Three-component formal

Gong, et al. reported a phosphoric acid derivative 258 catalyzed asymmetric three-component formal [4 + 2] cycloaddition reaction of azlactones 257, a,p-unsaturated aldehydes 28, and primary amines 256 to give the 3-amino-3, 4-dihydropyridinones 259 with high enantioselectivities (up to 96% ee), Scheme 3.82 [104],... 

A semiempirical three-component formalism using the same evaluation procedure for T2 and describing the molecular weight dependence with both characteristic breaks can be found in Ref. [35]. Note that the same sort of... 

Allylsilane additions were used in a formal synthesis of roflamycoin [51] (Eq. 24). A one-pot, three-component sequential coupling of bis-allylsilane 138 with 4-acetoxy-l,3-dioxanes 137 and 139 provided the C11-C22 polyol chain (140) in moderate yield. 

Oxidation of the tetrahydroindolizine 338 with sodium chlorite gives the lactam 339, which rapidly lactonizes to give the pyranoindolizine 340 (Equation 122) <2001T8647>, and the one-pot , three-component reaction between the keto ester 235, acrolein, and o-aminophenol (formally analogous to that of Equation 63) gives the benzoxazolo-naphthyridine 341 (Equation 123) <20010L2145>. 

Two examples of three-components coupling reaction are shown in Reactions (7.77) and (7.78) [27,87]. These radical chain reactions proceeded by the addition of an alkyl or vinyl radical onto carbon monoxide, generating an acyl radical intermediate, which, in turn, can further react with electron-deficient olefins to lead, after reduction, to a formal double alkylation of carbon monoxide. These three-components coupling reactions require the generation of four highly disciplined radical species, which have specific functions during the chain reaction. 

In extending this concept to transformations that formally deliver Diels-Alder products, a one-pot three-component Mannich/Michael reaction pathway was developed in which simple cyclic enones, formaldehyde, and aryl amines were treated with catalytic amounts of proline (2) to provide regio-, diastereo-, and enantioselective bicyclic compounds in high yields (Scheme ll.lOb). Multicomponent domino... 

The Lewis acid-catalyzed three-component reaction of dihydropyridines, aldehydes, and />-substituted anilines efficiently yields highly substituted tetrahydroquinolines in a stereoselective manner, through a mechanism believed to be imine formation followed by formal [4-1-2] cycloaddition (Scheme 41). The 1,4-dihydropyridine starting materials were also prepared in situ by the nucleophilic addition of cyanide to pyridinium salts, creating in effect a one-pot four-component reaction <20030L717>. 

Condensations between two three-atom fragments are surprisingly common in this field, and generally lead to thiopyran-2-ones, etc. The reader is referred to (B-79MI22504) for a tabulation of specific examples of the reaction type shown in equation (107). There are even formally three-component condensations known, though naturally they are really stepwise assemblies of the reactants (equations 108 and 109) (76JPR705,70JOC2438). 

Furthermore, a four-component cycloaddition reaction (7]6-thiepine I,l-dioxide)tricarbonylchromium(0) 52 with tethered diynes under photoactivation afforded pentacyclic adducts formally derived from a sequential [671+271]/ [67l+27t]/[2(T+27i] cycloaddition process <1999OL507>. Photocycloaddition of the complex 52 with excess 1,7-octadiyne 66a or 1,8-nonadiyne 66b (C1CH2CH2C1, hv (Pyrex filter)) afforded the pentacyclic triene sulfones 67a and 67b in 45% and 38% yields, respectively (Equation 4). In contrast, 1,6-heptadiyne 66c afforded only the three-component cycloadduct 68 in 56% yield (Equation 5). 

Unsymmetrical ketones can be synthesized by the formal double alkylation of carbon monoxide [21] in which the three-component coupling of alkyl halides, carbon monoxide, and electron-deficient alkenes is carried out using tributyltin hydride as a radical chain mediator (Scheme 6.13) [22], The use of a slower radical mediator such as (TMS)3SiH [23] has subsequently proven to be superior to tribu-... 

Isocyanides, formal divalent carbon functionalities, are ideal candidates for the development of MCRs. Their reaction with carbonyls and imines, through an a-addition process, generates a zwitterionic intermediate, which is then trapped by a nucleophile. The resulting double a-addition adduct is unstable and rapidly undergoes the Mumm rearrangement to afford the final product (Scheme 12.32). The venerable three-component Passerini reaction is the first MCR based on this type of reaction process [116]. It addresses the formation of a-acyloxycarboxamides, which constitute a class of very versatile synthons in organic chemistry. In the present context, this reaction was utilized by Schmidt and collaborators for the elaboration of intermediate 234 [117], a key fragment for the synthesis of the prolyl endopeptidase inhibitor Eurystatin A 231 (Scheme 12.33) [118]. 

Now that we have discussed the geometric interpretation of the rate of strain tensor, we can proceed with a somewhat more formal mathematical presentation. We noted earlier that the (deviatoric) stress tensor t related to the flow and deformation of the fluid. The kinematic quantity that expresses fluid flow is the velocity gradient. Velocity is a vector and in a general flow field each of its three components can change in any of the three... 

The state of strain in a body is fully described by a second-rank tensor, a strain tensor , and the state of stress by a stress tensor, again of second rank. Therefore the relationships between the stress and strain tensors, i.e. the Young modulus or the compliance, are fourth-rank tensors. The relationship between the electric field and electric displacement, i.e. the permittivity, is a second-rank tensor. In general, a vector (formally regarded as a first-rank tensor) has three components, a second-rank tensor has nine components, a third-rank tensor has 27 components and a fourth-rank tensor has 81 components. 

We assume, now, that the three component blend considered in the previous section consists of a copolymer A/B (could be a diblock, triblock, etc, or an alternating copolymer) and a homopolymer C [11-15]. The notation and formalism of the previous section hold but now XAB(Q) + 0 (note that Xab(Q) shows a peak in the scattering function). The partial structure factors become ... 

Consider one of the ternary blend mixtures described in the previous section. Data from sample 3 were taken from room temperature to 160°C and are analyzed [43], using the RPA formalism for a ternary blend. The three components are called A PSD, B PVME, C PSH. Also, temperature dependencies for the two known chi parameters (Xpsd/pvme/vo and Xpsd/psh/vo) were assumed [31, 32] ... 

A three component coupling reaction of A-acetyl-2-azetine, aromatic imines and aromatic amines allows a rapid stereoselective entry to 2,3,4-trisubstituted tetrahydroquinolines, via fused tricyclic azetidines 1 <02CC444>. Fused heterocycles 1 were formed through an aza Diels-Alder reaction between aromatic imines and A-acetyl-2-azetine, which acts as an enamide substrate. This strategy has been used for the formal synthesis of luotonin A <02TL5469>. 

As long ago as 1960, Tarasov et al. [121] presented some examples of the concrete three-component systems for which the existence of the azeotropic composition had already been predicted theoretically. The list of such systems was widened substantially after publication of the important paper [125], where a set of the known tabulated values of 653 pairs of reactivity ratios for a computer search of the possible multicomponent azeotropes was employed. For this aim one should, at first, reveal all the completely characterized multicomponent systems for which the values of reactivity ratios of all monomer pairs are tabulated. This problem can be formalized by reducing it to the search on the graph with 653 lines of a... 

There is a substantial literature on the thermodynamics of three-component systems—water, protein, and second solute. For a review of early work, methods, and theory, with emphasis on sedimentation experiments, see Kuntz and Kauzmann (1974). Timasheff and colleagues (see Lee et ai, 1979, and references cited therein) have developed a beautiful formalism for treating the thermodynamic nonideality of three-component systems in terms of the preferential interaction parameter... 

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