C Et& t-Hex Et,C t-Bu t-Bu t-Bu
(Me,Et,u-Pr)C
Eb
Pf
100 17.5 49 33.5 2.8 15.2 82 0.3 99.7 62 38 5 3.7 13 78.3 0.3 0.4 99.3 16 84 0.6 6 93.4 100 16 54 28 2
6 3 2 1
3 1
2 3 3 4 2 2 1 1 2 2 1 3 2 4 1 2 3 6 1 1 1
3
s-1
742 180 755 1030 40d 660 1775 9e 2990 183 224 35d 52d 182 548 4.2e 1l.le 918 26.6 70 1.6e 8d 86.5 5.5 840 2830 1470 35d
log kpgm + 8 Paths 2.87 2.2s 2.88 3.01 1.60 2.82 3.25 0.95 3.48 2.26 2.35 1.54 1.71 2.26 2.74 0.62 1.04 2.96 1.42 1.84 0.20 0.90 1.94 0.74 2.92 3.45 3.17 1.54
1 4 2 13 7 3 14 10 15 5 16 8 19 6 17 11 22 18 9 20 12 23 21 24 26 27 28 25
a T h e standard deviation is *2%. bE is the percentage of the different reaction pathways of the metathetical transposition of I. Depending on the percentage corresponding t o the paths and the GLC separation of the different compounds, the values are at t 0 . 5 or +1. For amounts below 2% the error may be as high as 25%. cThe constants (calculated from eq 2) depend on the values found for keXpt and B. Values (except those with a further reference) are at +3%. dValues are at + l o % .V a l u e s are at +25%.fP is the statistical factor equal t o the number of identical groups giving rise to the same product by migration.
these environments. Furthermore, verifications have been carried out on several intermediate structures. Determining Parameter G. Depending on the structure of the glycol, the value of G can be directly deduced from the sum percentages of formed products, if each of the two pathways (via ion V and VII) of the pinacol rearrangement lead to different products (Scheme 11). If both of these pathways lead to the same product, a tracer study with I3C, such as previously d e ~ c r i b e dis , ~required. All of these glycols I1 fall into three populations: population IIK, in which Rl = Rz = Rm; population IIL, in which R1 # R2 = Rm; and population IIM, in which R I = R2 # Rm, with R t = t-Bu, t-Am, t-Hex, and Et3C for each population. The glycols IIK are synthesized by the method described in the previous article4 RtCOCOOR + R , L i IIK R, = Me or Et +
and the glycols IIL and I I M by successive condensations of methyllithium and ethyllithium or vice versa, with the a-ketoester. When isotopic labeling is required, the a-ketoester is labeled on the carbonyl group with I3Cand the products yielded by the pinacol rearrangement are analyzed as already mentioned4 by mass spectrometry. For glycols I I M the tracer studies are not necessary because the products, formed via V and VII, re different (Scheme 11). For structures characterized by a given migrating group ( R m = M e or Et), the limited environments (Gco = Me,Me or Et,Et), and the environments &ct = t-Bu, t-Am, t-Hex, and
Et$, the values of H , A, and G, as well as those of log kpRm deduced from eq 1 (compared to log kpRmvalues obtained from eq 2), are given in Table 11. These results show that the G values are never smaller than 0.68 and the deviation between the values of log kpRm,determined from eq 1 and 2, never goes beyond 0.17, Le., it never exceeds the observed deviation for Ib by more than 0.01 (and this only once). Under these conditions the approximation on G appears to be acceptable; therefore, the values of log kpRm,calculated from eq 2, will serve as a basis for the following discussion. Linear Relationships. T o begin with, our results show that the partial rate constants kpRmof a migrating group R m can be considerably influenced by the structure in which the migration takes place.6 In effect, for methyl and ethyl groups, the range spans something approaching three powers of ten. This indicates clearly that in a determination of any quantitative scale of migratory aptitudes it is necessary to consider interactions between the overall structure and the migrating group. Influence of Environments 6c0 and 6ct. For a given R m group we see from Table I that each substitution of methyl groups by ethyl in &ctproduces a decrease in the migration rate of the group in question. Nevertheless, similar modifications in &cohave effects which appear less systematic, sometimes accelerating and sometimes retarding this rate. Linear Relationships between log kpRm and f(R , , R ~ ) . The results in Table I lead to some interesting observations. Thus, for a given migrating group and a constant terminal environment Ect, there exist linear relationships between log kpRmand Bauer, Dubois
/ Structural Effects on Alkyl Migration
7002 Table 11. Determination of G, Obtained by Pinacol Rearrangement of 11: Influence of G on Constants k p R m A
gco
Rm (R,,R,)
Bct (Rt)
Ha
Ab
GC
Me Me,Me
t-BU t-Am t-Hex Et,C t-B u
0.04 0.059 0.137 0.215 0.085 0.073 0.1 17 0.106 0.26 0.248 0.28 0.28 0.15 0.1 7 0.28 0.32 0.25
100 99.3 98.6 98 lOOf 100 100 100 96 95 94 93 100 100 100 100 >99
0.96 0.94 0.86 0.78 0.90 0.90 0.85 0.84 0.73 0.74 0.70 0.70 0.85 0.83 0.72 0.68 0.75
Me Et,Et
t-Am
t-Hex Et,C t-BU t-Am t-Hex Et,C t-BU
Et Me,Me
Et Et,Et
t-Am
t-Hex Et,C t-Hex1
Et Me,Et
log kpRm + 8d 2.89 2.28 1.67g 1.06h 2.87 2.31 1S O 0.28h
3.08 2.43 1.868 1.21h 3.61 3.09 2.09 0.90 1.97g
Paths
log kp Rm + 8e
1‘ 4‘ 7’ 10’ 3‘ 6’ 9’ 12‘ 13’ 16‘ 19’ 22’ 15’ 18’ 21’ 24’ 20’
2.87 2.25 1.608 0.95h 2.82 2.26 1.42 0.20h 3.01 2.35 1.718 1.04h 3.48 2.96 1.94 0.74 1.848
Paths
% of prod- hyperucts passing conjuvia ion VIIi gation
1 4 7 10
3 6 9 12 13 16 19 22 15 18 21 24 2w
0 0.7 1.4 2 16 26.5 22 32.5 4 5 6 7 0 0 0 0
