A Derivation of the Masamune Rule of Multiplicativity in Double Asymmetric Induction Kensaku Nakayama California State University, Long Beach, Long Beach, CA 90840 The ability to prepare one diastereomeric or enantiomeric isomer in excess in a given chemical transformation where a stereoisomeric distribution of products is possible is currently one of the most highly sought goals in the field of synthetic organic chemistry ( I ) . From a preparative viewpoint, the development of such a technology minimizes or eliminates the often difficult process of isomeric separation as well as the attendant loss of valuable starting material transformed into undesirable stereoisomers. Moreover, by achieving true control of the stereochemical outcome in chemical transformations, the synthesis of any stereoisomeric analogue of various biologically important compounds becomes possible. Clearly, such materials would be of great value in the area of bioorganic chemistry and biochemistry where the study of structure-activity relationships between a biomolecule and its substrate analogues - continues to be an important investigative method (2,31. The understandinn of thestereochemical course of a given chemical reaction has often been rewarded with further insight into the physical factors governing the reaction course (e.g., discovery of the Walden inversion in the S N mecha~ nism). Therefore, another major dividend from studies to achieve stereochemical control should be an increased understanding of the mechanism and, in particular, the steric and electronic factors involved in various chemical reactions. Currently, there exists in the literature a staggering number of examples that address the problem of achieving high stereoselectivities in a wide variety of chemical transformations, including (single) asymmetric synthesis (1). This methodology involves the reaction of an achiral reactant with a second optically pure (homochiral) (4) reactant to produce a mixture~ofop&ally active products. For example, in an investigation of the Diels-Alder reaction by l'rost et al. (5) (eq I ) , theR-enantiomerofdiene I (R-I)reartswith acrolein 2 as theachiral partner in the presenceof BF,. OF:[? affordine a 4.51 mixture of the diastereomeric cvcloadducts 3 and 4. k'hen diene 5, chosen by Masamune audco-workers (4) as an achiral model for 1, is allowed to react with the chiral dienophile R-6 (eq 2), the ratio of the diastereomers 7
20
Journal of Chemical Education
to 8 obtained is 8:l. One can now approximate the diastereofacial selectivity (DS)of R-1 as 4.5 while that of R-6 as 8.
In contrast to the numerous reports of single asymmetric
induction in the literature, there are far fewer examples that address the more complex issue of achieving high asymmetric induction when turi homochiral reactants &e allowed to react (double asymmetric induction). The Diels-Alder reactions involving two pairs of homochiral reactants, R-l with R-6 and R-1 with S-6, provide an elegant example (4). When the homochiral reactants R-1 and R-6 are allowed to react (eq 3), the ratio of diastereomers 9 to 10 generated is 40:1, a ratio greater than the DS of either reactant. Note that in reactions 1and 2, the same absolute configurations are preferentiallv formed a t the newly generated stereogenic centers for eachieartant K-l and R-6.The combination of reartanr R - l and R-6 is therefore termed a marched pair. In contrast, the Diels-Alder reaction of R-I and S-6 (eq 4 ) resulm in only amodeststeret~selectivitywiththeratioof 11 to 12heing 1 2 . Because this ratio is smaller than the DS of either reactant. the reacting pair R-1 and S-6 is referred to as the rnismatched pair.
quotient of the DS of R-6 to R-l (chosen in this order such that the calculated DS is greater than 1) is (8 + 4.5) or 1.8, which is also verv nearlv the ex~erimentallvdetermined ratio of 12 to 11. A corollarv of the above rule has an i m ~ o r t a n svnthetic t implication.'One can envision, in the reaction o f a chiral substrate with a chiral reagent, the use of an R or S reagent with a large diastereofacial selectivity that enhancesthe "apparent" facial selectivity of the substrate in the matched pair reaction and overrides i t in the mismatched pair. In this way, the reagent controls the stereochemical course of a reaction. creating either an R or an S stereoeenic center (or centers) in the desired manner. The followingstudies involving the aldol reaction exemplify this corollary. Reaction between homochiral aldehyde 13 and the boron enolate 14 (60) possessing the indicated 1Z(0)1olefinic geometry results in the formation of the two2,3-syn diastereomers 15 and 16 (eq 5) in a modest 3:2 ratio (DS of the substrate). Meanwhile, the condensation of 2-methylpropanal 17, chosen as the achiral analogue for 13, with the homochiral boron enolate S-18 (66) . . .Droceeds to eive a mixture of two 2,3-syn diastereomers 19 and 20 (eq 6)in a ratio exceeding 100:l (DS of the reagent).
-
-
13
\
SPh 14
Recentlv, a thorough review qualitatively relating the stereoselectivities in single asymmetric reacrions to that of the corresponding double asymmetric process was published by Vasamune ( 4 ) . In summarizing the large body of experimental data ol~tainedhoth in his laboratories and those of other workers, Masamune proposed the rule of multiplicarivity. l'his rule states that the degree of asymmetrir induction obtained in double asvmmetric induction is avproximated by (a X b) for a matched pair and (a ib j f o r a mismatched pair where a and b are the DS for each of the chiral reactants involved. When the multiplicativity rule is applied to reaction 3, we obtain (4.5 X 8) or 36 from the product of the DS of R-l and R-6, a value essentially the same as the 40:l experimental ratio of 9 to 10. Similarly, in the case of reaction 4, the Volume 67
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In a series of double asymmetric reactions (6c), homochiral aldehyde 13 is allowed to react with homochiral enolate S-18 to provide a mixture of 2,3-syn diastereomers 21 (3,4-anti) and 22 (3,4-syn) in a ratio greater than 100:l (eq 7). This clearly represents the result of a matched pair of reactants. A change in the sense of chirality of the boron enofate 18 from S toR brought about a dramatic reversal in the ratio of 3,4-syn and 3,4-anti products (eq 8). Thus, reaction of 13 and R-18 leads to the formation of isomers 23 and 24 inaratioof 1:30 where the 3,4-syn product constitutes the major stereoisomer. This example corresponds to the mismatched pairing of reactants.
The DS predicted for reactions 7 and 8 by the multiplicativity rule is approximately realized by the experimentally achieved DS. Specifically, the product of the DS's of aldehyde 13 and S-18 is effectively (100 X 1.5) or >loo, which translates to a ratio of >100:1 for the diastereomers 21 and 22.The quotient of the DS of S-18 and 13is (100 + 1.5) or 67, indicating a predicted ratio of 67:l for 24 to 23, whereas a ratio of 30:l was achieved experimentally. The aldol study ahove demonstrates the approximate, qualitative characteristic of the multiplicativity rule. This arises in part from the variable nature of the DS values assigned to each of the reactants, which critically depend on the chiral and achiral analogues chosen for the comparison reactions. The multiplicativity rule outlined ahove is not a coincidental result, hut has a firm theoretical basis for its validity. I t will he shown herein that the oualitative rule hvoothe. sized by Masamune can be derived. given some key assumptions regarding the nature of the chem~calprocess involved.
.
Rule Derlvatlon of the Multl~llcatlvit~ Let us consider a bond-forming reaction between achiral reactants X and Y where the creation of a new chiral center or centers takes place as a consequence of the reaction (eq 9). The symbol (*) indicates the generation of stereocenter(s), while the lines connecting X and Y with (*) designate the formation of a bond or bonds. Confining our discussion to the case where the oossihle stereochemical outcome a t the newly formedchiral centerta) islimited toonly enantiomeric relatiooshios. two ntereochemical descriotors. - . (--I . and i"). are defined where the former symbol represen& a stereo: chemical assignment that is enantiomeric in absolute configuration to that of the latter. We further define X*- as a homochiral analogue of reactant X with a kinetically controlled diastereofacial selectivity toward the (*-) stereochemical outcome. By employing these definitions, the reaction between X*- and the achiral reactant Y can be represented by reaction 10. Conversely, reaction between homochiral Y*- with also a kinetically controlled diastereofacial selectivity toward the (*-) stereochemical outcome and achiral X can he expressed as reaction 11.
-
x + Y x-(*)-Y x*-+ y X*--(*-)-y
-
major X + y*--X-(*-)-y*major
(9)
+ X*--(*+)-Y minor
+ X-(*+)-y*minor
(10) (11)
(n,
From transition state theory the rate constant for a kinetically controlled chemical process is related to the free energy of activation hy where k is the rate constant, K is the transmission coefficient, keis theBoltzmann constant, h isplanck's constant, T is the absolute temperature, R is the ideal gas constant, and AGt is the free energy of activation. If we assume the transmission coefficients of the competing diastereomeric pathways resulting in the two stereoisomers in reaction 10 to be the same, then the diastereofacial selectivity for reagent X*can he expressed as the ratio of the rate constants for each manifold (eq 12). In these formulations, k p ) , is defined as the rate constant for the (*) manifold for eq n and AGtp)," represents the corresponding activation free energy. Analogous analysis results in eq 13 as the expression for the DS of reagent Y*-. k(.-),,(.*,l = P
- R A G t , - ) , , - AG'*),I
(12)
.-l,,,.+l,l, = P - A G t . - , -G +I (13) According to our formalism, then, the reaction between the so-called matched pair of reactants, X*- and Y*-, can be
22
Joumal of Chemical Education
represented by reaction 14 and the DS for this process can then he formulated as eq 15.
x*-+ y*-
-
+ X*--(*+)-y*-
X*--(*-)-y*-
major
minor
(14)
Let us assume for reaction 14 that the physical factors present in reagents X*- and Y*- that impinge on the transition state and are responsible for the stereodifferentiation do not interact with each other along the reaction coordinate leading to each diastereomeric transition state. Then, X*- experiences the same energetics while undergoing reaction with Y as it would with Y*-. A similar conclusion is reached with respect to the reaction between Y*- and the reagents X and X*-. Therefore, the energetics for the two manifolds in reaction 14 can be expressed as
Clearly, reaction between homochiral reagents X*- and Y*+ (eq 26) would constitute the case of the mismatched pair and eq 27 formulates the DS for this reaction. x*-+ y * + x*--?-)-y*+ + x'--(*+)-y*+ (26)
-
If we allow for the same assumptions proposed for reaction 14 to operate for reaction 26, we can make the conclusions illustra&d in eqs 28 and 29.
Substitution of eqs 16 and 17 into eq 15 and rearrangement of terms as follows results in
Hence. with the aforementioned assum~tions.we obtain the result that the degree of asymmetric induction expected for t the individual diartereofaa matched i air is the ~ r o d u c of cial se~ectihties. In order to discuss the degree of asymmetric induction achieved in the case of the mismatched pair, we must now consider the two diastereoselective reactions, 18 and 19.
x*-+ y
-
X + y*+
+ X*--(*+)-y
X*--(*-)-y
major X-(*-)-y*+
minor
+ X-(*+)-y*+
minor
major
=
[email protected],,o
A@(.+
(19)
(20)
,, = A G ~ ~ . + , , , ~
Therefore, we obtain the conclusion that the degree of asymmetric induction achieved for a mismatched pair is the quotient of the individual diastereoselectivities.
(18)
Note that reaction 18 is identical to reaction 10, and hence A@l..,,,,
By employing eqs 22 and 25, we can recast eq 30 as
Acknowledgment The author is grateful to Stuart R. Berryhill (CSULB), Dorothy M. Goldish (CSULB), Satoru Masamune (MIT), and Robert M. Kennedy (MIT) for valuable comments:He is also indebted to Cheryl Muilenburg (CSULB) for her expert technical assistance. Lnerature Cited
(21)
Thus, the ratio of the diastereomers formed in reaction 18 is kl.-
,,,,lk(.+,, = exp
1(-11RT)(AGi~.-l,18
= ~l'-,,,o~~l.+,,lo
..
- AGi(.+j,l,)l
"., (22)
In contrast, since reaction 19 is enantiomeric to reaction 11, the equalities represented in eqs 23 and 24 must hold. Act(.-
= AGtl.+j,,l
(23)
AG'l.+,,,s
= Actl,-,,,,
(24)
This implies that the DS for reaction 19 can be expressed as
5. T m t , B . M.;O'Kmngly,D.:Balletire, J, L, J.Am. Chem.Soc. 1380,102,7595. TefmhedronLatL. 1979,3937, 6. a.Hirama,M.;Garuey,D.S.;Lu,L.D.-L.;Mssarnune.S. b. Masarnunc,S.: Choy, W.; Kerdesb, F. A. J.:Irnperiali. B. J. Am. Chrm. See. 1981, 103, 1566. c. Masamune, S.: Pratt, A. J., M-chusetta Institute of Technology, unpublishedresults.Al.osee: Massmune,S:Hirarna. M.: M o d S.:Ali,Sk.A.:Gauuey, D. S. J.Am. Chem.Sac. 1981,103,1566. 7. L0wry.T. H.:Riehardson,K. S. Merhoniamand Theory in O w n i c C h ~ m i 3 t r yHamer ; and Row: New York. 1976; p 113.
This paper is dedicated to Satoru Masamune on the occasion of his 60th birthday.
Volume 67
Number 1 January 1990
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