Equilibrium time evolutions and BBGKY hierarchy equations of large classical systems

Summary We show the existence of a time evolution {P _t ; t of a locally perturbed equilibrium state P of infinitely many particles in {suv}, v1, evolving under the action of the infinite Newtonian dynamics associated to the same smooth, finite range pair potential as the equilibrium state itself. Moreover, it is shown that {P _t ; t solves the weak BBGKY hierarchy equations. The treatment of this problem will be done in the general setting of so called ( ) point processes developed in [11, 10] and [4] and will require the method of moments.     

Säurekatalysierte Dienon-Phenol-Umlagerungen von 6-Propargyl-6-methyl-cyclohexa-2,4-dien-1-onen; ladungskontrollierte,aromatische [1s, 2s]- und [3s, 4s]-sigmatropische Reaktionen

The acid catalysed dienone-phenol rearrangement of methyl substituted o-propargyl-cyclohexadienones (scheme 3) was investigated. The rearrangements were carried out in acetic anhydride containing about 1⁰/₀₀ sulfuric acid. Under these conditions acetoxy benzenium ions are formed as intermediates. These then undergo charge-controlled [3s, 4s]- and [1s, 2s]-sigmatropic rearrangements. Thus, the [3s, 4s]-process leads to the formation of the corresponding allenyl-phenol acetates ( 19 , 21 , 23 , 25 , 28 , 30 ) whereas the [1s, 2s]-process yields propargyl-phenol acetates ( 20 , 22 , 24 , 26 , 29 ), respectively (cf. scheme 4).     

Umwandlung von 6-Methylen-tricyclo[3.2.1.02,7]oct-3-en-8-onen in Polymethyltropyliumsalze

When dissolved in trifluoroacetic or fluorosulfonic acid, 6-methylene-tricyclo[3.2.1.0^2,7]oct-3-ene-8-one derivatives of type 2 (;scheme 1); give polymethyltropylium salts in moderate to good yields by CO-extrusion. These tropylium salts can be isolated pure as hexachloroplatinates. Thus the tricyclic compound 6 gives 1,2,4-trimethyltropylium trifluoroacetate 19 in trifluoroacetic acid (;scheme 3);. This salt in CDCl₃ is in equilibrium with its covalent cycloheptatriene (;tropilidene); form 20 , the ratio of the two forms being 1.5–2.1/1. The tropylium salt 19 is reduced by lithium aluminium hydride to a mixture of 1,2,4-trimethylcycloheptatrienes, isomeric with respect to the double bonds, which on hydride abstraction with trityl-tetrafluoroborate gives again the 1,2,4-trimethyltropylium salt 19 (;scheme 3);. From the trimethyl-substituted tricyclic compounds 7 and 8 , in trifluoroacetic acid, are obtained respectively the 1,2,4,6- and 1,2,3,4-tetramethyltropylium ions (; 22 and 24 ); (;schemes 4 and 5);. In this way the 1,2,3,5,6-pentamethyl-tropylium ion (; 26 ); was obtained from 9 (;scheme 6);. With the higher substituted tropylium trifluoroacetates in CDCl₃ the equilibrium tropylium trifluoroacetate ? trifluoroacetoxycycloheptatrienes lies well to the left. The hexamethylated tricyclic compound 10 gives a small quantity of heptamethyltropylium trifluoroacetate (; 27 ); and as the main product the C(;3);-protonated species 28 (;scheme 7);, which when treated with aqueous sodium hydrogencarbonate yielded unchanged educt 10 . - The heptamethyltropylium ion (; 27 ); was, apart from polymeric species, the only product from the treatment of starting material 10 with fluorosulfonic acid (;50%);; its salts have as yet not been isolated in their pure form, however. The mechanism for the rearrangement of the tricyclic compounds of type 2 into tropylium salts is presented for compound 6 in scheme 8: The first step is the protonation at C(;9);. Ring opening of the cyclopropane of the tertiary carbenium ion 29 gives the allylic ion 30 , which then yields the aromatic tropylium salt 19 by carbon monoxide extrusion in a linear cheletropic reaction. The smooth conversion with strong acids of the easily accessible tricyclic compounds of type 2 to the corresponding polymethylated tropylium salts, presents a new and useful method for the synthesis of the latter compounds.     

Absolute Konfiguration von Picrocrocin

By correlation with (?)-3-methoxy-β-jonone picrocrocin has been shown to have R-configuration.     

Die elektrische Zerstäubung von Silicium in Aceton

Zusammenfassung Die Bildung kolloider L?sungen durch Hochspannungskurzschlu\funken zwischen kleinen Siliciumstücken in Aceton unter sauerstoffreiem Stickstoff wird untersucht: sowohl die Ver?nderungen der Siliciumoberfl?chen durch das kurzzeitige Schmelzen und Verdampfen des Siliciums, als auch die chemischen Eigenschaften der in L?sung befindlichen Kolloide. Das Interesse war nicht, wie bei der Svedbergschen Kolloidzerst?ubung, auf die Methode zur Herstellung kolloider Metalle, in diesem Falle kolloiden Siliciums, gerichtet, sondern auf die chemische Umsetzung des Siliciums unter den gegebenen extremen Temperaturbedingungen mit dem Aceton zu kolloiden Siliciumverbindungen. Durch fraktioniertes Zentrifugieren und Eindampfen der Restl?sung ist die kolloide L?sung der Siliciumverbindungen in 3 Anteile zerlegt worden: Ein braunes Pulver, schwarze Flocken und ein dem Silikagel ?hnliches Gel. Die 3 Substanzen enthielten alle Si, O, C und H in Form einer anorganischen Si-O-haltigen Komponente und einer unges?ttigten Kohlenwasserstoffkomponente. Je gr?\er der Anteil der organischen Komponente ist, desto kleiner und l?slicher sind die Kolloidteilchen in Aceton. Die Struktur der Gelteilchen ist sehr labil und geht unter Verglimmen in eine stabilere aber nicht kristalline über. Dieser Vorgang findet beim Erw?rmen, auch unter vollkommenem Ausschlu\ von Sauerstoff, statt. Das Gel l?st sich in Laugen und flockt wieder mit S?uren. Das ganze Verhalten, einschlie\lich der analytischen Befunde, l?\t darauf schlie\en, da\ die hier erhaltene kolloide L?sung, aber auch das Svedbergsche Siliciumsol nicht kolloides elementares Silicium enthalten, sondern Kolloidteilchen, die silikonharzartigen Charakter besitzen. Hans Kautsky Jun. Diss. (Marburg 1954). Mein Vater, Prof. Dr. Hans Kautsky, regte mich zu dieser Arbeit an und gab mir wertvolle Ratschl?ge; ich danke ihm herzlich dafür. Herrn Dr. E. Hellner vom mineralogischen Institut der Philipps-Universit?t Marburg/Lahn, der die R?ntgenuntersuchungen unserer Substanzen vorgenommen hat, sei an dieser Stelle auch vielmals gedankt. Zu besonderem Dank bin ich der Deutschen Forschungsgemeinschaft für die apparative Unterstützung der Arbeit verpflichtet, der Firma Rosenthal-Isolatoren Gesellschaft m. b. H., Selb, für die kostenlose überlassung der Kondensatorbatterie.     

The molecular and crystal structures of two diastereomeric 3,4-dihydropyrromethenones

The molecular and crystal structures of the two racemic diastereomeric 3,4-dihydropyrromethenone derivatives1 and2 of configurations (Z) and (E) were determined at 93 K (1, 2) and at room temperature (1). From an analysis of the crystallographically observed temperature coefficients a pseudorotation flexibility of the pyrrolidinone ring in the crystal is deduced. In both compounds a nearly orthogonal arrangement between the two heterocyclic ring systems is observed, which is ascribed to the steric bulk of the substituents in positions 1 and 3 of the pyrrolidinone ring.Herrn Prof.Josef Schurz zum 60. Geburtstag gewidmet.     

Säurekatalysierte Umlagerungen von 1,5-Dimethyl-6-methyliden-tricyclo[3.2.1.02,7]oct-3-en-8endo-olen

Acid Catalysed Rearrangement of 1,5-Dimethyl-6-methyliden-tricyclo[3.2.1.0^2,7]oct-3-en-8endo-ols The tricyclic alcohols 2,3,4 and 6 (Scheme 1) are synthesized by the reaction of the tricyclic ketone 1 with sodiumborohydrid or metalloorganic reagents. Their configuration at C(8) is determined by NMR. in the presence of Eu(fod)₃. The exo-attack of 1 by the nucleophil forming the endo-alcohol is favored, the π-electrons of C(3) = C(4) hindering the endo-attack. On treatment with sulfuric acid in dioxane/water at 25° the tertiary alcohols yield aryl-substituted ketones. 3 gives in 78.5% yield a mixture of the 3-(dimethylphenyl)-2-butanones 12 and 13 , in addition to 16.5% of (2,3,4-trimethylphenyl)-2-propanon ( 14 ) (Scheme 2). The alcohols 4 and 6 yield mixtures of the 2-(dimethylphenyl)-3-pentanones 19 and 20 (72%), and 2-(dimethylphenyl)-propiophenones 21 and 22 (68%), respectively (Scheme 2). In the case of the secondary alcohol 2 mainly products derived from hydration at the C(6), C(9) double bond are formed, namely the mixture of diols 23 and 24 (21%), and the mixture of the isomeric 2-(dimethylphenyl)propanals 25, 26 and 27 (3%) (Scheme 3). - The structures of 12–14, 19/20, 21/22, 23/24 and 25/26/27 were established by spectroscopic data. In the case of 12 and 13 the degradation of their mixture to the known 1-(dimethylphenyl)ethanols 17/18 confirmed the assignment. - The most probable mechanism for the rearrangement of 3 is shown in Schemes 4 and 5. The reaction proceeds from 3 through a, b and g to 12 and 13; 14 is formed via e, f and i . In the case of 4 and 6 only the reaction analogue to 3 → a → b → g ?12/13 takes place. The isomeric aldehyds 25–27 formed from 2 could have the structures s, t , and v . The former two could be generated in a similar way as 12/13 from 3 , the latter one as shown in Scheme 8.