Repetition scheme

To characterize a crystal, one must describe the motif and find the repetition scheme that generates the crystal. There are an unlimited number of different motifs, i.e., represented by atoms, ions, parts of molecules, molecules, or even groups of many molecules, but for the resulting crystals, there are only a limited number of repetition schemes. They are represented by the 230 space groups. The motifs and repetition-schemes in crystals and helices are discussed in Sects. 5.1.1-6. 

The combination of motifs and repetition schemes is the second topic of this section. The space group of the lattice is the scheme that acts on motifs placed into the unit cell and generates the crystal stracture. The space group is determined by X-ray diffraction or, less frequently, by electron or neutron diffraction. Typically one to 18 repeating units of a macromolecule exist within one unit cell, but helices with long translational repeats may place many more repeating units into one unit cell. For example, poly(m-methylstyrene)s with a 2 40/11 helix form a four-chain unit cell with... 

The plasma source implantation system does not use the extraction and acceleration scheme found in traditional mass-analy2ing implanters, but rather the sample to be implanted is placed inside a plasma (Fig. 4). This ion implantation scheme evolved from work on controlled fusion devices. The sample is repetitively pulsed at high negative voltages (around 100 kV) to envelope the surface with a flux of energetic plasma ions. Because the plasma surrounds the sample, and because the ions are accelerated normal to the sample surface, plasma-source implantation occurs over the entire surface, thereby eliminating the need to manipulate nonplanar samples in front of the ion beam. In this article, ion implantation systems that implant all surfaces simultaneously are referred to as omnidirectional systems. 

Finally, Vogtle and his coworkers have prepared a number of cascade molecules which are structurally related to the aforementioned systems. These are repeating ring units of increasingly large cavity size and are prepared by repetitive synthetic procedures. Typically, an amine is cyanoethylated, the nitrile reduced to an amine which may then be further cyanoethylated and reduced or cyclized with a diacid halide. The rather elaborate scheme is illustrated in ref. 61 and examples of the structural type are shown in Table 8.4. 

The outcomes of intramolecular cyclizations of hydroxy vinylepoxides in more complicated systems can be difficult to predict. In a study of the synthesis of the JKLM ring fragment of dguatoxin, epoxide 44 was prepared and subjected to acid-mediated cydization conditions (Scheme 9.24) [114]. Somewhat surprisingly, the expected oxepane 45 was not formed, but instead a mixture of tetrahydropyran 46 and tetrahydrofuran 47 was obtained, both compounds products of attack of the C6 and C5 benzyl ether oxygens, respectively, on the allylic oxirane position (C3). Repetition of the reaction with dimsylpotassium gave a low yield of the desired 45 along with considerable amounts of tetrahydropyran 48. 

When hydrogenolysis of vinylepoxides is used sequentially, it allows for the controlled formation of 1,3-polyols. In the synthesis of the C11-C23 fragment 92 of preswinholide A, hydrogenolysis of ( ) olefin 93 gave the syn isomer 94 (Scheme 9.37) [159]. Methylation, reduction, epoxidation, oxidation, and olefmation of this material then gave vinylepoxide 95, which was subjected to hydrogenolysis to afford 96 in excellent yield. Repetition of this sequence ultimately afforded the desired derivative 94. 

Mt. Wilson Observatory. The UnISIS excimer laser system is deployed on the 2.5 m telescope at Mt. Wilson Observatory (Thompson and Castle, 1992). A schematic of the system layout is shown in Fig. 11. The30W, 351 nm excimer laser is located in the coude room. The laser has a 20 ns pulse length, with a repetition rate of 167 or 333 Hz. The laser light is projected from the 2.5 m mirror and focused at 18 km. A fast gating scheme isolates the focused waist. A NGS is needed to guide a tip-tilt mirror. Even with relatively poor seeing, UnISIS has been able to correct a star to the diffraction limit. 

The mechanism of the orf/to-dibromination of phenol with NBS in the presence of amines is considered as follows. The hydrogen bonding between phenol and N-bromoamine which are generated from the reaction of NBS and amines (ref. 14), is the driving force, and causes the bromination at one o/t/io-position of phenol and regeneration of the amines. A catalytic amount of the amines is enough because of the regeneration of the amines. The repetition of the above process causes one more substitution at the other orf/io-position of 2-bromophenol. In the cases of 2-substituted phenols the orf/io-bromination can occur only once (Scheme 5). 

Statistical and algebraic methods, too, can be classed as either rugged or not they are rugged when algorithms are chosen that on repetition of the experiment do not get derailed by the random analytical error inherent in every measurement,i° 433 is, when similar coefficients are found for the mathematical model, and equivalent conclusions are drawn. Obviously, the choice of the fitted model plays a pivotal role. If a model is to be fitted by means of an iterative algorithm, the initial guess for the coefficients should not be too critical. In a simple calculation a combination of numbers and truncation errors might lead to a division by zero and crash the computer. If the data evaluation scheme is such that errors of this type could occur, the validation plan must make provisions to test this aspect. 

The subsequent chain extension can be accomplished by the pedestrian step-by-step homologation sequence via the acyclic diyne 12 or by a more efficient block-to-block strategy. The step-by-step approach includes protiodesilylation of diyne 12 followed by coupling with the propargyl chloride 9 following the same protocol as for the preparation of 12 from 11 and subsequent repetitions of protiodesilylation and alkylation with chloride 9 to reach stages 16 and 18, respectively (Scheme 3). 

The method that Shavlik developed to carry out the structure generalization is complex, and requires the introduction of an extension to the horn clause deduction scheme to allow the repetitive application of a... 

All reactions of benzotriazole derivatives of the type Bt-CR RbS discussed above are based on electrophilic or nucleophilic substitutions at the ot-carbon, but radical reactions are also possible. Thus, the first report on unsubstituted carbon-centered (benzotriazol-l-yl)methyl radical 841 involves derivatives of (benzotriazol-l-yl)methyl mercaptan. 3 -(Benzotriazol-l-yl)methyl-0-ethyl xanthate 840 is readily prepared in a reaction of l-(chloromethyl)-benzotriazole with commercially available potassium 0-ethyl xanthate. Upon treatment with radical initiators (lauroyl peroxide), the C-S bond is cleaved to generate radical 841 that can be trapped by alkenes to generate new radicals 842. By taking the xanthate moiety from the starting material, radicals 842 are converted to final products 843 with regeneration of radicals 841 allowing repetition of the process (Scheme 134). Maleinimides are also satisfactorily used as radical traps in these reactions <2001H(54)301>. 

The synthesis of the macrocycles 43 (Scheme 9) is an example of repetitive, highly stereoselective Diels-Alder reaction between bis-dienes 41 and bis-dienophiles 42, containing all oxo or methano bridges syn to one another. The consecutive inter- and intramolecular Diels-Alder reactions only succeed at high pressure. Obviously, both reactions are accelerated by pressure. The macrocycles are of interest in supramolecular chemistry (host-guest chemistry) because of their well-defined cavities with different sizes depending on the arene spacer-units. 

If the oxo (or methano) bridges are not exclusively syn to one another in either the bis-dienophiles or bis-dienes, then the pressure-induced repetitive Diels-Alder reactions (proceeding again highly stereoselectively) produce rigid ribbon-type oligomers on a nanometer scale (Scheme 10 entry 1). Bis-diene 45 reacts less stereoselectively than bis-diene 44 and forms with bis-dienophiles such as 46 the ribbon-type oligomers 47... 

SCHEME 9. Repetitive Diels-Alder reactions in the synthesis of macrocycles having cavities of different size93-94... 

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