Open chain transform

The open-chain transform should be used when dealing with the overall size of the chain and, in dynamics, when separate consideration of the first, most collective modes of motion is required. In the following, the more expedient periodic-chain transform will generally be adopted unless specified otherwise. 

A more accurate evaluation of the first modes with the open-chain transform [83] leads to a coefiicient 0.467 instead of 0.425.] The correlation function B k, t) cannot be easily evaluated in closed form for the Zimm limit. However, it may be seen from Eqs. (3.1.18) that for sufficiently short times, B(k, t)/Ai is a universal function of the two variables k/N and t/r ax- In particular, the time dependence of the self-correlation function B(0, t) is again a simple power law if t is comprised between the two extremal relaxation times. We get, from (3.1.18) and (3.2.12) [90],... 

In a similar way Table II summarizes how the phase changes upon interconversion among the isomers. Inspection of the two tables shows that for any loop containing three of the possible isomers (open chain and cyclobutene ones), the phase either does not change, or changes twice. Thus, there cannot be a conical intersection inside any of these loops in other words, photochemical transformations between these species only cannot occur via a conical intersection, regardless of the nature of the excited state. 

In stereoselective antitheses of chiral open-chain molecules transformations into cyclic precursors should be tried. The erythro-configurated acetylenic alcohol given below, for example, is disconnected into an acetylene monoanion and a symmetrical oxirane (M. A. Adams, 1979). Since nucleophilic substitution occurs with inversion of configuration this oxirane must be trens-conilgurated its precursor is commercially available trans-2-butene. 

It was noted early by Smid and his coworkers that open-chained polyethylene glycol type compounds bind alkali metals much as the crowns do, but with considerably lower binding constants. This suggested that such materials could be substituted for crown ethers in phase transfer catalytic reactions where a larger amount of the more economical material could effect the transformation just as effectively as more expensive cyclic ethers. Knbchel and coworkers demonstrated the application of open-chained crown ether equivalents in 1975 . Recently, a number of applications have been published in which simple polyethylene glycols are substituted for crowns . These include nucleophilic substitution reactions, as well as solubilization of arenediazonium cations . Glymes have also been bound into polymer backbones for use as catalysts " " . 

According to Quinkert, photoexcited cyclic ketones may be transformed to open-chain unsaturated carboxylic acids in the presence of molecular oxygen. This reaction may compete efficiently with a-cleavage and secondary transformations thereof. Thus, both stereo iso meric 17-ketones (109) and (110) yield as much as 20% of the unsaturated acid (111) when irradiated in benzene under a stream of oxygen. This photolytic autoxidation has been used notably for partial syntheses of naturally occurring unsaturated 3,4-seco-acids from 3-oxo triterpenes (for references, see ref. 72). 

Based on Watanabe s intermolecular hydroacylation of olefins with aldehydes,348 Kondo and Misudo developed the first ruthenium-catalyzed hydroacylation of 1,3-dienes with aldehydes (Scheme 71). Usually, palladium-mediated hydroacylations of 1,3-dienes with aldehydes give tetrahydropyran and/or open-chain homoallylic alcohol derivatives.350 However, in the present ruthenium-catalyzed transformations, the corresponding /3,7-unsaturated... 

A disputable problem of the cationic oxa-Cope rearrangement (equation 258) is whether open-chain oxonium ions are formed during transformations of 4-vmyl-l,3-dioxoianes 604 into acyltetrahydrofurans 605 (equation 259) as well as of methyl... 

Degenerate ring transformations have also been observed in reactions of 6-ethoxy-4-oxopyrimidinium salts (25, R = H, CH3, C6H5) with liquid ammonia (77RTC68). Besides open-chain compounds, 2-R-l-ethyl-4-(ethylamino)pyrimidin-6(l//)-one is formed. The presence of the ethyl-... 

This degenerate transformation of 30 into 30 can be explained when the incorporation of the label into the pyrimidine ring occurs by ring closure of the open-chain species, which is formed by ring opening of the covalent hydrazino adduct, probably at position 6 (Scheme III.18). 

The reaction of l,4-diaryl-2-methylthiopyrimidinium iodide (39) with hydrazine did not lead to the corresponding 2-hydrazino compound, as expected, but to the rearranged l-amino-2-arylaminopyrimidinium salt (40) (90JHC1441). This transformation also occurs via an Sn(ANRORC) process, involving the open-chain intermediate 41 (Scheme III.22). It cannot... 

In the case of thiazoline-2(3//)-thiones, the mesoionic thiazolo[2,3-h][l,3,4]thiadiazoles are obtained by two different routes (Scheme 65). On the one hand, thione 166 reacts with isothiocyanate via intermediate 167 and with a second equivalent isothiocyanate to afford the mesoionic 168 on the other hand, in the presence of isocyanate, the thione preferentially dimerizes 167 with the open-chain carbodiimide 169 to give the mesoionic 170. Addition of acid with removal of an amine group converts 170 into the symmetric heteroaromatic amine (171) (88CB1495 92T1285). The related transformation of an imidazoline into 1,3,4-thiadiazoles has also been described (90T4353). 

In the second group of ring-chain tautomeric interconversions, an open-chain system is transformed into a cyclic system through the intramolecular reversible addition of a functional group to a polar multiple bond lA IB 2A 2B 3A 3B and 4A 4B. The book (I) and this article deal with... 

Trichloroacetylbenzoic acid reacts with thionyl chloride to produce a mixture of both chloride isomers. However, the open-chain isomer readily transforms into the cyclic form, which was the only isomer isolated from the mixture in the solid state. The presence of the open-chain isomer in the reaction product mixture, which is generally uncharacteristic for 2-acylbenzoyl chlorides, may be caused by the strong -I effect of the trichlo-romethyl group which decreases the nucleophilicity of the ketone oxygen atom (88MI4). 

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