Thermal Aliphatic Claisen Rearrangement
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Thermal Aliphatic Claisen Rearrangement

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Chemical Reviews Volume 88. Number 8 December 1988 The Thermal, Aliphatic Claisen Rearrangement FREDERICK E. ZIEGLER steriing Ctmm!.qtry Labaatory. Yale UnivennV, New Haven. Connecticur 08511-8118 Receh.ed April 25. 1988 (Revised Manusnipt Received Seplember 8. 1988) Contents I. Introduction 11. Historical Overview 111. Mechanistic Aspects A. Kinetics B. Retro-Clalsen Rearrangement C. Competitive Rearrangements...

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Reviews Volume Chemical 88. Number 8 December 1988 The Thermal, Aliphatic Claisen Rearrangement FREDERICK E. ZIEGLER steriing Ctmm!.qtry Labaatory. Yale UnivennV, New Haven. Connecticur 08511-8118 Receh.ed April 25. 1988 (Revised Manusnipt Received Seplember 8. 1988) Contents I. Introduction 11. Historical Overview 111. Mechanistic Aspects A. Kinetics B. Retro-Clalsen Rearrangement C. Competitive Rearrangements 1. [3.3] Claisen vs [2,3] Wmig Rearrangement 2. Diinylcarbinol Derivatives 3. Elimination D. Stereochemistry 1. Transition State 2. Vinyl Double-Bond Geometry 3. Secondary Allylic Alcohols 4. Tertiary Allylic Alcohols 5. RingBearing Substrates Heteroatom Substituents A. The Vinyl Group 1. C, Hetero Substituents 2. C, Carbon Hetero Substituents B. The Allylic Group 1. Oxygen Substituents 2. Silicon Substituents Remote Asymmetry A. Acyclic Substrates B. Ring-Bearing Substrates Consecutive Rearrangements A. Sequential Rearrangements 8. Tandem Rearrangements C. Iterative Rearrangements Synthetic Applications A. (1,llRearrangements 8. (1.2JRearrangements C. (1.41-Rearrangements D. (1.5lRearrangements E. (1.61-Rearrangements F. (2.41-Rearrangements G. (4.5l-Rearrangements H. (4.61-Rearrangements I. (5.61-Rearrangements Biochemical Aspects Concluding Remarks 1423 1424 1425 1425 1427 1427 1427 1428 1429 1429 1429 1429 1431 1433 1433 A. Frederick E. Ziegier received his B.S. from Fairiegh Dickinson University in 1960 and Ph.D. in 1964 from Columbia University where he studied under Gilbert Stork. As an NSF postdoctoral student. he spent 1 year in the laboratory of George Buchi at The Massachusetts Institute of Technology. He joined the Yale University facuHyin 1965 where he currently hokk the rank of Professor of Chemistry. Hs research interests include the synthesis of i physiologically active natural products, the study of the stereochemistry of aganic reactions. and the development of new synthetic methods. IV. 1435 1435 1435 1435 1436 1436 1437 V. VI. 1438 1438 1438 1440 1440 1440 1441 I . Introduction This past year the diamond annivenary of the publication of Ludwig Claisen's paper "Uber Umlagerung von Phenol-allyl-athern in C-allyl-phenole^ describing his now eponymous rearrangement' was observed. And what a gem it has proved to he! Ironically, the majority of the text of the paper and all the experimental details dealt with the substance of the title while the first paragraph mentioned, in almost parenthetical fashion, the rearrangement of the 0-allylation product of acetoacetic ester 1 to its C-allylated isomer 2 upon distillation in the presence of ammonium chloride. Arguably, the aliphatic rearrangement has stimulated more interest in both its mechanistic and synthetic aspects than its aromatic counterpart. Today, the aliphatic Claisen rearrangement is but one member of the class of [3,3] sigmatropic rearrangements. The prototype for the rearrangement is the transformation of allyl vinyl ether 3 into 4-pentenal (4). 0 1988 American VII. 1442 1442 1442 1443 VIII. IX. 1444 1444 1444 1445 1446 1446 1448 1448 0009-2665/88/078&1423$06.50/0 Chemical Society 1424 Chemical Reviews, 1988, Vol. 88,No. 8 Ziegler 1 2 dehydrohalogenation to form the archetypical allyl vinyl ether (3), which underwent successful rearrangement to aldehyde 4 at 255 "C. In addition, allyl isopropenyl ether (9) was prepared by acid-catalyzed elimination and was subjected to rearrangement to afford ketone 10. xo4 0 H` 8 This review will deal with the history, mechanism, stereochemistry, and applications of the thermal, aliphatic rearrangement2 over the past 75 years, as recent publications have provided excellent summaries of the effect of catalysts on the rea~angement.~ While the contributions to this area are legion, an effort will be made to deal with both historical contributions and those reports that exemplify the scope of the reaction. Although heteroatom Claisen rearrangements will not be covered, examples will be provided as they apply to the discussions at hand. -L 2550c 9 10 I I . Hlstorlcal Overvlew Bergmann and Corte (1935)4and Lauer and Kilburn ( 1937)5investigated the rearrangement of ethyl 0-cin- namyloxycrotonate ( 5 ) in the presence of ammonium chloride to determine if "transposition" of the allyl unit occurs, as had been established in the aromatic series? The former collaborators reported the formation of the "nontransposed"product 6 and "transposed" 7 while the latter investigators observed only the product of "transposition". The formation of P-keto ester 7 provided access to a product formally derived from the s$' C-alkylation of cinnamyl halides with acetoacetic ester anion. In the early 1940s, Carrolllo investigated the basecatalyzed reaction of acetoacetic ester with allylic alcohols to produce olefinic ketones.ll In particular, the stereospecificity of the reaction was demonstrated in the case of the structural isomers cinnamyl alcohol (11) and phenylvinylcarbinol (13), each giving a transposed product. Aware of the results of Bergmann and Lauer, Carroll proposed a mechanism that invoked s N 2 ' displacement of hydroxide by acetoacetate anion. Kimel and Cope12(1943) clarified the mechanism by demonstrating that acetoacetic acid esters derived from allylic alcohols undergo the rearrangement. Moreover, the use of diketene provided a reactive equivalent of acetoacetate that made the formation of substrates routine. Thus, this variation of the reaction provided nonacidic conditions, compared to those of Hurd, for the generation of y,d-butenyl methyl ketones. CH3COCH2C02EWNaOE1 Ph* H O ). !& 12 P h + EtOH + CO, 11 or diketene; NaOEt CH3COCH,C02EWNaOEt L Ph PhT + EtOH + CO, or diketene; NaOEt 13 14 5 P.31 oTph C0,Et 7 Bergmann and Corte employed Claisen's method7 of ammonium chloride catalyzed exchange of cinnamyl alcohol with ethyl 3-ethoxy-2-crotonate for the formation of 5 while Lauer and Kilburn used sodium cinnamylate and ethyl P-chlorocrotonate. The use of ammonium chloride in the rearrangement step soon disappeared, although it had been shown to have "a small, but significant, increase in rate" as a heterogeneous catalyst.8 While the @-ketoesters provided access to y,b-unsaturated acids by Haller-Bauer cleavage (Le., retroClaisen condensation) and y,d-unsaturated ketones by acid hydrolysis, formation of y,d-unsaturated aldehydes had not been realized. In 1938, Hurd and Pollackga subjected @-bromoethylallyl ether to base-promoted The generation of vinyl ethers by the dehydrohalogenation procedure of Hurd did not provide a general route for the derivatization of allylic alcohols. A solution to this problem was provided by Burgstahler and Nordin13 who adapted the mercuric acetate catalyzed exchange of alcohols with alkyl vinyl ethers14 to the formation of allyl vinyl ethers (15 16).15 These investigators were able to demonstrate that the rearrangement was successful in systems wherein at least one of the double bonds is contained in a ring (16 - 17). - ROCH=CH, Hg(OAc)z 15 16 P A q? CHO 17 In 1967, Marbet and Saucy reported16the acid-catalyzed exchange and rearrangement of seemingly labile tertiary allylic alcohols with 2,2-dimethoxypropane or 2-methoxypropene that resulted in the formation of methyl ketones.17 The conversion of linalool to gera- Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1425 nylacetone laid the groundwork for a commercial synthesis of vitamin A alcohol. The first practical example of the preparation of y,b-unsaturated carboxylic acids via the aliphatic Claisen rearrangement was demonstrated by Arnold and co-workers18in 1949.19 The allylic esters 18 and 20 of diphenylacetic acid underwent stereospecific rearrangement upon treatment with mesitylmagnesium bromide at ambient temperature. diradical 0% Ph diyl - 0 100% 20 21 Figure 1. Transition-state profile of the aliphatic Claisen rearrangement. Other variations employed sodium hydride as the base in refluxing toluene;18a9z0 however, a significant breakthrough was reported by Irelandz1who, following Rathke's reportzz of the use of lithium dialkylamide bases for the generation of ester enolates, demonstrated that the method served as a means to achieve the Claisen rearrangement of acylated allylic alcohols at ambient temperature (22 23) and, as will be seen later, provided a method for the control of enolate geometry. Both the enolates and their 0-silyl ketene acetals underwent facile rearrangement.z3 ZZZ. Mechanistic Aspects A. Kinetics - 0 OTMS 22 23 Although Ireland's contribution improved the formation of y,b-unsaturated acids, it was preceded by two independent contributions that realized amides and esters via the Claisen rearrangement. In 1964 Eschenm ~ s e r adapted Meerwein's observationsz4c the ~~~p~ on exchange of amide acetals with allylic alcohols, thereby facilitating the formation of y,b-unsaturated amides upon rearrangement (25 26). In a similar fashion, 1970 witnessed Johnson's reportz5of the acid-catalyzed exchange of ethyl orthoacetate with allylic alcohols and the subsequent formation of y,b-unsaturated esters upon rearrangement (27 28). - MeC(OMe)?NMeZ, xylene 1 4OoC, 14h ''O OH 25 I m OH OH 27 MeC(OEt),, propionic acid 138'C, 3h Et02C C02Et 28 +03H Y "'rf l)L'cA'THF 2) TMSCI e 0 7 7 * 0 24 0 MezNC II C02Me * Me' 26 + The ability of the Claisen rearrangement to give transposed structures led Hurd and Pollackgbto suggest a cyclic mechanism. The rearrangement of allyl vinyl ethers displays a negative entropyz6 and volumez7of activation, both of which support a constrained transition state relative to ground-state geometries. Firstorder kinetics8Vz6and the lack of crossover products8 argue for the intramolecularity of the reaction. The overall exothermicityz6of the rearrangement of allyl vinyl ethers indicates an early transition ~ t a t e . ~ J ~ Using secondary deuterium isotope effects as a mechanistic probe, Gajewskiz9 has concluded that bondbreaking is more advanced than bond-making in the rearrangement of allyl vinyl ether itself. Thus, the transition state (TS) has been suggested to resemble more closely the diradical than the 1,4-diyl. Figure 1 (More O'Ferrall-Jencks diagram) locates the transition state for allyl vinyl ether above diagonal A (diradical > diyl) and below diagonal B (early, not late, TS). Dewar, using MIND0/3 calculations, has supported an early transition state for allyl vinyl ether with bondmaking being more advanced than bond-breaking, thereby requiring diyl character in the transition state.3o Substituents play an important role in affecting the rate of the Claisen rearrangement. Burrows and Carenter,^^ using phenyl anion as a transition-state model, have predicted that ?r-donor substituents at C1, Cz, and C4 of allyl vinyl ether should increase the rate of the rearrangement, while substitution at C5and c should 6 cause deceleration. However, Dewar30has argued that a C5-methoxysubstituent should have a greater accelerating effect than a C,-methoxy group. The presence of electron-donating groups, e.g., EtO-, R3SiO-, and Me2N-, at Cz of the allyl vinyl ether causes a dramatic rate acceleration. Thus, the 2-(trimethylsily1)oxy (29; tllz = 210 f 30 min at 32 0C)21 and the 2-(tert-butyldimethylsilyl)oxy(31a; t l j z = 107 min at 35 0C)3zderivatives rearrange with facility under near ambient conditions, while allyl vinyl ether (tllz= 1.7 X lo4 min at 80 0C)33 requires higher temperatures for rapid rearrangement. While both 29 and its 6-methyl congener 30a (tl,z = 150 f 30 min at 32 oC)zlrearrange 1426 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler at nearly the same rate, the C4-alkyl-substitutedisomer 3 1b rearranges an order of magnitude more rapidly than This difference suggests a kinetic stabilization of the bond-breaking process by the alkyl group in 31b. R - I O Y OTBS GTMS 29 GTMS 30a, R,=R,=H b, R,=Me, R,=H c, R,=R,=Me OMe 31a. R=H b , R=C,Hll O 32 4 O 33 4 O 4 34 Coates and C ~ r r a have~measured the rates of ren~ arrangement of the C4-, C5-, and C6-methoxy-substituted allyl vinyl ethers at 80 "C in benzene. The 4methoxy derivative 32 rearranges 100 times faster than the parent while the 6-methoxy isomer 34 is 10 times faster, thereby demonstrating a strong kinetic stabilization in the former case and a vinylogous, kinetic anomeric effect in the latter.35 The observation of this effect is contrary to the Burrows-Carpenter model. In addition, the 5-methoxy isomer 33 is found to rearrange 40 times slower than the parent, in disagreement with the Dewar prediction. Coates and Curran have suggested a transition state for these systems with dipolar character (enolate-oxonium ion pair). When the solvent is changed from benzene to methanol, 32 and 34 show a 20- and 70-fold rate increase, respectively. In general, solvents have little effect on the rate of the rearrangement. G a j e ~ s khas ~ i ~ attributed the rate enhancement and the greater degree of bond-breaking in the transition state of the Ireland-Claisen rearrangement to the greater stability of the 2-[(trimethylsilyl)oxy]-1-oxaallyl moiety over its oxaallyl counterpart (Figure 1). This conclusion derives from an examination of the heats of formation of the oxaallyl radicals and supports21bthe finding that the relative rates of rearrangement of silyl ketene acetals 30 are 30c > 30b > 30a.37 The effect of the (trimethylsily1)oxygroup is not general to all [3,3] sigmatropic rearrangements as 2-[(trimethylsily1)oxy]-3-methyl-1,5-hexadiene undergoes a Cope rearrangement with a half-life of 2 h at 210 "C. Although the Johnson and the Eschenmoser variants are conducted at elevated temperature, these conditions are required for the alcohol exchange reaction, not necessarily for the rearrangement. This point is amply demonstrated in the latter instance when ketene OJVacetals are generated by an alternative route (35 + 36 37).38 kinetic parameters. Rate accelerations are observed for the C2-CN(krel = ill), C3-CN (krel = 270), and C4-CN (krel = 15.6) compounds while decelerations occur for the C1-CN (krel= 0.90) and C5-CN (krel= 0.11) isomers relative to allyl vinyl ether. The formation of anionic species increases the rate of the rearrangement. The enolates of allyl esters should be considered as the prototypes of strong C2 ?r-donors as they rearrange at ambient temperatures.21 Denmark has reportedm the first example of a carbanion-accelerated Claisen rearrangemen~~l use of The hexamethylphosphoramide (HMPA), as opposed to l&crown-G/THF, accomplishes the conversion of 38a 39a at a lower temperature (50 "C) and in a higher yield (78%). This solvent-induced rate enhancement has been interpreted as ion-pair dissociation. Disubstitution at C1 (38b 39b) causes a greater rate enhancement (20 "C, 15 min),42similar to the silyl ketene acetal case. - - P h s o q ] R HMPA * / R 38 PhSO, 39 a, R=H b, R=Me 40 - 0 35 36 37 In an independent study, Carpenter and Burrows39 have synthesized the five isomeric cyano-substituted derivatives of allyl vinyl ether and have measured their The Carroll rearrangement is accelerated by carbanion formation. Wilson43has demonstrated that /3-keto (DMAP) ester 41, formed by 4-(dimethylamino)pyridine catalyzed addition of (E)-2-buten-l-ol to diketene,44 provides the @-keto acid 43 when treated with 2 equiv of lithium diisopropylamide (LDA) at -78 "C in THF followed by heating to reflux. Decarboxylation is readily accomplished in refluxing carbon tetrachloride to give the ketone in 95% yield. When 1equiv of base is used, no reaction is observed. The thermal reaction in the absence of base requires heating at 200 "C, and the ketone is isolated in only 37% yield. In a similar fashion, BUCK& observed acceleration has in the rearrangement of 3-(allyloxy)-2-butenoicacid 44 prepared by alkoxide addition to the 3-chloro-2-butenoate. When the acid is treated with 1equiv of KH in refluxing toluene for 2-6 h, the potassium carboxylate is stable. However, the use of 2 equiv of KH effects rearrangement via dianion 45 under the same conditions, affording ketone 46 in 68% yield upon acidification and decarboxylation. The rate enhancement occurs for substrates derived from secondary allylic alcohols, but not for primary allylic alcohols. Silyl ketene acetals prepared from secondary alcohols have been observed to rearrange faster than those derived from primary allylic alcohols.21b a-Allyloxy ketones have displayed remarkable rate accelerations. For example, Koreeda and L u e n g ~ ~ ~ ~ have generated the enolate 48a by conjugate addition of Me,CuLi to 2-(allyloxy)-2-cyclohexenone(47); rearrangement to acyloin 49a is complete in 15 min at 0 oC.46bThe rate enhancement has been attributed to an allyl radical/oxyoxaallyl radical anion (semi-dione) pair. For comparison, the silyl enol ether 48b is slower Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88,No. 8 1427 7 0 41 2 equiv. LDATHF * 0 ether as its tetracyanoethylene derivative and to the left by formation of the bisulfite adduct of the aldehyde. Decomposition of the bisulfite adduct reestablishes the equilibrium. These equilibria are presumably driven by the strain of the cyclopropane ring.49p50 -78 'C ---> 65 O C wo 42 I F * +CO2H U'CHO 53 43 THF 73 u54 L 44 &CO~H 2 equiv. KH g+= 55 4 56 0 r 1 I ) toluene, 120 "C 2) H30i L J 45 46 to rearrange, having t l / P= 1.6 h at 62.5 "C. In a related study, P ~ n a r a has ~ s ~ compared the relative rates of rearrangement of 2-(allyloxy)-3-methyl-2cyclohexenone and its derivatives. In refluxing THF (65 "C), the parent ketone 50a has tll2 = 340 h, affording the diosphenol51, while the rearrangement of carbomethoxyhydrazone 50b to 52a is appreciably faster (tl = 22 h). The sodium salt of the hydrazone (50c) is the fastest of the three, rearranging to give 52b with t,,2 = 1.5 h. This method has proved amenable to forming vicinal quaternary centers, and in the case of the carbomethoxyhydrazones 52, a subsequent Wolff-Kishner reduction can be conducted to remove the accelerating f ~ n c t i o n a l i t y . ~ ~ Oppolzer51has observed that silica gel chromatography of aldehyde ester 57a provides recovered substrate (68%) in addition to unsaturated ester 58. During the same period, B o e ~ k m a nobserved that the rear~~ rangement of 57a to 58 occurs quantitatively at room temperature in 24 h. However, the less strained homologue 59a, upon heating in refluxing toluene in the presence of a catalytic amount of HOAc, provides an equilibrium mixture of 59a and 60 (89:ll). Support for a sigmatropic rearrangement rather than a pathway invoking stepwise formation of carbocation intermediates follows from the observation that the stereoisomer 59b does not undergo rearrangement under conditions that are successful with 59a. However, BF3-Et,0 at room temperature is able to convert stereoisomer 57b into 58, ostensibly through a carbocation intermediate that may only be required for the isomerization (57b 57a) and not necessarily for the rearrangement. These investigators have also observed acceleration in the BF3.Et20-catalyzed rearrangement at -78 "C in alkyl-substituted congeners of 59a. These observations have led Boeckman to suggest that the minor product, unsaturated ester 62, formed in the BF,.EkO-catalyzed Diels-Alder reaction (-78 "C) between cyclopentadiene 61 and methyl 2-acetylacrylate, may well arise from the major product of the reaction, norbornene 63, by way of the catalyzed retro-Claisen rearrangement.53 - 47 48a. R=MeCuLi b, R=TMS 49a, R=H b, R=TMS C0,Me R OH RN 57a, R,=CHO, Rz=C02Me b, R1=CO2Me, Rz=CHO 58 , a l% R=O b, R=NN(H)CO,Me c, R=NN(Na)CO,Me 51 52a, R=NN(H)C02Me b,R=NN(Na)CO,Me 59a, Rl=CHO, R2=C02Me b, Rl=COzMe, R A H O 60 61 B. Retro-Claisen Rearrangement The Claisen rearrangement, unlike its all carbon analogue the Cope rearrangement, is an irreversible reaction, except for several specially designed substrates. Vinylcyclopropanecarboxaldehyde (53) has been shown to be in rapid equilibrium with dihydrooxepine (54). Similarly, unsaturated aldehyde 55 forms a 7:3 equilibrium mixture with vinyl ether 56. The equilibrium is shifted to the right by trapping the vinyl Br COMe 62 63 C. Competitive Rearrangements 1. [3,3] Claisen vs [2,3] Wiffb Rearrangement Conceptually, a-allyloxy enolates of the type 65a can undergo either [3,3] sigmatropic rearrangement (anionic 1428 Chemical Reviews, 1988, Vol. 88, No. 8 2iegI er 1) LDA - oxy-Claisen rearrangement)46 or [2,3] Wittig rearrangement.54 Thomas55has observed that ketone 67, upon exposure to t-BuOKlt-BuOH, undergoes a [2,3] Wittig rearrangement to "mainly" keto1 68. In contrast, K ~ r e e d a has *reported that the enolate of phenyl ~~ ketone 69 (from MH and MeOH) in toluene not only shows rate enhancement (M = K, -23 "C, t l l z = 3.3 h; M = Na, 0 "C, t l j z= 2.6 h; M = Li, 96.5 "C, t l j z = 1.1 h) but also gives a ratio of Claisen to Wittig product (70:71) of >98:<2 (M = K, Na) and a ratio of -80:20 when M = Li. To ensure exclusive formation of the Claisen product, enolates need only be 0-silylated (65a 65b) and rearranged to aldehydes (64b). Accordingly, the 0-trimethylsilyl enol ether of ketone 69 affords the 0-trimethylsilyl derivative of ketone 70 upon heating (71 "C, t l j z= 0.5 h). Earlier, Sa10mon~~ had demonstrated the utility of the transformation 65b 64b by preparing the 0-trimethylsilyl enol ethers with (TMS)C1/Et3N. The a-silyloxy aldehydes could be cleaved readily with methanolic periodic acid to afford P,y-unsaturated ketones. e 'yC0zMe R 72a, R=H b , R=TMS 2) TMSCl or TBSCl 73 74 - 64 65 66 a, X=M, R=alkyl b, X=TMS. R=alkyl c, X=M. R=O-alkyl d, X=M, R=OM e, X=TMS, R=NR,' f. X=TMS, R=O-alkyl I 67 6e OH 69 C ' 1 Surprisingly, the ester enolates of generic structure 65c do not undergo a [2,3] Wittig rearrangements7 while their carboxylate-derived dianions (65d) and dialkylamide anions (65e) do rearrange by this pathway.58 Exclusive Claisen rearrangement of these substances can be accomplished via the trimethylsilyl ketene acetals (65f 64f). This procedure has been described independently by Nakai57and R a ~ c h e in~ ~ transr the formation of ester 72a to its (2)-0-silyl ketene acetal 73 followed by Claisen rearrangement to the masked a-keto aldehyde 74. Significantly, when the C-silylated ester 72b is treated with tetra-n-butylammonium fluoride, formation of the [2,3] Wittig product occurs. On the other hand, the 0-silyl derivative 73 gives the starting ester 72a. This observation has led Nakai to suggest that a common "naked" anion is not involved in the two pathways but that separate C- and O-hypervalent silicon species are responsible for the dual reaction pathways. of substituted allyl residues. Scheme I illustrates such a study60wherein the P-substitution pattern of the allylic residue of allyl vinyl ether 75 is systematically altered. The vinyl residue reacts twice as fast as the (E)-P-vinylgroup (76a:77a)and 19 times faster than the (Z)+vinyl(76b:77b). A t first hand, these data suggest that, in a competition between the (E)-and (Z)-p-vinyl groups, the E isomer should react 9.5 times faster (76b:77b to 76a:77a); the observed result is -3:l ( 7 6 ~ 7 7 ~As has been suggested,61each nonreacting ). group is a substitution for its reacting partner and need not offer additive substituent effects in each rearrangement. The presence of a 6-methyl substitution ( E configuration) has a limited effect on the rate of rearrangement of vinyl ethers or silyl ketene acetals (cf., 29 vs 30a). Terminal 6,6-substitution with two methyl substituents completely favors formation of 76d over 77d. Parker and Farmar62have uncovered a subtle selectivity in the rearrangement of the series of divinylcarbinol derivatives 79. The methyl substituent in 79a and 79b provides a small steric decelerationm while the less sterically demanding methoxyl group manifests itself as a decelerating C5-donorgroup in both 79c and 79d. These observations lend additional support to the Burrows-Carpenter model for C5-donors.31 For divinylcarbinols wherein one of the vinyl substituents is contained in a ring, rearrangement with the acyclic vinyl group is preferred when the acyclic unit is unsubstitued. Thus, vinyl ethers 82a and 82b give 81a and 81b, respectively, with high selectivity. The presence of an (E)-P-methylvinyl group retards acyclic rearrangement, but it still remains the major pathway for the rearrangement of 82d.64965 SCHEME I - 75 75 76 76'77 77 2. ' 95'5 2. Divinylcarbinol Derivatives The competitive rearrangement of 4-vinylallyl vinyl ethers has provided information on the relative rates a R1=R2=R3=H &Me b Rl=R2=Rd=H. R,=Me c R,=R,=H R,=Rj=Me d R.=R,=H. R,=R.,=Me 78 22 '00 0 Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1429 78 84a, R,=OH. Rz=H b, Rl=H, R,=OH 85 80 Ho :zH *? 78180 a, R=Me, X=OEt b, &Me, X=NMez c, R=OMe, X=OEi d, R=OMe, X=NMe, 65135 74126 9515 9713 86 phcH* 87a, R=CONMe2 b, R=COzEi R 0 - 81 82 a , R=H, n = l b, R=H, n=2 c, R=Me, n=l d , R=Me, n=2 81/83 (CHZ)" d y H0 8911 1 8811 2 50150 65/35 83 3. Elimination Alternative sigmatropic rearrangements are not the only irreversible processes that can compete with the Claisen rearrangement; elimination reactions are troublesome. This undesirable, competitive process is particularly acute when at least one olefin is contained in a ring. Cyclohex-2-en-1-01s have been particularly notorious in this regard. Ireland and co-workers@have prepared the isomeric allylic alcohols 84a and 84b by reduction of the corresponding enone. The minor axial alcohol 84a, when subjected to mercuric ion catalyzed exchange with ethyl vinyl ether, undergoes elimination to dienic products. On the other hand, the major, equatorial allylic alcohol rearranges to aldehyde 85 without incident. An unfavorable transition state for the Claisen rearrangement in the former case may be the result of steric interactions between the angular methyl group and the forming C-C bond. When confronted with the problem of elimination, the use of an alternative strategy is often beneficial. Thus, allylic alcohol 86, when subjected to the Eschenmoser ketene 0,N-acetal variant, provides only a 45% yield of the desired amide 87a along with the products of disproportionation of the dihydropyridine, the immediate product of elimination. However, the Johnson orthoester route gives the ester 87b in 74% ~ield.~'?~~ D. Stereochemistry 1. Transition State certed, nonsynchronous pericyclic process that may be considered phenomenolologically as an intramolecular SN2' alkylation. When the sp2-hybridized C1- and C6-positionsof allyl vinyl ether are substituted to provide enantiotopic faces at both termini, the rearrangement can proceed through two pairs of stochastically achiral transition states to provide two racemic diastereomers bearing newly created centers of asymmetry at C2and C3of the products (Scheme 11). Thus, achiral allyl vinyl ether 91 can provide two enantiomeric chairlike transition states 88 and 90,both of which lead to the racemic diastereomer 89. Similarly, the enantiomeric boatlike transition states 92 and 94 provide racemic, diastereomeric aldehyde 93. The two transition states are inherently unequal in energy and the ratio 89:93 reflects the transition-state geometry. In a detailed study modeled after the Doering and Roth experiments that revealed the preferred chairlike transition state for the Cope rearrangement,69 Schmid26bic his collaborators have examined the rate and and stereochemistry of rearrangement of the four crotyl propenyl ethers 91a-d in the gas phase at 160 "C. All isomers show the expected negative entropy of activation (AS*= -10 to -15 eu) with enthalpies of activation ranging from 25 to 27 kcal/mol. Each isomer shows a clear preference for the chairlike transition state (91a, 95.9:4.1; 91b,94.7:5.3; 91c,95.54.5;91d,95.4:4.6). The E isomer 91a is found to rearrange an order of magnitude faster than the Z,Zisomer 91b,with the other two geometric isomers intermediate in rate. The E,E and Z,Zisomers rearrange through a chairlike transition state to give the threo isomer 89a (89b)as the major product; likewise, the Z,E and E,Z isomers give the erythro isomer 89c (89d)as the predominant stereoisomer. Since the four isomers 91 all proceed through the chairlike transition state, a change in the geometry of a single double bond exchanges the enantiotopicity of the faces of the double bond and leads to the opposite stereoisomer. Indeed, any pairwise change in olefin geometry for a given transition state, or single change of olefin geometry and change in transition state, results in the formation of the same dia~tereomer.'~ 2. Vinyl Double-Bond Geometry The Claisen rearrangement is a suprafacial, con- Before proceeding to other substituent effects and how they control the transition state of the Claisen rearrangement, it is appropriate to consider the methods that are available to control the geometry of the vinyl double bond. Unfortunately, no convenient 1430 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler SCHEME I1 r Chair A Chair B L 92 93 (racemic) 94 methods are available for the selective preparation of propenyl ethers. The same difficulty exists with the Johnson orthoester method. The use of orthoesters derived from propionic acid derivatives and their higher analogues fail to give stereochemically defined ketene acetals.71 However, the ketene 0,N-acetal rearrangement does provide for selectivity. Sucrow and Richter72 have examined the Claisen rearrangement of the dimethyl acetal of N8-dimethylpropionaide with (E)and (2)-crotyl alcohol (Scheme 111). Although the intermediate ketene 0,N-acetals are generated in situ and are not isolated, the assumption that a chairlike transition state is operable, coupled with a preferred axial orientation of the C1-methyl group of the (E)ketene O,N-acetal(95, loo), correctly accounts for the stereochemistry of the products. The latter supposition is tenable as the dimethylamino group assists in delocalizing charge in the transition state and interacts with the C1 substituent when it is equatorially disposed.73 An alternative approach to the use of the ketene 08-acetals has been offered by the work of F i ~ i nwho~ i~ (101) as has employed 1-(N8-diethylamino)-l-propyne the propionate source; however, no stereochemical study was conducted. Recognizing that the (2)-ketene 0,Nacetals of Scheme I11 are the products of thermodynamic control, Bartlett and H a l ~ n have prepared the e~~ less stable, kinetic @)-ketene 0,N-acetal by the stepwise, cis addition of the crotyl alcohols across the triple bond of the Ficini ynamine (Scheme IV). The slow addition of the crotyl alcohol to the ynamine at 140 O C serves to make rearrangement, a trap for the kinetic addition product, competitive with isomerization. Protonation of the ynamine provides the ketene immonium cation 102, which adds alkoxide preferentially syn to the hydrogen atom via path A. In the case of the (2)-alcohol, a 2.51 ratio of 108 to 107 is obtained; the (E)-alcohol also preferentially follows path A through 105 leading to a 2:l ratio of 107 to 108. The Ireland variant21 of the Claisen rearrangement has proved the most adaptable for the control of vinyl SCHEME I11 95 (E, axial) NMe2 96 (E,equatorial) I I 95% CONMe, CONMe, Me 98 (threo) 97 (erythro) 1 3 % I 99 (Z, equatorial) 100 (Z, axial) olefii geometry. The deprotonation of esters by lithium dialkylamide bases developed by Rathke22-76 proved has amenable to the generation of specific enolates. Thus, treatment of butenyl propionates 110 and 114 (Scheme V) with lithium diisopropylamide (LDA) in THF under these kinetic conditions forms principally the (2)-lithium enolates, which upon silylation (tert-butyldimethylsilyl (TBS) gives the (E)-0-silylketene Rearrangement of silyl ketene acetal 109 provides an 87:13 mixture of acids 111 and 115 after desilylation while 116 gives an 89:ll ratio of 115 and 111. These two products can also be obtained by using 23% HMPA-THF (HMPA = hexamethylphosphoramide) Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1431 TABLE I. Geometry of Enolate Formation RICH~CO~R~ 117 H 118 OR2 OX R H ox OR2 llQ entry 1 2 ester 117a 117b 117c 3 4 5 6 7 8 9 10 11 117d 117e 117a 117b 117c 117c 117f 117d X" TBS TBS TMS TBS TES TBS TBS TMS TES TES TBS solventb THF THF THF THF 23% HMPA-THF 23% HMPA-THF 23% HMPA-THF 23% HMPA-THF 23% HMPA-THF 23% HMPA-THF 23% HMPA-THF "TBS = tert-butyldimethylsilyl; TMS = trimethylsilyl; TES = triethylsilyl. *Enolates were generated with LDA, -70 to -78 "C. SCHEME IV SCHEME V rr NE!, 0 11 0 111 23% HMPA-THF 112 OSIR, I NE!, I 23% HMPA-THF 103 104 105 106 I 116 107 (threo) OSIR, Y C O N E t , Me 108 (erythro) tion of the ester group for a given solvent. In general, enolate formation by the kinetic deprotonation procedure is somewhat more selective than the thermodynamic conditions. Because the silyl ketene acetal ratios are approximately equal to, or better than, the ratio of diastereomers 11 1 to 115,the chairlike transition state is virtually the exclusive pathway for rearrangement. 3. Secondary Allylic Alcohols as an optimal solvent system for the generation of the therm~dynamic'~ (E)-lithium enolates ((2)-0-silyl ketene acetals 112 and 113). 2-(0)-Silyl ketene acetal 112 provides an 81:19 mixture of 115 and 111 while 113 affords an 86:14 mixture of 111 and 115. The major diastereomer in each rearrangement arises through the chairlike transition state, and once again, a single exchange of olefin geometry results in the other diastereomer becoming the major product. The erosion of diastereoselectivity can be attributed to two factors: the geometric integrity of the silyl ketene acetals and the selectivity of the chairlike vs boatlike transition state. Table I provides examples for the selectivity of enolate formation by the LDA/silylation procedure.82 The entries are listed in ascending bulk of the alcohol por- Although the aliphatic Claisen rearrangement of secondary allylic alcohols had been recognized to provide E double bonds,83Faulkner and Petersen@have examined the selectivity of olefin formation as a function of C2substituents. The vinyl ether rearrangement of vinyl ether 120a provides a 9O:lO ratio of (E)-to (2)-unsaturated aldehydes 121a. The congener 120b bearing an isopropyl rather than an ethyl substituent is more selective affording a 93:7 ratio of (E)-to (2)olefinic aldehydes 121b. An increase i the steric bulk n of the C2 substituent produces higher stereoselectivity. Thus, ketene 0,N-acetal rearrangement of 120c gives an E:Z ratio of 99.4:0.6 while the product from the 2methoxypropene derivative of 2-methylpent-1-en-3-01 (120d)provides less than 1% of the (Z)-olefin. Simi- 1432 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler larly, Katzenellenbogena5 has reported less than 1% of (Z)-olefin in the silyl ketene acetal rearrangement of 120e and Johnsona6has observed >98% E selectivity in the orthoester rearrangement of 120f. This dramatic increase in selectivity observed in the C2,C4-substituted examples has been rationalized as the result of a pseudo-1,3-diaxial interaction in chairlike transition state 123 that leads to the (2)-olefin as opposed to the less congested chairlike transition state 122 that gives the (E)-~lefin.~~~~~~~~ Z 120 a, %El, Z=H b, R=i-Pr, Z=H c , R=Et. Z=NMe, d. R=Et, Z=Me e, R=n-C,H,3, Z=OTBS 1, R=CH,CH,CH(Me)=CH, /-/f *\<<,.,i,\ n .... .*-.-7 L*-o....-' /fl R 122 When the secondary allylic alcohol has a substituent at the terminus of the double bond (i.e., C6), a center of asymmetry is destroyed during the rearrangement as a new one is created. This process has been often called "self-immolative"a9 and involves the "transfer of chirality".2f In the sense that racemic substances bearing centers of asymmetry are chiral, and recognizing the concerted, suprafacial nature of the rearrangement, the transformation of Scheme VI is, by necessity, chiral throughout. In more modern terms, that which is transferred is stereogenicityw (Le., stereochemical information), and when practiced with enantiomerically pure allyl vinyl ethers (124), the rearrangement affords SCHEME VI L 124 127 + Yo + tR Z 121 % . &,.*. .---, 123 enantiomerically pure products (126). In the example of Scheme VI, the R,E enantiomer 124 bearing an equatorial R1substituent undergoes bond formation on the si face of the allylic double bond to produce the R,E enantiomer 126. Conformational inversion of 124 leads to (R,E)-127. This conformation can undergo re bond formation through transition state 128 having the R1substituent axial, resulting in the formation of S,Z enantiomer 120. Thus, the transition-state integrity may be monitored with enantiomerically pure reactants by measuring the enantiomeric excess of the dihydro aldehydes from reduction of 126 and 129. In the racemic series, the value ( E - Z ) / ( E + 2) equals the enantiomeric excess that would be obtained using enantiomerically pure allylic alcohols. The chairlike vs boatlike transition state is not detectable in this case because there is no C1 substituent. Hill has observed the "transfer of chirality" in the vinyl ether rearrangement of enantiomerically pure cyclopent-2-en-l-ol.g1a The Eschenmoser and Johnson variants with enantiomerically pure (E)-pent-3-en-2-01 give products with 90% retention of enantiomeric purity as determined by optical r o t a t i ~ n . ~ ~ ~ ~ ~ ~ ~ ~ An ingenious, enantioconvergent variation on this theme has been executed by Chan.93aThe enantiomers of propargyl alcohol 130 are prepared by resolution. The R enantiomer is reduced to the (R,Z)-allylic alcohol 131 while the S enantiomer is converted to the (S,E)-allylic alcohol 132. Rearrangement to form the aldehyde, ester, or amide 133 occurs with "chirality transmission" of 94-99%. Thus, the (R,Z)-olefin exposes the re face while the (S,E)-olefin invokes the same re face, affording a single enantiomer, the (S,E)-olefin 133. Clearly, the other enantiomer, (R,E)-133,is accessible by exchanging the reduction procedure for each enantiomer of 130.94 The advent of the Sharpless kinetic resolution procedureg5 and the Midland asymmetric reduction of a,@-acetylenic ketones%has made a variety of secondary allylic alcohols readily available in both enantiomeric forms, thereby obviating the use of classical resolution. (R, and R, lowest carbon priority) R L 125 J 126 128 129 Thermal, Aliphatic Claisen Rearrangement OBn Chemical Reviews, 1988, Vol. 88, No. 8 e ! 1433 I R-I30 S-I30 Lindlar Reduction Na/NH3 1)25`C 2) MeOH/HCI OBn Me0,C + + I 131 OTBS 138 139 140 7 u 132 R / 133a. R=H b. R=OE1 c, R=NMe, 4. Tertiary Allylic Alcohols Tertiary allylic alcohols fail to give trisubstituted olefins with high selectivity. The transition states 134 and 135 are nearly isoenergetic when the substituents S (small) and L (large) are not branched. The lack of selectivity is present even when C2 is substituted. R 134 135 E-olefin 0 0 2-olefin 136 137 As an example, linalool acetoacetate (136),when subjected to the Carroll rearrangement, gives a 54:46 E:Z ratio of olefinic ketones 137.97 A similar ratio is realized with linalool using the Marbet-Saucy conditions (2-methoxypropene).15*J6 Rearrangement of (2)-silyl ketene acetal 138, which is derived from a tertiary allylic alcohol bearing an a-branched "large" group and a methyl, provides a 7:l ratio of esters 139 and 140,r e s p e ~ t i v e l y . ~ ~ olefin geometry is excluThe sively of the E geometry which requires the branched group to occupy an equatorial position in the transition state. The ratio of diastereomers is in accord with the enolization stereoselecti~ity.~~ 5. Ring-Bearing Substrates tained in a ring, i.e., acyclic substrates. In ring-bearing allyl vinyl ethers, the boatlike transition state can be the major, if not exclusive, pathway for rearrangement. Before proceeding, it is worthwhile to consider a mnemonic device to describe various ring systems. The carbons (see structure 3) to which the tether bridging the pericyclic array is attached are expressed in the form (m,n;o,p; Thus, acyclic system 138 139 would ...I. be designated as a (O,O), 86 87 a (4,6),and 54 53 a (1,6}-rearrangement. Bartlett and Pizzo68dhave investigated the (4,6)-rearrangement illustrated in Table I1 with several propionate equivalents. Entries 1-4 involve routes that control C1 stereochemistry; entry 5 does not. Entries 1 and 2 permutate two control elements, vinyl group geometry, and transition state, thereby providing the same major isomer. Entry 3, wherein the vinyl group has predictable 2 geometry,72 partitions equally between the chairlike and boatlike transition states. The ynamine experiment suggests high E selectivity in the formation of the vinyl group and a strong preference for the boatlike transition state as any (a-olefin would cause erosion of stereoselectivity. Ireland and his collaborators have examined the stereochemical course of the (4,6)-rearrangementof a number of carbohydrate-derived pyranoid and furanoid glycals as a prelude to the synthesis of complex natural products. (2)-0-Silyl ketene acetal 144a,derived by deprotonation of the propionate ester with lithium hexamethyldisilazide (LiHMDS, a reagent equivalent to 23% HMPA-THF for the generation of 2 OLi enolates)," rearranges to provide ultimately a 9010 mixture of esters 145 and 146, respectively, wherein the boatlike transition state dominates. However, (E)-0silyl ketene acetal 144b gives a 6535 ratio of the two diastereomers, with ester 145 still predominating, re- - - - TABLE 11. Chair vs Boat Transition States in Cyclohexenol Derivatives n 141 142 143 entry 1 2 Thus far the stereochemical discussions have focused upon rearrangements wherein neither olefin is con- 3 4 5 method LDA/THF LDA/THF. 23% HMPA orthoamide ynamine orthoester X R 1 OTBS Me OTBS H RS 1421143 H Me 85/15 75/25 favored TS chair boat ~~ ~~ NEt, NEt, OEt Me H 50150 neither H Me >90/10 boat (Me,H) 70130 ??? 1434 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler quiring the chairlike transition state to be slightly favored. In a related example, the (E)-0-silyl ketene acetal of the furanoid glycal 147 (from LDA deprotonation) gives principally (86-89 % selectivity) stereoisomer 148 via a boatlike transition state.l0' OTBS having been transformed into the ring of 155,exacerbate the steric interactions and allow only the boatlike transition state 156 to prevail. PfOY"' 153 144 a, R,=H, R p M e b, &=Me, R= ,H 145 a, R=Me b. R=H 154 Meo*"Yio&& Me H 146 OTMS 1) rearrangement 155 e M 156 2) hydrolysis 3) esterification e. o H ~ c ~ o M o Me 148 147 The BartletPd and Ireland"Jo1 studies have been rationalized for the 6-membered ring case as is illustrated in Scheme VII. Chairlike transition state 149 is disfavored relative to the boat 150 as the methyl and X groups interact with ring substituents. The chairlike transition state 151 is slightly favored over the boat 152 as the steric interactions of the methyl group with the ring in 152 are seemingly greater than the interactions experienced by the X substituent in 151. Once again, the change of two stereocontrol factors produces the same diastereomer. Perhaps the most dramatic example of the intercedence of the boatlike transition state comes from Lythgoe's elegant application of the Claisen rearrangement to syntheses in the vitamin D field.lo2 Ketene acetals 153a,b of the (1,2;4,6}-type,whose vinyl olefins are perforce of the E geometry owing to the presence of the ring, rearrange exclusively through the boatlike transition state. The substituents of conformation 149, SCHEME VI1 Y = CH,. 0 Conformationalrestraints on the transition state can be observed in both the (1,4}-and (1,6)-rearrangements. The former case, the operational equivalent of a "meta-Diels-Alder reaction" (157 158) when the tether is two carbons in length,lo3 is constrained t o proceed through boatlike transition state 159,as the chairlike transition state 160 would lead to a strained (E)-cyclohexene. M - 157 158 i Z-cyclohexene E-cyclohexene (Y = hrghest priority] The (1,6}-rearrangement, when constrained by a short tethered chain (54 53,56 55,or 161 162),can proceed with greater facility through the boatlike transition state 163 rather than the more strained chairlike transition state 164.14 Me - - - 149 >-SI,6-Si 150: 1-Re, 6-SI 161 ___) 162 4 151 1-Re 6-Si 152 1-Si. 6-Si ' 163 '64 I_/ Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1435 I V . Heteroatom Substlfuents A. The Vlnyl Group 7. C1Hetero Substituents rangement of a-phenylthio ester 175 leads after several operations to @)-dieno1 176a,a model transformation for the preparation of diol 176b,a degradation product of vitamin D2.10Gg PhS The presence of a C1-hydroxyl or -alkoxy group has been utilized to control enolate geometry. While early investigations exploited the reaction from the synthetic viewpoint,lo5a detailed analysis of the stereochemistry of the reaction awaited the studies of BartlettlOGaon lactate and mandelate esters and, contemporaneously, Burke,lOGbFujisawa,106c@*f Kallmerten948J06don and glycolate esters. The hydroxyl or alkoxy group serves to form a chelated enolate. In the case of the a-hydroxy ester dianion, rearrangement does not proceed smoothly;106c but, it may be expedited by bis-0-silylation prior to rearrangement. The a-alkoxy ester enolates are also converted to their 0-silyl ketene acetals prior to rearrangement. The (E!)-butenyl glycolate ester 165a affords a 98:2 ratio of esters 167 and 168,respectively, after rearrangement, hydrolysis, and esterification. The reaction is stereospecific as the (2)-butenoate gives a 2:98 ratio (167and 168) of the two a-hydroxy esters." Similarly, allylic esters 169a and 169b rearrange with 1OO:l diastereoselectivity; (E)-allylic ester gives principally a-benzyloxy ester 170 while 169b provides mainly ester 171.94a Worthy of note is the observation that an a-[ (tert-butyldimethylsilyl)oxy]acetate ester forms the nonchelated 2 lithium enolate.94h107 phsTo 172 y oTMS 173 ps h% e 175 SPh 176a. R=H b, R=OH :: T M S P1 ?TMS O ~ Cooksonlloahas examined the addition of allylic alkoxides to allenic sulfoxide 177. When the isolated adduct 178 is subjected to rearrangement, subsequent sulfoxide elimination occurs, leading to dienone 180. Similar processes have been initiated by the addition of allylic alcohols to (pheny1thio)acetylene to form dienalsllob and to phenylthio ynamines to produce a,@;@,y-unsaturated amides.lloc I O Ho40 7 1 I 165 1) LHMDS * R2 0 I 2) TMSCI RZ 3) CH2Nz 177 166 178 - 4 C O ; OH M e + a C O z 6H M e 167 168 L " 179 180 2. C 1 Carbon Hetero Substituents U C 0 2 M e OB" 170 a , Rl=H R,=Me b R1=Me R,=H 171 60" While the role of a-amino functionality has been explored, the reaction has been applied principally to the synthesis of unique amino acids.lo8 On the other hand, a-thio substituents have proved useful as agents for the manipulation of functionality. The rearrangement of allyl a-(phenylthio)acetates,which can lead to a variety of sulfur-free products, has been reported by Lythgoe.lW The a-phenylthio ester 174 can be oxidatively degraded to 2,2-dimethyl-3-butenal. The rear- An increase in the oxidation level at the @-position of propionate residues permits the formation of amethylene esters and a-methylene y-butyrolactones,the latter functionality arising through halo- and selenolactonization techniques. Still'll has demonstrated that allyl 3-pyrrolidinopropionate 181 can be deprotonated without elimination and the resultant triethylsilyl ketene acetal rearranges to ester 182. The silyl ester is transformed into the methyl acrylate in a single operation. Similarly, Raucher112 has used 3-methylcyclohex-2-en-1-01 in conjunction with trimethyl 3(phenylse1eno)orthopropionate to produce acid 184. Selenolactonization and subsequent double selenoxide elimination leads to the a-methylene y-butyrolactones 186. Owing to the thermal instability of the seleniumbased reagent, trimethyl @-methoxyorthopropionateis a suitable substitute. The resultant 0-methoxy esters undergo facile elimination to the acrylates with potassium t e r t - b ~ t 0 x i d e . l ~ ~ + 1436 Chemical Reviews, 1988, Vol. 88; No. 8 Ziegler ?I Et,SiC 0 i 182 G" 183 PhSe K2C0, MeOH C0,Me The 4-(phenylse1eno)butyrate ester 194 serves as a source for radical-initiated carbocyclization. Rearrangement of the silyl ketene acetal of 194 provides the cyclopentene 195, which is subject to reductive cyclization with triphenylstannane followed by transesterification to methyl ester 196.116 Qyo-Hq:pb184 An intriguing variation on the preceding themes employs triethyl orthoacrylate ( 188).l14 The presence of the acrylate double bond in exchange product 189 prohibits elimination to a ketene acetal until a nucleophile (ethanol or propionic acid) adds to the highly stabilized carbocation 190. The use of catalytic acid is deleterious as the cation consumes the acid (191a).l15 Use of excess acid (1.5 equiv) provides 192a and 192b in 66 and 16% yields, respectively. While the major product undergoes elimination with 1,5-diazabicyclo[4.3.0]non-5-ene (DBN), the use of potassium tert-butoxide, as described by Raucher,l13 should also afford acrylate 193. @ n A // 194 /I *w I C0,TBS 195 03 196 C02Me SePt 1 85 q Me o ' 86 The fluorine-containing phospholipid 200, designed as an inhibitor of cobra venom phospholipase A2, has been prepared via rearrangement of trifluorovinyl ether 198.'17 Not only is the vinyl ether prepared by a unique method not available in the protio series, but the rearrangement is markedly accelerated by the presence of the fluorine atoms.4s F 199 n-C,H,;O, OH I Et0 200 I a7 188 r 1 B. The Allylic Group 1. Oxygen Substituents Et0 OEt 189 190 OEt 191 DEN C02E1 a R=C(O)Et 3 R=Et 193 Dimedone (201) is in facile equilibrium with its enol, which can effect autocatalytic exchange with 2-methoxy-1,3-butadiene to generate the 4-methoxy allyl vinyl ether 202. Rearrangement affords enol ether 203, whose hydrolysis product is the equivalent of having effected a Michael addition of dimedone to methyl vinyl ketone.'18 Similarly, /%keto nitrile 204 reacts with the diethyl acetal of acrolein in refluxing benzene to provide enol ether 205, with bond formation occurring on the convex face of the bicyclooctanone ring system.'lg In the transformation 201 203, the 3,4 double bond of Z-methoxy-1,3-butadiene functions as an allyl component. The 1,2 double bond of the diene may also serve as a vinyl component in reactions with allylic alcohols (206 207).25 These processes are also accomplished with ketals of a,&unsaturated ketones.120 - - Thermal, Aliphatic Claisen Rearrangement 7 Chemical Reviews, 1988, Vol. 88, No. 8 1437 1 ~$2 OMe extremely unstable, requiring in situ generation of the acylation products, enolization, and rearrangement. Operationally, the preparation of acids 212 and 214 is equivalent to a diastereoselective aldol condensation. L 201 2 202 Me0 213 203 1) LDA; HMPA, THF 2) TBSCI fie 21 4 2. Silicon Substituents +* + 204 OMe HI OH 206 I 2)LICA, TMSCl ) EtOH H I 205 0 207 The use of C5-oxygen-substituted allyl vinyl ethers can serve as 1,6dicarbonyl compounds that lead to cyclopentenones via an intramolecular aldol condensation. This process had been implemented by Ireland and Mueller21ain their early studies on the ester enolate rearrangement. Rearrangement of vinyl ether 208, having C5 at a ketone oxidation level, results in the isomeric vinyl ether that undergoes facile lactonization to 209. Generation of an intermediate hemiacetal by reduction with DIBAL and subsequent mild base treatment realizes cyclopentenone 210; more vigorous base treatment isomerizes enone 210 to the more stable dihydrojasmone (211).121 The ability of silicon to direct and facilitate the reactions of olefins has led to the introduction of silicon substituents into the framework of allyl vinyl ethers. K ~ w a j i m ahas~ l ~ formed C6-substituted allyl vinyl ether 215 in situ by the exchange of a-ethoxymethylenecyclohexane and (E)-p-(trimethylsily1)allylalcohol in the presence of acid. Rearrangement gives allylsilane 216, which provides the spiro-@,y-unsaturated alcohol 217 upon Lewis acid catalysis. In a related experiment,124the propionamide acetal rearrangement of allylic alcohol 218 affords amides 219a and 219b in a 3 1 ratio, respectively. Protodesilylation of either isomer gives the P,y-unsaturated amide 220. The formation of alcohol 217 and amide 220 involves the migration of the y,b-double bond from the initial Claisen products toward the carbonyl carbon. TMS 21 5 216 IMS y C O N M R2 217 -y L T M 218 EtC(OMe),NMe2 S e 2 HF Me BF,/AcOH ~ RI O 0 V 208 219a. R,=Me,RR,=HM b, R,=H, 2 = 0 209 1) DIBAL Yco 210 ~ T M I)LDA S 2) TBSCI 222 2 ) a q OH 0 - 220 1 I C T M S ?fo 21 1 0 221 The rearrangement of systems bearing C6-oxygen substituents has been explored by Ireland as a prelude to the synthesis of ionophores.106cJ22 The preparation of P-alkoxy alcohols and their acyl derivatives is troublesome because they are susceptible to polymerization and isomerization. The Claisen rearrangement of ester 213 (R = H, Me) is -7040% diastereoselective, presumably the result of a lack of control over enolate geometry. Secondary allylic alcohols in this series are Me 223 The olefin migration may be practiced in the opposite sense. Rearrangement of the (E)-0-silylketene acetal of ester 221 occurs with 90% stereoselectivity, providing acid 222 as the major diastereomer. Acid-catalyzed migration of the olefin away from the carbonyl realizes A the b,c-acid 223.125J26 severe erosion of stereochem- 1438 Chemical Reviews, 1988, Vol. 88,No. 8 Ziegler istry has been observed when the rearrangement of the allylic alcohol component of 221 is conducted as its Eschenmoser variant,lZ7 similar to the selectivity in the formation of 219a and 219b. A silicon substituent at C4serves to introduce asymmetry into achiral allylic alcohols. Propionate ester 226 is prepared from the resolved alcohol and subjected to stereospecific rearrangement. Reduction, alkylation, and protodesilylation of acids 224 and 227 give enantiomerically pure ethers 225 and 228, respectively.lZ8 Me Bn O stereoisomer has the same relative stereochemistry at the 0- y-positions and has been suggested to be in and accord with F e l k i ~ and~ H o ~ k transition-state ~l ~ ' ~ ~ m0de1s.l~~ GTHP OTHP 0 4 231 2 232 Me 225 / '1 TBS 226 1) 6TMS 233 234 LDA Me 227 2) TBSCl il m Me Me y 228 V. Remote Asymmetry A. Acyclic Substrates Kurth has examined the rearrangement of the dianion of the (E)- and (2)-butenyl esters of 0-hydroxybutyric acid in THF (Scheme VIII) and has applied the reaction to the synthesis of the mycotoxin botryodiIn principle, the reaction can provide four diastereomers; only two are detected. Bond formation cis to the methyl group of the ring formed by chelation is inoperative on steric grounds while bond formation trans to the methyl occurs via the chairlike and the boatlike transition states. The E isomer provides an 81:19 mixture and the 2 isomer gives a 15:85 ratio of 0-hydroxy esters 236 and 238, respectively. In both instances the chairlike transition states predominate.lS The availability of enantiospecificenzymatic reductions of @ketoesters139makes this rearrangement amenable to the preparation of enantiomerically pure products. Indeed, the hydroxyethyl unit functions as a "chiral auxiliary" 140 as it can be oxidized to a ketone and the resultant P-keto ester can undergo Haller-Bauer deacylation or d e c a r b ~ x y l a t i o n . ' ~ ~ J ~ ~ B. Ring-Bearing Substrates The only asymmetric effects discussed thus far have been related strictly to the C4 carbon, an integral part of the Claisen rearrangement framework. But what of remote asymmetry and its ability to induce diastereoselective reactions? The rearrangement of allyl vinyl ether 229, wherein the remote asymmetry at the quaternary center (C, 0-substituent) renders the faces of the olefin diastereotopic, shows no sign of diastereoselection; both isomers 230 are produced in equal amounts.129 When the The effect of the chelated ring discussed in the previous section leads logically to the influence of remote ring substituents on stereochemistry. A more elaborate (153 154) version of the Lythgoe experimentsloZb involves the union of an enantiomerically pure reactant, 6 (S)- (benzoyloxy) -3-methylcyclohex-2-en- (S)-01, with 1 the R or S enantiomers of 2,2-diethoxy-3-methyltetrahydrofuran. Ketene acetal 239a, derived from the - SCHEME VI11 R,.R,=CH,,H Me center of asymmetry is located vicinal to the developing center of asymmetry, modest selectivity is observed. Thus, ketene acetal 23 1, derived from (S)-ethyl L-lactate,130 rearranges with 3:l diastereoselectivity (232, major diastereomer), while D-glyceraldehyde acetonide derived silyl ketene acetal 233 affords principally 234 (75% ds).131J32 In each instance, the predominant Me A 237 238 Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1439 (S)-ortholactone,rearranges to give exclusively diastereomer 240 through the boatlike transition state. However, the diastereomeric reaction with the (R)ortholactone via 239b affords a 70:30 mixture of diastereomers 241 and 242,respectively, with the chairlike transition state leading to the major isomer. The transition state for the rearrangement of these systems normally favors the boat 156 (no substituents on the heterocyclic ring). The presence of the substituent in 239a (R, = Me) serves only to destabilize further the chairlike transition state 243 relative to the boatlike transition state 244. On the other hand, 239b possesses the methyl substituent in a sterically demanding position in the boatlike transition state 244 that is mitigated in the chairlike transition state 243. The preference for the chairlike transition state in the latter example requires the substituent effect to be more influential than the chair-boat factor. SCHEME IX 245 246 w s B, 0 247 248 ws 0 rYMe 239a Me '%A * JJ 240 'L 249 250 PhCO. 239a,R,=Me, Rz=H b, Rl=H. Rz=Me 251 252 SCHEME X (E)-olefin Products n (2)-olefin 241 ,Me 242 253 81 243 244 In this laboratory, the reaction of the enantiomers of the ortholactones of 3-methyl-y-butyrolactone with enantiomerically pure secondary (E)-allylicalcohols has been s t ~ d i e d . ' ~Scheme IX provides details on the ~J~~ stereochemistry of these reactions. The transition states 245,247,249, 251 represent the four possible perand mutations of olefin facial selectivity. The four control elements are chair (C) vs boat (B) and trans (t) (to the methyl group) vs cis (c). The four products me derived from the (S)-ortholactonewith the R and S substituents representing the absolute configuration of the allylic alcohol residue when an isopropyl group occupies the R or S position. When the (R)-alcoholis employed, only the lactone 246 is obtained. Transition states 247 and 249 are precluded as they lead to products 248 and 250, respectively, bearing (2)-olefins. While boatlike transition state 251 would lead to an (E)-olefin, steric interactions make this pathway less favorable than 245 246. Indeed, when R = S = H, (i.e., (E)-2-buten-l011, no product having the stereochemistry of 252 is formed. Alternatively, the (S)-alcohol excludes transition states 245 and 251;transition states 247 and 249 provide 256 257 258 259 260 \/ 261 262 263 264 - lactones 248 and 250,respectively, in a 55:45 ratio. In spite of this mixture, either diastereomer is able to be prepared from the other by chemical means. The aza Claisen rearrangement,,& in conjunction with an amino acid derived type I chiral auxiliary, has been employed by K ~ r t hto ~ ~ l provide 2'- and 3'-alkyl, and 2',3'-dialkyl 2-substituted oxaz01ines.l~~ starting The 1440 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler N-allyl-N,O-acetals are prepared by N-alkylation of the 2-ethyloxazoline with the requisite allylic tosylate followed by stereoselective n-butyllithium deprotonation of the oxazolinium salt. The removal of the oxazoline moiety liberates an enantiomerically pure carboxylic acid. Scheme X illustrates this principle for the formation of the four possible diastereomeric 2',3'-di-0xazo1ines. When an ( E ) butenyl residue methyl-2 ( S ) is employed, the four transition operative states 253, 256, 259, and 262 lead to products 254, 257, 260, and 263, respectively, in a ratio of 81:15:2:2. Thus, the isopropyl group is an effective control element for the facial selectivity of bond formation at the oxazoline double bond (96%, facial excess (fe) = 92%),'47 while the chair vs boat selectivity is not as effective (fe = -67%). When the (2)-butenyl group is employed, the products 254, 257, 260, and 263 are formed in a ratio of 14:82:2:2,respectively. While the energetics of the transition states remain the same as for the (E)-olefin, the major product 257, arising through the Ct transition state, provides a product with the opposite configuration at the @-positionof the chain from that which was obtained in the (E)-butenyl series. The synthetic success of type I chiral auxiliaries is dependent on the facility with which diastereomers 254 and 260 can be separated from 257 and 263 and the ease with which the members of each pair (or their hydrolysis products prepared without epimerization) can be separated from one another. V I . Consecutive Rearrangements mediate allyl vinyl ether produces the aldehyde 267. Isolation of the aldehyde and subsequent Wittig methylenation provide the &&diene, which undergoes a Cope rearrangement to the more substituted, thermodynamically more stable diene 269. As an outgrowth of their extensive studies on the [2,3] Wittig rearrangement of diallyl ethers,w Nakai and his c o l l a b ~ r a t o r shave executed a sequential [2,3] Wit'~~ tig-Claisen rearrangement. Selective metalation of diallyl ether 270 at the allyl residue followed by rearrangement produces dienol271. Subsequent Claisen rearrangement provides the 4,7-dienal 272. The sequence is also successful when the Johnson and Ireland variants are employed. Dienol 271 provides the opportunity for an oxy-Cope rearrangement to unsaturated aldehyde 273. The oxy-Cope process provides an unsaturated aldehyde bearing one more carbon between the functional groups than is obtained in the Claisen rearrangement. 270 271 OH I CHO 272 The Claisen rearrangement and its associated sigmatropic processes create the opportunity for the design and execution of consecutive rearrangements. These processes may be divided into three categories: sequential, tandem, and iterative. A sequential rearrangement requires derivatization of a rearrangement product prior to a subsequent rearrangement. A tandem rearrangement has all the atoms for consecutive rearrangements installed in t,he starting substrate prior to the first rearrangement. An iterative rearrangement requires a number of transformations to be conducted on a rearrangement product prior to a subsequent "identical" rearrangement.'48 A. Sequential Rearrangements B. Tandem Rearrangements Cookson and Hughes149 have performed a sequential Claisen and Cope rearrangement in preparing the diene 269. When the acetal 265 is heated with P,P-dimethylallyl alcohol (266) in mesitylene with o-nitrobenzoic acid as a catalyst, rearrangement of the inter- The seminal studies on aliphati~,'~'tandem rearrangements-namely, the Claisen-Cope rearrangement, have come from the laboratories of Thomas152 and C o ~ k s o n . ' ~ ~ - ' ~ ~ investigations are best exThese emplified by the synthesis of @-sinesal(276), essential an oil of the Chinese orange.'528 The dienyl ether function of 274 is generated from (E)-l-ethoxy-2-methyl-173butadiene with mercuric ion catalysis. The intermediate aldehyde(s) 275 from Claisen rearrangement undergo Cope rearrangement to form the (Z,GE)-P-sinesal (276). The presence of the G(E)-olefin requires the chain bearing the 1,3-diene of 275 to be equatorial in the transition state for the Cope rearrangement. The 2(E) configuration may arise either by direct means from the rearrangement or by isomerization of any 2(2)-olefin produced. The success of the tandem [3,3] sigmatropic process requires a substituent (in this instance a methyl group) at C1 of allyl vinyl ether 274 to avoid conjugation of the P,y double bond of 275, which ' " '0 2E5 266 h L 274 275 267 268 t90c n-c5H"9 269 276 Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1441 would short-circuit the Cope rearrangement.153bv155b For the purpose of synthetic planning, the reaction should be recognized as a formal y-allylic alkylation of an (E)-2-butenal. The tandem Claisen-Cope rearrangement has two other important characteristics. First, the Claisen rearrangement, which generally has the lower activation energy, precedes the Cope rearrangement, thereby creating the opportunity for the isolation of intermediates. Second, the success of the reversible Cope rearrangement depends upon the judicious choice of target substrate because the more stable product is the 1,5-diene having the more substituted double bonds. In the context of several synthetic projects, the reverse order of these sigmatropic processes-namely, the Cope-Claisen rearrangement has been explored in this and other laboratories. An unfavorable equilibrium in the Cope step would be inconsequential as the irreversible Claisen rearrangement would drive the reaction; no intermediates would be anticipated. The Cope rearrangement of triene 277 to 278 is a thermodynamically unfavorable process that is driven to aldehyde 279 by the Claisen rearrangement. Similarly, the Cope rearrangement of trienes 280 (R = H, Me) gives rise to 281, the stereochemistry of which is created through a chairlike transition state. The olefin facial selectivity of the Claisen rearrangement (281 282) occurs principally trans to the substituent at the newly created center of asymmetric of the ring to afford aldehyde 282. The process permits the generation of three contiguous, stereodefined centers of a ~ y m m e t r y . ' ~ ~ J ~ ~ OTBS 283 284 I O 285 4 Bis(ally1ic alcohol) 287 (cf., 206 207), prepared by the reduction of the enone, is subject to chain extension using the Johnson variant. Conversion of the terminal esters of 288 to propylidene groups provides an ''insideoutside" synthesis of the symmetrical triterpene squalene (289), with each of the four central double bonds having their stereochemistry controlled by the Claisen rearrangement.25 - 286 - w)2d-L2 EtOpC OH 287 288 P 289 277 278 279 The C18-Cecropia juvenile hormone (JH) (294) has lent itself to iterative synthesis. Olefinic ketal 291 serves as the agent for two chain extensions (290 292 293). The enone functionality of 293 is readily converted into J H (294). The iteration of 292 has also been accomplished with both enantiomers of the chiral ketals, 295161 and 296,162 which has led to the synthesis of both diastereomers and the enantiomers of the hormone. An iterative process has converted ester 133b to ester 297, a unit utilized in the synthesis of the vitamin E side ~ h a i n . ~ ~ ~ i ~ ~ ~ - 280 281 282 An excellent test for the tandem Cope-Claisen rearrangement is the formation of (E,E!)-1,6-~yclodecadienes from the more stable 1,2-divinylcyclohexanes.Raucher'" has successfully converted the isobutyrate-derived silyl ketene acetal 283 to the decadiene 284. The use of the disubstituted silyl ketene acetal is critical in obtaining the desired product. Since the starting material is prepared from (S)-(+)-cawone,the product is obtained in enantiomerically pure form. This method has been utilized in the preparation of the sesquiterpene, (+)-dihydrocost~nolide.~~~ earlier study, In an three of the four diastereomers of triene 285 gave aldehyde 286 as the only 10-membered ring product.1m'60 C. Iterative Rearrangements A f CO,Me +E:. H' * 0 CO,Me iterat,on * OH 290 292 293 294 295 296 297 The use of 3-methoxyisopreneMand related ketals permits the repetitive formation of olefinic residues. Lythgoe and have employed an iterative Claisen sequence to construct the enantiomerically pure ketone 302, an intermediate in the synthesis of tachysterol and precalciferol. The relative stereochemistry of the two oxygen functionalities of 298 sets the stereochemistry of the acetic acid residues of 301 and thereby assures the trans-fused ring system of 302. The lack of stereocontrol adjacent to the ester group 1442 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler in ester 300 is inconsequential as equilibration during the Dieckmann ring closure (301 302) achieves the required s t e r e ~ c h e m i s t r y . ~ ~ ~ ~ ' ~ ~ + BZO 1 ''',,m * C(OMe13 299 - bulk of the phenyl substituent in 306 directs bond formation to the concave face of the tricyclic nucleus. The less sterically demanding acetylenic residue of 308 allows bond formation to occur on the inherently more accessible convex face. OH 298 Me BZO 390 Me 30 1 '",,/\/\I * &O 302 ' 308 309 V I I . Synfheflc Applicafions Although numerous synthetic applications of the aliphatic Claisen rearrangement have been discussed in previous sections to illustrate various aspects of the reaction, this section considers additional applications from the perspective of the tethered rings attending the rearrangement nucleus. A. { 1,l )-Rearrangements The lack of stereochemical control in the {1,1;5,6}304 has been overcome by rearrangement of 303 employing a different construction of the vinyl ether residue. The {1,2;5,6}-rearrangementof nitrile 3 10 provides ketone 31 1 having vicinal quaternary centers with the desired stereochemistry of the trichodienederived trichothecenes. The rearrangement occurs exclusively on the face of the cyclopentene ring remote from the oxygen substituent with 16:l chair/boat selectivity. Ketone 31 1 serves as an intermediate in the synthesis of neosporol (312).170 P O - This system is typified by efforts to synthesize trichodiene (305a), the biogenetic progenitor of the trichothecenes, via a {1,1;5,6] Claisen rearrangement. Allyl vinyl ether 303, as an undetermined mixture of geometrical isomers, gives rise to a 1:l mixture of aldehydes 304 and, ultimately, to the same mixture of trichodiene and bazzanene (305b).165The chairlike transition state is recognized as the dominant pathway,l- but the inability to control vinyl ether or ester enolate geometry166bdhas made this route non~e1ective.l~~ U 31 0 U yy J& OH 312 TBSO 31 1 303 % 304 In a model study directed toward the synthesis of the quassinoid bruceantin (316),the { 1,2]-rearrangementof unsaturated ester 313 results in bond formation on the a-face of ring B, remote from the angular methyl group through a chairlike transition state. With the stereochemistry set in the side chain, the sequential construction of rings C, E, and D is accomplished to provide pentacyclic lactone 315.171,172 305a. R= a - M e b . R= 0-Me Tsso\ \ v OB" B. (1,2)-Rearrangements The rearrangement of the allyl enol ether of cyclohexanone to 2-allylcyclohexanone is the prototype of this group." In a study related to the synthesis of the fungal phytotoxins betaenone B and stemphyloxin I, hop kin^'^^ has investigated the rearrangement of allyl vinyl ethers 306 and 308. While both rearrangements occur through the chairlike transition state, the steric 31 3 314 HO 3'5 3'5 Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1443 C. (1,4]-Rearrangements The {1,4) group was discussed earlier (III.D.5) in the context of a "meta-Diels-Alder reaction",lo3a method that creates carbocycles from heterocycles. P i n n i ~ k ' ~ ~ has employed the (1,4)-rearrangement in the synthesis of the cannabinoid, trans-Al-THC (319). A 1:l mixture of styrenes 317 gives the same mixture of ketones 318. Remarkably, the reaction proceeds at ambient temperature as opposed to the elevated temperatures (200-400 "C) often required for this class of rearrangement. O-Methoxystyrene 317 appears to be ideally suited for dissociation at the allylic ether bond, suggesting the possibility of extensive bond breaking in the transition state, or even the intercedence of an ionic process. n "% 0 Me0 n-C5H11 -b Me0 n-CsH11 I 323 317 31 8 322 31 9 In an investigation directed toward the total synthesis of aphidicolin (322), Ireland and A r i s t ~ f fhave realized ~~* the stereospecific (1,2;1,4}-rearrangementof allyl vinyl ethers 321. While olefin 320 provides the correct substitution pattern to solve the synthetic problem, isomer 323 is suitable as an intermediate in the synthesis for the closely related stemodane skeleton. This good fortune is not always withstanding, and the success of such a venture is predicted upon the stereoselective introduction of the substituents R1and R2in allyl vinyl ethers such as 321. In this instance, a hetero DielsAlder reaction between methyl methacrylate and the appropriate exo-methylene a,o-unsaturated ketone is regioselective, but not stereoselective. Danishefsky and his collaborators have extended the (1,4}-rearrangement silyl ketene acetals. Thus, the to lactone 324 rearranges as its silyl ketene acetal through the obligatory boatlike transition state175a give rise to to acid 325. Subsequent oxidative decarboxylation provides the sesquiterpene widdrol (326).175bJ76 The ionophore antibiotic indanomycin (X-l4547A, 327) provides two opportunities for the application of the { 1,4)-rearrangement. The obvious application is the construction of the perhydroindane ring system. Burke177has utilized the Danishefsky approach to this end, but not without a surprise. Rearrangement of silyl ketene acetal 328 at 135 "C affords a mixture of four diastereomers (31:9:5:1) of 329, the major component of which is the product allegedly arising from the { 1,4]-rearrangement (329, a - H , a-Et). However, at 95-100 "C,the triene 330 is isolated, thermolysis of which at 135 "C produces the same mixture of diastereomers. A similar result is obtained with the dia- 324 325 326 stereomer of 328 that is epimeric at the vinyl center, although a single ester 329 (P-H, a-Et) is realized. An additional caveat is warranted. Since the source of the lactones for these reactions is invariably derived from the 1,Baddition of a vinyl organometallic to an aldehyde 327 - -x 330 1444 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler followed by lactonization, it is important to control the stereoselectivity of the addition, whether or not the Diels-Alder pathway is 0 p e r a t i ~ e . l ~ ~ ~ Me \ 331 332 is formed upon rearrangement of the (E)-0-silyl ketene acetal of lactone 337. The boatlike transition state 340 ( n = l),bearing the tethered chain in a cis relationship, accounts for the observed stereochemistry. For (E)-0silyl ketene acetals, the cis-fused ring system is observed for n = 1-4. Transition state 341 is found to be operable, in part, when n = 7. Similarly, KnightlBIbhas accomplished the stereoselective ring contraction of lactone 342 to afford ester 343, an intermediate in a proposed route to guaianolide and pseudo-guaianolide sesquiterpenes. C02Me 337 333 338 Although the propionic acid residue in the "left-wing'' of indanomycin seemingly dictates the Ireland strategy (144 145 + 146), an alternative analysis reveals that the ester 332 is accessible via the (1,4) route.178 Its conversion to ketone 333 creates a viable synthon for further elaboration. The caveat offered above is also applicable to the formation of the lactone precursor to 331.178c - 0 @ 339 OTBS H D. { 1,5)-Rearrangements The (1,5)-rearrangement results in a two-atom ring contraction. In an approach to the synthesis of quadrone (336), Funk179 demonstrated that fused lachas tone 334, by way of its silyl ketene acetal, gives rise to the bridged, ring-contracted ester 335. Mechanistic restraints require the ester group to be axial to the newly formed ring, thereby setting the stage for further transformations directed toward quadrone. CO2TBS 340 341 342 343 F. (2,4]-Rearrangements 334 335 336 E. { 1,C)-Rearrangements The (1,6)-rearrangement permits ring contraction by four atoms wherein the newly formed ring bears vicinally substituted vinyl and carbonyl substituents. Thus far, the examples studied have been medium to macrocyclic lactones for which there are ample methods for their synthesis. Funkle0and Knight181have provided the seminal contributions to this class of Claisen rearrangement. In a synthesis of the iridoid iridomyrmecin (339), Funkla has demonstrated that the key intermediate 338 This class of Claisen rearrangements permits ring expansion by two carbons and is the exocyclic vinyl ether analogue of the {1,4)-rearrangement. The vinyl ether functionality can be generated by intramolecular bromoetherification followed by base-catalyzed elimination of HBr,lB2alkoxide-promoted addition to an acetylene,la3dehydration,lM or radical cycli~ation.'~~ For example, nerolidol(344) affords allyl vinyl ether 345 upon implementation of the bromoetherification procedure and elimination. Subsequent thermolysis of 345 gives the cycloheptenone 346. Several operations convert the cycloheptenone into 2,5-cedradiene (347).182b A variation on the bromoetherification theme has been developed by Petrzilka-namely, selenoxide elimination to generate ketene acetals.186"*b This technique is exemplified by the synthesis of the decenolide 350, phoracantholide J. The eight-membered acetal is prepared under high-dilution conditions by intramolecular phenylselenenyl etherification of an acyclic chain bearing allylic alcohol and vinyl ether termini. Oxidation of selenide 348 to the selenoxide, subsequent elimination to ketene acetal 349, and rearrangement afford the target substance. The formation of the (2)-olefin is derived from transition state 351 (assuming Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1445 353 344 345 354 I 346 347 a chairlike transition state) rather than the seemingly more strained transition state 352 that would lead to the ( E ) - ~ l e f i n . l ~ ~ ~ J ~ ~ One of the difficulties associated with this class of rearrangement is the problem of vinyl ether isomerization that can partition products between the {1,4]and (2,4)-manifold~.l~~ An intriguing case of this process is seen in the Paquette synthesis of the sesquiterpene precapnelladiene (355).lg8 Epimeric allyl vinyl ethers 353 and 356, both prepared from their respective lac- & 356 357 358 0 355 m 348 * 349 and acetaldehyde followed by dehydration. The latter condition is achieved by selective Luche reduction (CeC13/NaBH4)of the enone. 0 350 w-w 359 361 (CozEt 360 351 352 tones with Tebbe's reagent (CpzTiCHzC1A1Mez),17 undergo rearrangement via different pathways. Isomer 353, bearing the @-methyl group, rearranges to give the desired cyclooctenone 354. On the other hand, the a-isomer 356 is susceptible to prototropic isomerization of the vinyl ether double bond. Rearrangement via the (1,4}pathway gives the cyclohexene 358. The prototropic shift appears less favorable in isomer 353 as the allylic proton is less accessible on the concave face than it is on the convex face of 356. G. (4,5)-Rearrangements This type of rearrangement has been utilized by Paq ~ e t t e in~the synthesis of the sesquiterpene dactylol ' ~ (361). The reaction permits the control of allylic side chain stereochemistry (360) if the geometry of the exocyclic double bond and the stereochemistry of the hydroxyl group can be controlled. In the case at hand, allylic alcohol 359, the former requirement is readily met by introduction of the ethylidene group via condensation between a l-methyl[5.1.0]bicyclooctan-2-one The {4,5]-rearrangementhas served admirably in the steroid field to provide a route for the stereospecific introduction of the Czoside-chain stereochemistry and clearly indicates how product stereochemistry may be controlled if double-bond geometry and alcohol stereochemistry can be appropriately manipulated. Pregnane (362), readily available by a-face epoxidation of the D-ring enone, is reduced under Wharton conditionslgO a mixture of allylic alcohols 364a (63%) and to 365 (27%). Carroll rearrangement of (E)-alcohol 364a affords the Czo a-stereochemistry of 363a while (2)olefin 365 provides the Czo@-stereochemistry(363b).lg1 Side-chain stereoisomers 363a and 36313 are converted to cholesterol and Czo-isocholesterol, respectively.192 Alcohol 364b, formed by oxidation and a-face reduction of the intermediate enone, gives rise to aldehyde 366. Thus, 2 a-allylic alcohol 365 and E P-allylic alcohol 364b are operationally equivalent as they both yield the same relative stereochemistry at CZ0.lg3 1446 Chemical Reviews, 1988, Vol. 88, No. 8 TMS Ziegler I TMS I 367 368 362 363a, R,=H, &Me b. R,=Me. R,=H \ / 369 364a, R,=H, Rz=OH b, R,=OH, Rz=H 365 370 371 JjTCHO 6Me 366 372 373 &OTBS * * + $H O H (4,6)-Rearrangements . THPo CHO 374 OH 375 The perceptive reader will have recognized many examples of this common version of the Claisen rearrangement in earlier discussions. The {4,6)-rearrangement is typified by the formal SN2'addition of an acetic acid residue to an endocyclic cycIoalkeno1 and provides a convenient route to quaternary allylic carbon at0ms.l" In a synthesis of quadrone (3361, Burkelg5has employed two {4,6)-rearrangements.The first, 367 368,creates a quaternary allylic center that serves to form subsequently a spirocyclopentenone. Whereas the allylic alcohol precursor of vinyl ether 367 arises via 1,2-reduction of the parent enone, the a-allylic alcohol progenitor of vinyl ether 370 would not, owing to the steric effect of the gem-dimethyl group, be accessible by the same pathway. Accordingly, the accessible a-face of the six-membered ring is exploited by employing the isomeric enone 369 in conjunction with the Wharton rearrangement.lW The stereochemistry of the carbon-oxygen bond in the sequence is established during the a-face epoxidation of enone 369. The combination of the Wharton and Claisen rearrangements results in the net substitution of the carbonyl of 369 by the acetaldehyde moiety of 371 with retention of the site of the double bond. Another method for the all-important control of allylic alcohol stereochemistry, albeit target-dictated, is illustrated in the preparation of the Inhoffen-Lythgoe diol 375,1g6a critical intermediate in vitamin D syntheses, and the steroid C/D ring synthon 379.Ig7 Both approaches utilize cis-fused [3.3.0] bicyclic lactones (372and 376,respectively) to generate the correct allylic alcohol stereochemistry. In each instance, a Baeyer-Villiger oxidation of a bicyclo[2.2.l]heptenone serves as the source of the lactones. - 376 377 BnO 378 379 OHC I . (5,6)-Rearrangements The (5,6)-rearrangement is closely related to the (1,Z)-rearrangement as the two processes serve to interchange carbonyl and olefin functionality. Horeaulg8 has observed the stereoselective (1,2)-rearrangementof allyl vinyl ether 380 to allyl ketone 381,an intermediate in a synthesis of equilenin. Application of the (5,6) variant as the second step of the tandem rearrangement 382 383 384 results in aldehyde 384 that is transformed into estrone 385 in several operations.156b Both seco derivatives 381 and 384 are the major stereoisomers from their respective rearrangements as the bulky naphthalene and dihydronaphthalene groups direct the bond formation. The propensity for this class of rearrangement to give axial bond formation in cyclohexenyl systems with the attendant ring in a chair conformation has been demonstrated by Ireland.lWThis tendency is often observed - - Thermal, Aliphatic Claisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1447 380 381 The major isomer arises from equatorial, &face attack on ring B (chair conformation), avoiding the 1,3-diaxial interaction with the axial methyl group of the a-face. The use of secondary allylic alcohols in the (5,6]-rearrangement generally follows the tendency of secondary allylic alcohols in (0,OJ-rearrangements to give "trans" double bonds. An unsuccessful approach to the synthesis of the alkaloid geissoschizine (392) utilizes the rearrangement of a 1:l mixture of the stereoisomers 3932021203 provides stereoisomeric (2)-olefins 394 that and 395. Allyl vinyl ether 393a rearranges through OH 392 393a,Rl=Me, R2=H b, R,=H, R, Me = 384 385 in rigid systems as typified by the conversion 386 387.200aBond formation occurs axially from the a-face of 386 with ring B in a chairlike conformation. However, steric factors can play an important role in altering the course of events. In a synthetic route to the clerodane diterpene annonene (388). Kakisawamlhas observed an 85:15 ratio of aldehydes 390 and 391, respectively, upon rearrangement of allyl vinyl ether 389. OH OH 394 395 chairlike transition state 396 as opposed to its alternative chair conformation 397 which can encounter 1,3-diaxial interactions. Similarly, isomer 393b rearranges through transition state 398 rather than 399. In addition, transition state 399, if late enough, can suffer from All3 interactions (cf. the ground-state equivalent, 392). 386 387 396 397 308 q & 0 0 U 389 @ 0 0 lCHO MeO,CzO 398 399 U 390 & 0 0 U 39 1 Unfortunately, high stereospecificity in this rearrangement is not always the case. In a synthesis of africanol (402), PaquettelE9 observed the expected has ester product 401 from orthoester rearrangement of alcohol 400. However, the rearrangement of epimeric alcohol 403 gave a 1:l mixture of isomers 404 ( ( E ) olefin) and 405 ((2)-olefin). Ester 404, the anticipated product, encounters steric interactions with the gemdimethyl group in the transition state for its formation, thereby allowing bond formation to occur trans to the cyclopropane ring in spite of the axial methyl group in 1448 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler O chorismate mutase z C g the transition state for the formation of 405.204 2 * OH OH 406 400 40 1 407 402 OH OH 408 409a, R=H b, R=C(O)NHCH&H&HZ 403 404 P(405 C02Et challenge, the synthetic organic community has had the opportunity to expand the scope of the reaction and apply it to complex syntheses, and bioorganic chemists have solved a formidable challenge in the chemistry of enzymes. Perhaps a new and imaginative generation will see new opportunities for this reaction and expand upon the chemistry discussed in this review. VII I . Blochemlcal Aspects All the rearrangements that have been discussed thus far are inventions developed over the course of 76 years. The elucidation of the structure and absolute stereochemistry of chorismate (406)205and the discovery of its [3,3] sigmatropic rearrangement to prephenate (407),206 precursor to aromatic amino acids via the the shikimic acid pathway, demonstrates that Nature has been regularly executing the "Claisen" rearrangement for some time. The synthesis of racemic chorismic acidm7Gb labeledmc chorismate was followed by the and studies of Knowles, who has shown that chorismate rearranges through a chairlike transition state both in vivo and in vitro.m The process is catalyzed in vivo by the enzyme chorismate mutase by a factor of 106.209 The accrued evidence suggests that rearrangement under either set of conditions proceeds through dipolar transition state 408 with both the hydroxyl and enol pyruvate units diaxial.210Bartlett has recently prepared transition-state analogue 409a and has found it to be a potent inhibitor of chorismate mutase-prephenate dehydrogenase from Escherichia coli.211p212 Monoclonal antibodies have recently been employed to catalyze the chorismate to prephenate rearrangement. The transition-state model 409a is bound to the carrier protein using the diazonium salt 409b, and monoclonal antibodies are isolated that catalyze the conversion of chorismate to prephenate with a rate enhancement of 10OO0.213 ZX. Concluding Remarks Acknowledgments. I express my gratitude to my colleagues J. A. Berson, J. M. McBride, and A. Schepartz, for their advice on theoretical issues; to former co-workers G. Bennett, S. Klein, A. Kneisley, A. Nangia, J. Sweeny, J. Thottathil, P. Wender, and R. Wester, who have contributed to the subject matter over the years; to current co-workers M. Becker, W. Cain, P. Floreancig, and S. Sobolov for helpful suggestions; to R. Fogel for technical assistance; and to L.C. References Claisen, L. Chem. Ber. 1912,45,3157.For a rememberance of the life and works of Ludwig Claisen see: Zbid. 1936,69, 79. For general reviews on [3,3] sigmatropic rearrangements, see: (a) Rhoads, S. J.; Raulins, N. R. Org. React. (N.Y.) 1975,22, 1. (b) Ziegler, F.E. Acc. 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(b) Bartlett, P. A.; Barstow, J. F. Ibid. 1982.23.623. (c) Bartlett. P. A.: Barstow, J. F. J . Om. Chem. 1982; 47, 3933. (109) (a) Lythgoe, B.; Milner, J. R.; Tideswell, J. Tetrahedron Lett. 1975, 2593. (b) Lythgoe, B.; Manwaring, R.; Milner, J. R.; . I I Moran, T. A.; Nambudiry, M. E. N.; Tideswell, J. J . Chem. SOC., Perkin Trans. 1 1978, 387. (a) Cookson, R. C.; Gopalan, R. J. Chem. SOC., Chem. Commun. 1978,608. (b) Cookson, R. C.; Gopalan, R. Ibid. 1978, 924. (c) Nakai. T.: Setoi. H.: Kaeevama. T. Tetrahedron . I " Lett. Mi, 22, 4097. Still, W. C.; Schneider, M. J. J. Am. Chem. SOC. 1977,99,948. Raucher, S.; Hwang, K.-J.; Macdonald, J. E. Tetrahedron Lett. 1979, 3057. Raucher, S.; Macdonald, J. E.; Lawrence, R. F. Tetrahedron Lett. 1980, 21, 4335. Saucy, G.; Cohen, N.; Banner, B. L.; W l i n g e r , D. P. J. Org. Chem. 1980,45, 2080. The problem of alcohol esterification with unhindered carboxylic acids in non (0,O) rearrangements is discussed in ref 2b. Mohammed, A. Y.; Clive, D. L. J. J . Chem. SOC.,Chem. Commun. 1986.588. Yuan, W.; Berman, R. J.; Gelb, M. H. J . Am. Chem. SOC. I I 1987, 109, 8071. (118) Dolby, L. J.; Ellinger, C. A.; Esfandiari, S.; Marshall, K. S. J. Om. Chem. 1968.33.4508. (119) (ajcoates, R. M.'; Hobbs, S. J. J. Org. Chem. 1984, 49, 140. Some concern has been expressed about the mechanism of this reaction: Mukaiyama, T.; Murakami, M. Synthesis 1987, (124) (125) (126) (127) 1983, 285. (128) Ireland, R. E.; Varney, M. D. J. Am. Chem. SOC. 1984, 106, 3668. (129) Ziegler, F. E.; Reid, G. R.; Studt, W. L.; Wender, P. A. J. Org. Chem. 1977,42, 1991. (130) Hatakeyama, S.; Saijo, K.; Takano, S. Tetrahedron Lett. 1985, 26, 865. (131) Cha,'J. K.; Lewis, S. C. Tetrahedron Lett. 1984, 25, 5263. (132) Also see: (a) Suzuki, T.; Sato, E.; Kamada, S.; Tada, H.; Unno, K.; Kametani, T. J. Chem. SOC., Perkin Trans. 1 1986, 387. (b) Takano, S.; Kurotaki, A.; Takahashi, M.; Ogasawara, K. Zbid. 1987, 91. (133) Cherest, M.; Felkin, H.; Prudent, N. Tetrahedron Lett. 1968, 2199. (134) (a) Paddon-Row, M. N.; Rondan, N. G.; Houk, K. N. J. Am. Chem. SOC. 1982,104, 7162. (b) Houk, K. N.; Moses, S. R.; Wu, Y.-D.; Rondan, N. G.; Jager, V.; Schohe, R.; Fronczek, F. R. Ibid. 1984. 106. 3880. (135) For a recent ankysisof the alkoxy effect, see: Kahn, S. D.; Hehre, W. J. J. Org. Chem. 1988, 53, 301. (136) (a) Kurth. M. J.: Yu. C.-M. Tetrahedron Lett. 1984.25. 5003. (b) Kurth, M. J.; Yu, C.-M. J . Org. Chem. 1985,'50,`1840. (137) For other Claisen rearrangement based routes to botryodi' (a) Johnson, W. S.; Brocksom, T. J.; Loew, P.; Rich, D. H.; Werthemann, L.; Arnold, L. A,; Li, T.; Faulkner, D. J. J. Am. Chem. SOC. 1970,92,4463. (b) Faulkner, D. J.; Petersen, M. R. Zbid. 1973, 95, 553. For a C6-sulfur-substituted system, see: (a) Takeda, T.; Fujiwara, T. Chem. Lett. 1982, 1113. For a C5-C1-substituted system, see: (b) Lansbury, P. T.; Wang, N. Y.; Rhodes, J. E. Tetrahedron Lett. 1972, 2053. Ireland, R. E.; Wilcox, C. S. Tetrahedron Lett. 1977, 2839. Kuwaiima. I.: Tanaka. T.: Atsumi. K. Chem. Lett. 1979.779. JenkiGs, P. R.; Gut, R.; Wetter, H.; Eschenmoser, A. kelu. Chim. Acta 1979, 62, 1922. Wilson, S. R.: Price, M. F. J. Am. Chem. SOC. 1982.104.1124. The preparation of 8,cunsaturated aldehydes and ketones are often prepared through the oxy or alkoxy Cope rearrangement. For a Cope rearrangement that also produces 8,t-unsaturated acids and esters by formation of the @,-y u bond bond, see: Ziegler, F. E.; Wang, T.-F.J. rather than the a,@ Am. Chem. SOC. 1984,106, 718. Smith, E. H.; Tyrrell, N. D. J. Chem. SOC., Chem. Commun. _-_-. 1 nAR ' plodin, see: (a) McCurry, P. M., Jr.; Abe, K. Tetrahedron Lett. 1973, 4103. (b) Wilson, S. R.; Meyers, R. S. J . Org. Chem. 1975,40, 3309. (138) The same study has been conducted by Japanese investigators using DME as a solvent. Different stereochemical assignments have been made based upon coupling constants of the 8-hydroxy esters. The Kurth experiments employ the more reliable coupling constants of the dioxanes derived by reduction of the esters to 1,3-diols followed by acetonide formation. Fujisawa, T.; Tajima, K.; Ito, M.; Sato, T. Chem. Lett. 1984, 1169. (139) Wipf, B.;, Kupfer, E.; Bertazzi, R.; Leuenberger, H. G. W. Helu. Chm. Acta 1983, 66, 485. (140) A type I chiral auxiliary may be defined as an enantiomerically pure entity that is bound to an achiral unit, induces diastereoselectivity in a subsequent reaction, and is then removed (and ideally recycled) leaving a new enantiomerically-pure substance. A type I1 chiral auxiliary is not removed but may be altered in the substrate. Thus, the hydroxyethyl unit is a type I1 chiral auxiliary in the decarboxylation. Thermal, Aliphatic Ciaisen Rearrangement Chemical Reviews, 1988, Vol. 88, No. 8 1451 (141) For other applications of chiral auxiliaries in acyclic Claisen rearrangements, see: (a) Chillous, S. E.; Hart, D. J.; Hutchinson, D. K. J. Org. Chem. 1982,47,5418.(b) Kallmerten, J.; Gould, T. J. Ibid. 1986,51, 1152. (c) Denmark, S. E.; Marlin, J. E. Ibid. 1987,52,5742. (d) Welch, J. T.; Eswarakrishnan, S. J.Am. Chem. SOC. 1987,109,6716.(e) Strauss, H. F.; Wiechers, A. Tetrahedron Lett. 1979,4495. (142) (a) Ziegler, F. E.; Kneisley, A.; Thottathil, J. K.; Wester, R. T. J. Am. Chem. SOC. 1988,110,5434.(b) Ziegler, F. E.; Cain, W. T.; Kneisley, A,; Stirchak, E. P.; Wester, R. T. J. Am. Chem. Osc. 1988,110,5442. (143) For a study of a related system, see: Daub, G. W.; Griffith, D. A. Tetrahedron Lett. 1986,27,6311. (144) When oxygen is replaced by nitrogen in an allyl vinyl ether, the reaction is an aza Claisen rearrrangement. The substitution of C1 or C2 of a 1,5-hexadiene with nitrogen leads to an aza Cope rearrangement. (145) (a) Kurth, M. J.; Decker, 0. H. W. Tetrahedron Lett. 1983, 42, 4535. (b) Kurth, M. J.; Decker, 0. H. W.; Hope, H.; 1985,107,443.(c) Kurth, Yanuck, M. D. J. Am. Chem. SOC. 5769. (d) M. J.; Decker, 0. H. W. J. Org. Chem. 1985,50, Kurth, M. J.; Decker, 0. H. W. Ibid. 1986,51, 1377. (e) Kurth, M. J.; Soares, C. J. Tetrahedron Lett. 1987,28, 1031. (146) For a different approach to this type of rearrangement, see: Ireland, R. E.; Willard, A. K. J. Org. Chem. 1974,39, 421. (147) Facial excess is a measure of the relative amount of bond formation on the two diastereotopic faces of the double bond % fe = [(C, + E,) - (C, + E , ) ] / C , E, + C, + B , (148) See ref 54,footnote 91. For a review on sequential sigmatropic rearrangements, see: Nakai, T.; Mikami, K. Kagaku no Ryoiki 1982,36,661;Chem. Abstr. 1982,96,1601. (149) Cookson, R. C.; Hughes, N.W. J. Chem. SOC., Perkin Trans. 1 1973,2738. (150) Mikami, K.; Kishi, N.; Nakai, T. Chem. Lett. 1981, 1721. (151) The tandem Claisen-Cope rearrangement appears in the aromatic series with aryl allyl ethers. See ref 2a. (152) (a) Thomas, A. F. J. Am. Chem. SOC. 1969,91,3281. (b) C Thomas, A. F.; Ozainne, M. J. Chem. SOC. 1970,220. (c) Thomas. A. F.: Ohloff. G. Helu. Chim. Acta 1970.53. 1145. (153) (a) Bowden, B:; Cookson, R. C.; Davis, H. A. J. C h e k SOC., Perkin Trans. 1 1973,2634. (b) Cookson, R. C.; Rogers, N. R. Ibid. 1973,2741. (154) These authors chose the adiective seauential to describe these rearrangements. We pref& the more descriptive term t n adem that muore accurately captures the nature of the process. Tandem: [Having] a relationship between two things involving cooperative action, or mutual dependence...". Webster'sNew World Dictionary;World Publishing: 1978. (155) For other Claisen-Cope rearrangements, see: (a) Fujita, Y.; Onishi, T.; Nishida, T. Synthesis 1978,532. (b) Baker, R.; Selwood, . L. Tetrahedron Lett. 1982,23,3839.For a system with the potential for a tandem rearrangement, see: (c) Wilson, S. R.; Myers, R. S. J. Org. Chem. 1975, 40, 3309. (156) (a) Ziegler, F. E.; Piwinski, J. J. J. Am. Chem. SOC. 1982.104, 7181 &d references cited therein. (b) Ziegler, F. E.; Lim, H. J. Org. Chem. 1982,47,5229. ( c ) Ziegler, F. E.; Lim, H. J . Ore. Chem. 1984.49. 3278. (157) F& an oxy Copek!laisen rearran ement, see: Mikami, K.; Taya, S.; Nakai, T.; Fujita, Y. J. 8rg. Chem. 1981,49,5447. (158) Raucher, S.; Burks, J. E., Jr.; Hwang, K.-J.; Svedberg, D. P. J. Am. Chem. SOC. 1981,103,1853.(159) Raucher. S :Chi. K.-W.: Hwane. K.-J.: Burks. J. E.. Jr. J.Ore. . . . -. . , Chem. 1986,51;5503.' (160) For an example of a tandem Claisen ene reaction, see: Ziegler, F. E.; Mencel, J. J. Tetrahedron Lett. 1984,25, 123. 1971,93,3765. (161) Loew, P.; Johnson, W. S. J. Am. Chem. SOC. (162) Faulkner, D. J.; Petersen, M. R. Ibid. 1971,93,3766. (163) For a similar system executed in tandem, see: Reference 34; Curran, D. P. Tetrahedron Lett. 1982,23, 4309. (164) For other iterative Claisen rearrangements in the aliphatic series, see: (a) Fleet, G. W. J.; Gough, M. J.; Shing, T. K. M. Tetrahedron Lett. 1983,24,3661.(b) Donch, M.; Jiiger, V.; Sponlein, W. Angew. Chem., Int. Ed. Engl. 1984,23,798.(c) Oplinger, J. A.; Murtiashaw, C. Burke, S.D.; Saunders, J. 0.; 1131. W. Tetrahedron Lett. 1985,26, (165) Suda, M. Tetrahedron Lett. 1982,23,427. (166) (a) Gilbert, J. C.; Wiechman, B. E. J. Org. Chem. 1986,51, 258. (b) Kraus, G. A.; Thomas, P. J. Ibid. 1986,51,503. (c) Gilbert, J. C.; Kelly, T. A. Zbid. 1986,51, 4485. (d) VanMiddlesworth, F. L. Ibid. 1986,51,5019. (167) For studies concerning diastereofacial selectivity in the (1,l) and {6,6)-rearran ements, see: (a) Morrow, D. F.; Culbertson, T. P.; Hofer, R. % .Chem. 1967,32,361.(b) House, J. Org. l H. 0.; Lubinkowski, J.; Good, J. J. Ibid. 1975,40, 86. (c) Tulshian, D. B.; Tsang, R.; Fraser-Reid, B. Ibid. 1984,49, 2347. (d) Fraser-Reid, B.; Tulshian, D. B.; Tsang, R.; Lowe, D.; Box, V. G. S. Tetrahedron Lett. 1984, 25, 4579. (e) Tulshian, D. B.; Tsang, R.; Fraser-Reid, B. J. Org. Chem. 1984,49, 2347. (f) Baraldi, P. G.; Barco, A.; Benetti, S.; Pollini, G. P.; Polo, E.; Simoni, D. Ibid. 1985,50, 23. .+ ... I , (168) (a) Lorette, N. B.; Howard, W. L. J. Org. Chem. 1961,26, 3112. For asymmetric induction in this rearrangement, see: (b) Mikami, K.; Takahashi, K.; Nakai, T. Tetrahedron Lett. 1987,28,5879.(c) Grattan, T. J.; Whitehurst, J. S. J. Chem. SOC., Chem. Commun. 1988,43. (169) Pratt, D. V.;Hopkins, P. B. Tetrahedron Lett. 1987,28,3065. (170) (a) Ziegler, F. E.; Nangia, A.; Schulte, G. J. Am. Chem. SOC. 1987,109,3987.(b) Ziegler, F. E.; Nangia, A.; Tempesta, M. S. Tetrahedron Lett. 1988,29, 1665. (c) Ziegler, F. E.; Nangia, A. Ibid. 1988,29,1669. (171) Ziegler, F. E.; Klein, S. I.; Pati, U. K.; Wang, T.-F. J. Am. 1985,107,2730. Chem. SOC. (172) For other examples of this class see: Reference 47. (a) Pelletier, s. W.; Yang, D. T. C.; Ogiso, A. J. Chem. SOC., Chem. Commun. 1968,830. (b) Stork, G.; Uyeo, S.; Wakamatsu, T.; Grieco, P.; Labovitz, J. J. Am. Chem. SOC. 1971,93,4945.(c) Burke, S. D.; Pacofsky, G. J.; Piscopio, A. D. Tetrahedron Lett. 1986,27, 3345. (d) Okawara, H.; Nii, Y.; Miwa, A.; Sakakibara, M. Ibid. 1987,28,2597. (173) Childers, W. E., Jr.; Pinnick, H. W. J. Org. Chem. 1984,49, 5276. (174) Ireland, R. E.; Aristoff, P. A. J. Org. Chem. 1979,44,4323. (175) (a) Danishefsky, S.;Funk, R. L.; Kerwin, J. F., Jr. J. Am. Chem. SOC. 1980,102,6889.(b) Danishefsky, S.;Tsuzuki, K. Ibid. 1980,102,6891. (c) For one solution to this problem, see: Danishefsky, S.; Audia, J. E. Tetrahedron Lett. 1988,29, 1371. (176) For a related rearrangement in the aromatic series. see: ' Nemoto, H.; Shitara, 8 ;Fukumoto, K.; Kametani, T.'Heterocycles 1987,25, 51. (177) Burke, S.D.; Armistead, D. M.; Shankaran, K. Tetrahedron Lett. 1986,27,6295. 1178) (a) Burke. S. D.: Armstead. D. M.: Schoenen. F. J. J. O w . Chem. 1984,49,'4320.(b) Burke, S . D.; Armistead, D. M ; Fevig, J. M. Tetrahedron Lett. 1985,26, 1163. (c) Burke, S. D.; Armistead, D. M.; Schoenen, F. J.; Fevig, J. M. Tetrahedron 1986,42, 2787. Also see: (d) Burke, S. D.; Schoenen, F. J.; Murtiashaw, C. W. Tetrahedron Lett. 1986,27,449.(e) Burke, S.D.; Schoenen, F. J.; Nair, M. S. Ibid. 1987,284143. (f) Burke, S.D.; Chandler, A. C., 111; Nair, M. S.; Campopiano, 0. Ibid. 1987,28,4147. Funk, R. L.; Abelman, M. M. J. Org. Chem. 1986,51,3247. (a) Funk, R. L.; Munger, J. D., Jr. J. Org. Chem. 1984,49, 4319. (b) Funk, R. L.; Munger, J. D., Jr. Ibid. 1985,50,707. (c) Funk, R. L.; Abelman, M. M.; Munger, J. D., Jr. Tetrahedron 1986,42, 2831. (d) Funk, R. L.; Olmstead, T. A.; Parvez, M. J. Am. Chem. SOC.1988,110,3298. (a) Cameron, A. G.; Knight, D. W. Tetrahedron Lett. 1982, 23,5455. (b) Begley, M. J.; Cameron, A. G.; Knight, D. W. J. Chem. SOC., Chem. Commun. 1984,827. (c) Cameron, A. G.; Knight, D. W. Tetrahedron Lett. 1985,26, 3503. (d) Cameron, A. G.; Knight, D. W. J. Chem. SOC., Perkin Trans. 1 1986,161. (a) Demole, E.; Enggist, P. Helu. Chim. Acta 1971,54, 456. (b) Demole, E.; Enggist, P.; Borer, C. Ibid. 1971,54, 1845. (c) Gonzdez, A. G.; Darias, J.; Martin, J. D.; Melih, M. A. Tetrahedron Lett. 1978,481. Marvell, E. N.; Titterington, D. Tetrahedron Lett. 1980,21, 2123. (a) Rhoads, S.J.; Brandenburg, C. F. J. Am. Chem. SOC. 1971, 93,5805.(b) Rhoads, S.J.; Watson, J. M. J.Am. Chem. SOC. 1971,93,5813. Johns, A,; Murphy, J. A. Tetrahedron Lett. 1988,29, 837. (a) Pitteloud, R.; Petrzilka, M. Helu. Chim. Acta 1979,62, 1319. (b) Petrzilka, M. Ibid. 1978,61,2286.(c) Petrzilka, M. Ibid. 1978,61,3075. Also see: (a) Carling, R. W.; Holmes, A. B. J. Chem. SOC., Chem. Commun. 1986,325. (b) Ireland, R. E.; Varney, M. D. J. Org. Chem. 1986,51,635. Kinney, W. A.; Coghlan, M. J.; Paquette, L. A. J . Am. Chem. SOC. 1985,107,7352. Paquette, L. A.; Ham, W. H. J. Am. Chem. SOC.1987,109, JULO. onor Wharton, P. S.; Bohlen, D. H. J. Org. Chem. 1961,26,3615. Tanabe, M.; Hayashi, K. J.Am. Chem. SOC.1980,102,862. Mikami, K.; Kawamoto, K.; Nakai, T. Chem. Lett. 1985,115. For a similar application of the alkoxy Cope rearrangement, see: Kooreda, M.; Tanaka, Y.; Schwartz, A. J. Org. Chem. 1980,45,1172. For a route to angular methyl groups, see: Dawson, D. J.; Ireland, R. E. Tetrahedron Lett. 1968,1899. Burke, S.D.; Murtiashaw, C. W.; Saunders, J. 0.;Oplinger, J. A.; Dike, M. S. J. Am. Chem. SOC.1984,106,4558. Trost, B. M.; Bernstein, P. F.; Funfschilling, P. C. J. Am. Chem. SOC. 1979,101,4378. Grieco, P. A.; Takigawa, T.; Moore, D. R. J. Am. Chem. SOC. 1979,101,4381. Horeau, A.; Lorthioy,; Guette, J. P. C.R. Hebd. Seances Acad. Sci., Ser. C 1969,269,558. Ireland, R.E.; Varney, M. D. Ibid. 1983,48, 1829. 1452 Chemical Reviews, 1988, Vol. 88, No. 8 Ziegler (200) (a) Ireland, R. E.; Marshall, J. A,; Church, R. F. J. Org. Chem. 1962,27, 1118. Also see: (b) Ireland, R. E.; Marshall, J. A. Ibid. 1962, 27, 1620. (201) Takahashi, S.; Kusumi, T.; Kakisawa, H. Chem. Lett. 1979, 515. (202) Rackur, G.; Stahl, M.; Walkowiak, M.; Winterfeldt, E. Chem. Ber. 1976,109, 3817. (203) Also see: (a) Ziegler, F. E.; Sweeny, J. G. Tetrahedron Lett. 1969,1097. (b) Uskokovic, M. R..; Lewis, R. L.; Partridge, J. J.: DesDreaux. C. W.: Pruess. D. L. J . Am. Chem. SOC. 1979. 101, 6742. ' (204) For other examples of {5,6)-rearrangement,see: (a) Church, R. F.; Ireland, R. E. J. Org. Chem. 1963,28,17. (b) Tang, C.; 1972,94,8615. (c) Buchi, Rapoport, H. J . Am. Chem. SOC. G.; White, J. D. Ibrd. 1964,86, 2884. (d) Burke, S. D.; Pacofsky, G. J. Tetrahedron Lett. 1986,27, 445. (205) (a) Gibson, M. I.; Gibson, F. Biochem. Biophys. Acta 1962, 65, 160. (b) Gibson, F.; Jackman, L. M. Nature (London) 1963,198, 388. (c) Edwards, J. M.; Jackman, L. M. Aust. J. Chem. 1965,18, 1227. (206) Andrews, P. R.; Haddon, R. C. Aust. J . Chem. 1979,32,1921. (207) (a) McGowan, D. A.; Berchtold, G. A. J . Am. Chem. SOC. (208) (209) (210) (211) . , (212) 1982,104,1153. (b) Hoare, J. H.; Policaatro, P. P.; Berchtold, G. A. J. Am. Chem. 1983, 105, 6264. (c) Hoare, J. H.; Berchtold, G. A. J. Am. Chem. SOC. 1984, 106, 2700. (a) Sogo, S. G.; Widlanski, T. S.; Hoare, J. H.; Grimshaw, C. E.; Berchtold, G. A.; Knowles, J. R. J . Am. Chem. SOC. 1984, 106, 2701. (b) Copley, S. D.; Knowles, J. R. J. Am. Chem. SOC.1985, 107, 5306. (a) Andrews, P. R.; Smith, G. D.; Young, I. G. Biochemistry 1973,12,3492. (b) Gorisch, H. Biochemistry 1978,17,3700. (a) Gajewski, J. J.; Jurayj, J.; Kimbrou h, D. R.; Gande, M. E.; Ganem, B.; Carpenter, b. K. J. Am. !!hem. SOC. 1987,109, 1170. (b) Copley, S. D.; Knowles, J. R. J . Am. Chem. SOC. 1987,109, 5008. (c) Guilford, W. J.; Copley, S. D.; Knowles, J. R. J. Am. Chem. SOC.1987,109,5013. (a) Bartlett. P. A.: Johnson. C. R. J . Am. Chem. SOC.1985. ., 107,7792. (b) Bartlett, P. A.; Nakagawa, Y.; Johnson, C. R.: Reich, s. H.; Luis, A. J. Org. Chem. 1988, 53, 3195. Also see: Delany, J. J. III; Berchtold, G. A. J. Org. Chem. 1988,53, 3262. (213) Jackson, D. Y.; Jacobs, J. W.; Sugasawara, R.; Reich, S. H.; Bartlett. P. A,: Schultz. P. G. J. Am. Chem. SOC. 1988. 110. 4841.

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Harvard - CHEM - 215
Harvard - CHEM - 215
MyersGeneral References:Organolithium ReagentsHandling of Organolithium Reagents: H2OChem 215Organometallics in Organic Synthesis, Schlosser, M., Ed.; Wiley: New York, 1994. Organolithium Methods, Wakefield, B. J.; Academic Press: London, 198
Harvard - CHEM - 215
MyersRLi + R'X RX + R'LiLithium-Halogen ExchangeH Br H OEtChem 2151.1 eq n-BuLi Et2O, 80 CH Li H OEt Lithium-halogen exchange reactions are kinetically controlled. The position of the equilibrium varies with the stabilities of the carbanion
Harvard - CHEM - 215
MyersReview:Magnesium-Halogen ExchangeChem 215Knochel, P.; Dohle, W.; Gommermann, N.; Kneisel, F. F.; Kopp, F.; Korn, T.; Sapountzis, I.; Ahn Vu, V. Angew. Chem., Int. Ed. Engl. 2003, 42, 4302. General References on the Preparation and Reactio
Harvard - PHYSICS - 15a
Physics 15aMini-ExamLecture # 3Name:.it what angle should a projectile 1)c fired so t h a t tlic iilasilrll~i~l height eql~illsthe horizontal distancr tra~rcleci?Feedback: Lect,ures are (circle appropriate aiis~ver)too fastnhout riglit
Harvard - PHYSICS - 15a
Physics 15aMini-ExamLecture #4Name:TF:A bead sits at the top of a frictionless hoop of radius 0.5rn. It is given a tiny push sothat, it slides down arid around the lioop. The ~elocities four points arc shown. Draw at (fairly accurately) tl
Harvard - PHYSICS - 15a
Physics 15aMini-ExamLecture #5Name:TF:Considcr the At~vood'srnachinc 5llon.11 ( n it11 nliisslcss rope alld pullevs). \'list ale tlie accelerations of m l and 7n2?C o&amp;N(L+~o~%ri iO(M ySap t)\Pf l(rCflM*, Pm \ by 1 ,z - &amp; &amp; '
Harvard - PHYSICS - 15a
Physics 15aMini-ExamLecture #6Name:TF:A11 airplane flies at speed I: in a hori~olitalcircle of' radius R. .At what aiiglc should thc plant be banked so that yo11 don't feel like yo11 are getting flulig t o thc side in yo111 scat?rn\gklre
Harvard - PHYSICS - 15a
Physics 15aMini-ExamLecture #7Name:TF:a4 kg person stands at rest on a mot,ionless 120 kg boat. Slie then walks a t 2 m/s with 60respcct t,o the boat. mTha,tis the resulting speed of the boat,?The'r,:halpis W+Feedback:too fast
Colorado - MATH - 3130
ISM: Linear AlgebraSection 1.1Chapter 1 1.11. x + 2y x + 2y = 1 -y 2x + 3y = 1 -2 1st equation x + 2y = 1 -2 2nd equation x y=1 y 2. 4x + 3y 7x + 5y3 x + 4y 1 -4y 3 x + 4y = 2 4 =3 7x + 5y=1 = -1 (-1)= -1 , so that (x, y) = (-1, 1). =
Colorado - MATH - 3130
Chapter 2ISM: Linear AlgebraChapter 2 2.11. Not a linear transformation, 0 2 2. Linear, with matrix 0 0 1 0 9 3 -3 1 2 -9 4. A = 4 -9 -2 5 1 5 5. By Fact 2.1.2, the three columns of the 2 3 matrix A are T (e1 ), T (e2 ), and T (e3 ), so
Colorado - MATH - 3130
ISM: Linear AlgebraSection 3.1Chapter 3 3.11. Find all x such that Ax = 0: . 1 2. 0 . . . 0 3 4. - . 1 0. 0 , so that x = x = 0. . 1 2 . . 0 0 1.ker(A) = {0}. 2. Find all x such that Ax = 0: . . 3. 2 3. 0 - 1 2 . 0 , so that . . . 6 9. 0 .
Colorado - MATH - 3130
ISM: Linear AlgebraSection 4.1Chapter 4 4.11. Not a subspace since it does not contain the neutral element, that is, the function f (t) = 0, for all t. 2. This subset V is a subspace of P2 : The neutral element f (t) = 0 (for all t) is in V .
Colorado - MATH - 3130
Chapter 5ISM: Linear AlgebraChapter 5 5.1 72 + 112 = 49 + 121 = 170 13.04 2. v = 22 + 32 + 42 = 4 + 9 + 16 = 29 5.39 3. v = 22 + 32 + 42 + 52 = 4 + 9 + 16 + 25 = 54 7.35 1. v = 4. = arccos 5. = arccos 6. = arccosuv u v uv u v uv u
Colorado - MATH - 3130
Chapter 6ISM: Linear AlgebraChapter 6 6.11. Fails to be invertible; since det 2. Invertible; since det 3. Invertible; since det 1 2 = 6 - 6 = 0. 3 62 3 = 10 - 12 = -2. 4 5 3 5 = 33 - 35 = -2. 7 11 1 4 = 8 - 8 = 0. 2 8 4. Fails to be invertib
Colorado - MATH - 3130
Chapter 7ISM: Linear AlgebraChapter 7 7.11. If v is an eigenvector of A, then Av = v. Hence A3 v = A2 (Av) = A2 (v) = A(Av) = A(Av) = A(2 v) = 2 Av = 3 v, so v is an eigenvector of A3 with eigenvalue 3 .1 2. We know Av = v so v = A-1 Av = A-1 v
Colorado - MATH - 3130
ISM: Linear AlgebraSection 8.1Chapter 8 8.11. e1 , e2 is an orthonormal eigenbasis. 2. 3.1 21 1 , 12 1 -1is an orthonormal eigenbasis.2 -1 , 15 is an orthonormal eigenbasis. 1 2 1 1 1 1 1 1 4. 3 1 , 2 -1 , 6 1 is an orthono
Colorado - MATH - 3130
Chapter 9ISM: Linear AlgebraChapter 9 9.11. x(t) = 7e5t , by Fact 9.1.1. 2. x(t) = -e e-0.71t = -e1-0.71t , by Fact 9.1.1. 3. P (t) = 7e0.03t , by Fact 9.1.1. 4. This is just an antiderivative problem: y(t) = 0.8 t2 + C = 0.4t2 + C, and C = -0.
UCLA - MATH - 33B
UCLA - MATH - 33B
Math 33b, Quiz 5ac, February 26, 2008 Name: UCLA ID:1. Find the solution with initial conditions y(0) = 0, y (0) = 0 to the differential equation y +y = 1, 0t&lt;3 -2(t-3) e , t 3.Solution. Observe that the function f (t) on the right-hand-side of
UCLA - MATH - 33B
Math 33b, Quiz 7ac, March 11, 2008 Name: UCLA ID:Consider the system of differential equations x (t) = Mx, where M is each of the matrices below. For each system of differential equations, a sample solution in the x-y plane is plotted below. Below
UCLA - MATH - 33B
Math 33b, Quiz 6ac, March 4, 2008 Name: UCLA ID: 2 , to the system of differential 31. Find the solution, with initial condition x(0) = equations dx = dt -1 -1 x. 4 -5-1 - -1 , 4 -5 - which is 2 + 6 + 9. The roots are = -3, -3, so there is onl
UCLA - MATH - 33B
Math 33b, Quiz 6bd, March 6, 2008 Name: UCLA ID: 2 , to the system of differential 41. Find the solution, with initial condition x(0) = equations dx = dt 2 1 x. -5 42- 1 , which is -5 4 - 2 - 6 + 13. The roots of this polynomial are 3 2i, so th
UCLA - MATH - 33B
Math 33b, Quiz 7bd, March 12, 2008 Name: UCLA ID:Consider the system of differential equations x (t) = Mx, where M is each of the matrices below. For each system of differential equations, a sample solution in the x-y plane is plotted below. Below
Colorado - APPM - 2350
APPM 2350FINAL EXAMFALL 2007INSTRUCTIONS: Electronic devices, books, and crib sheets are not permitted. Write your (1) name, (2) instructor's name, and (3) recitation number on the front of your bluebook. Work all problems. Show your work clear
Colorado - APPM - 2350
APPM 2350EXAM 1FALL 2007INSTRUCTIONS: Computers, calculators, books, and crib sheets are not permitted. Write your (1) name, (2) instructor's name, and (3) lecture number (010, 020 or 030) on the front of your bluebook. Work all problems. Start
Colorado - APPM - 2350
APPM 2350EXAM 2FALL 2007INSTRUCTIONS: Computers, calculators, books, and crib sheets are not permitted. Write your (1) name, (2) instructor's name, and (3) recitation number on the front of your bluebook. Work all problems. Show your work clear
Colorado - APPM - 2350
APPM 2350EXAM 3FALL 2007INSTRUCTIONS: Computers, calculators, books, and crib sheets are not permitted. Write your (1) name, (2) instructor's name, and (3) recitation number on the front of your bluebook. Work all problems. Show your work clear
Colorado - APPM - 2350
APPM 2350Exam #2Summer 2007Be sure to include your name and a grading table on the front of your blue book. You must work all of the problems on this exam. Show ALL of your work and BOX IN YOUR FINAL ANSWERS. A correct answer with no relevant w
UCSB - GEOG - 5
Global 2Introduction to Global Studies: Socioeconomic and Political ProcessesInstructor: Francesca DegiuliWho We AreProfessor Francesca DegiuliOffice Hours: Wednesday 3:30 to 5:30 in Girvetz 2306 E-mail: degiuli@global.ucsb.eduWho We AreTe
Washington State - MATH - 315
- CHAPTER 10. -Chapter TenSection 10.1 1. The general solution of the ODE is CaBb oe -&quot; -9= B -# =38 B Imposing the first boundary condition, it is necessary that -&quot; oe ! . Therefore CaBb oe -# =38 B . Taking its derivative, C w aBb oe -# -9= B
Washington State - MATH - 315
- CHAPTER 5. -Chapter FiveSection 5.1 1. Apply the ratio test : lim aB $b8&quot; k a B $b 8 kHence the series converges absolutely for kB $k &quot; . The radius of convergence is 3 oe &quot; . The series diverges for B oe # and B oe % , since the n-th ter
Washington State - MATH - 315
Math 219, Homework 4Due date: 30.12.2005, Wednesday Suppose that K &gt; 0, and f (t) is defined as 1 0 if 4n t &lt; 4n + 1 otherwisef (t) =where n runs through the set of integers. (a) Determine the Fourier series for f (t). (b) Consider the differen
Washington State - MATH - 315
Math 219, Homework 3Due date: 9.12.2005, Friday 1. Consider the initial value problem d2 x dx + + x = u4 (t), dt2 dt y(0) = y (0) = 0(a) Solve this initial value problem using the Laplace transform. dx dt with respect to t (You can use the functio
Washington State - MATH - 315
- CHAPTER 7. -Chapter SevenSection 7.1 1. Introduce the variables B&quot; oe ? and B# oe ? w . It follows that B&quot;w oe B# and B#w oe ? ww oe #? !&amp; ? w . In terms of the new variables, we obtain the system of two first order ODEs B&quot;w oe B# B#w oe #B&quot;
Washington State - MATH - 315
- CHAPTER 8. -Chapter EightSection 8.1 2. The Euler formula for this problem is C8&quot; oe C8 2^&amp; &gt;8 $C8 , C8&quot; oe C8 &amp;82# $2 C8 ,in which &gt;8 oe &gt;! 82 Since &gt;! oe ! , we can also writea+b. Euler method with 2 oe !&amp; &gt;8 C8 8oe# !&quot; &quot;&amp;*)! 8oe% !
Washington State - MATH - 315
- CHAPTER 9. -Chapter NineSection 9.1 2a+b Setting x oe 0 /&lt;&gt; results in the algebraic equations OE &amp;&lt; $For a nonzero solution, we must have ./&gt;aA &lt; Ib oe &lt;# ' &lt; ) oe ! . The roots of the characteristic equation are &lt;&quot; oe # and &lt;# oe % . For
Washington State - MATH - 315
- CHAPTER 11. -Chapter ElevenSection 11.1 1. Since the right hand sides of the ODE and the boundary conditions are all zero, the boundary value problem is homogeneous. 3. The right hand side of the ODE is nonzero. Therefore the boundary value prob
Washington State - MATH - 315
- CHAPTER 1. -Chapter OneSection 1.1 1.For C &quot;&amp; , the slopes are negative, and hence the solutions decrease. For C &quot;&amp; , the slopes are positive, and hence the solutions increase. The equilibrium solution appears to be Ca&gt;b oe &quot;&amp; , to which all
Washington State - MATH - 315
- CHAPTER 3. -Chapter ThreeSection 3.1 1. Let C oe /&lt;&gt; , so that C w oe &lt; /&lt;&gt; and C ww oe &lt; /&lt;&gt; . Direct substitution into the differential equation yields a&lt;# #&lt; $b/&lt;&gt; oe ! . Canceling the exponential, the characteristic equation is &lt;# #&lt; $ o
Washington State - MATH - 315
- CHAPTER 2. -Chapter TwoSection 2.1 1a+ba,b Based on the direction field, all solutions seem to converge to a specific increasing function. a- b The integrating factor is .a&gt;b oe /$&gt; , and hence Ca&gt;b oe &gt;$ &quot;* /#&gt; - /$&gt; It follows that all s
Washington State - MATH - 315
- CHAPTER 4. -Chapter FourSection 4.1 1. The differential equation is in standard form. Its coefficients, as well as the function 1a&gt;b oe &gt; , are continuous everywhere. Hence solutions are valid on the entire real line. 3. Writing the equation in
Washington State - MATH - 315
- CHAPTER 6. -Chapter SixSection 6.1 3.The function 0 a&gt;b is continuous. 4.The function 0 a&gt;b has a jump discontinuity at &gt; oe &quot; . 7. Integration is a linear operation. It follows that (E !-9=2 ,&gt; /=&gt; .&gt; oe&quot; E ,&gt; =&gt; &quot; E ,&gt; =&gt; ( / / .&gt;
Washington State - MATH - 315
Math 219, Homework 2Due date: 23.11.2005, Wednesday This homework concerns two (fictitious) design problems about the solar car &quot;MES e&quot; of the METU Robotics Society, which won the Formula-G trophy in September 2005. Just for the purposes of this hom
Cal Poly - ME - 341
1Problem 1.22Problem 1.33Problem 1.445Problem 1.6Make a guess at the order of magnitude of the mass (e.g., 0.01, 0.1, 1.0, 10, 100, or 1000 lbm or kg) of standard air that is in a room 10 ft by 10 ft by 8 ft, and then compute this ma
Cal Poly - ME - 341
Problem 2.1For the velocity fields given below, determine: (a) whether the flow field is one-, two-, or three-dimensional, and why. (b) whether the flow is steady or unsteady, and why. (The quantities a and b are constants.)Solution (1) V = V (
Cal Poly - ME - 341
Problem 3.1D = 0.75 m. The gas is at an absolute pressure of 25 MPa and a temperature of 25C. What is the mass in the tank? If the maximum allowable wall stress in the tank is 210 MPa, find the minimum theoretical wall thickness of the tank. Given:
Cal Poly - ME - 341
Problem 4.2A mass of 3 kg falls freely a distance of 5 m before contacting a spring attached to the ground. If the spring stiffness is 400 N/m, what is the maximum spring compression?Given: Data on mass and spring Find: Maximum spring compression
Cal Poly - ME - 341
Problem 5.3Problem 5.4Problem 5.6Problem 5.9The x component of velocity in a steady incompressible flow field in the xy plane is u = Ax/(x2 + y2), where A = 10 m2/s, and x and y are measured in meters. Find the simplest y component of velocity
Cal Poly - ME - 341
Problem 7.4Problem 7.5Nondimensionalizing the velocity, pressure, spatial measures, and time:u* =u Vp* =p px* =x Lr* =r Lt* = tV LHenceL t* Vu =V u*p = p p *x = Lx*r = Dr*t=Substituting into the governing equati
Cal Poly - ME - 341
Problem 8.1Problem 8.2Given: Data on air flow in duct Find: Volume flow rate for turbulence; entrance length Solution The given data is D = 0.25 m2 -5 mFrom Fig. A.3 = 1.46 10sThe governing equations are Re = V D Recrit = 2300 Q = 4
Cal Poly - ME - 341
Problem 9.1 (In Excel)Solution Governing equations: The critical Reynolds number for transition to turbulence is Re crit = VL crit/ = 500000The critical length is then L crit = 500000/V Tabulated or graphical data: = = 3.79E-07 0.00234 (Table A.
Cal Poly - ME - 341
Problem 11.2Given: Data on an air compressor Find: Whether or not the vendor claim is feasible Solution The data provided, or available in the Appendices, is: p1 = 101 kPa p2 = ( 650 + 101) kPa J cp = 1004 kg K T1 = ( 20 + 273) K T2 = ( 285 + 273
Washington State - BIO - 101
Bio 101/102 Spring 2008, Practice Exam I these are the types of questions I ask. The exam will be 50 multiple choice questions. I will use a couple of exact questions asked below on the actual exam. 1. Which of the following is a scientific conclusi
Washington State - COMM - 101
Understand the Models of Media as discussed in class and in Chapter 1 of Baran as well as Grossberg, et al., Chapter 1. Characteristics of Oral, Writing, Printing, and Electronic Cultures, and how each changed the nature of communication and society
Columbia - MATH - V1202
Practice Questions for the 1st MidtermThe following consists of practice questions to help you prepare for the midterm. They are similar in style and difficulty to what you can expect to see on the actual midterm. The actual midterm will be shorter,
Columbia - MATH - V1202
Solutions to the 1st Practice Midterm1. Evaluate the following integrals. (a)1 0 021-x2ex2+y 2dy dxWe can't just proceed by taking the anti-derivative of ey , because it doesn't have an antiderivative given by elementary functions. I
Columbia - MATH - V1202
Solutions to the 1st Midterm1. Consider the following integral1 0 1-2x -1 0 1-y 2f (x, y, z) dz dy dx. (a) Rewrite this integral so that the inner-most integral is with respect to z, the middle integral is with respect to x, and the outer integra
Columbia - CHEM - C3443
Columbia - CHEM - C3443
&quot;Name:UtA\Jpage I Chernisuy C3zl43 Fall 200? Midterm #3 75 minutes November 2007 14.you have a choiceof which problem(s)to answer. &quot; .- ' InstructioDs: (1) For somequestions, For these,cross out (X) answersyou do not want counted, (2) Notice
Columbia - CHEM - C3443