On cubature formulae with a minimal number of knots

Summary In this paper an approach is outlined to the two-dimensional analogon of the Gaussian quadrature problem. The main results are necessary and sufficient conditions for the existence of cubature formulae which are exact for all polynomials of degree m and which have a minimal number of 1/2k(k+1) knots,k=[m/2]+1. Ifm is odd, similar results are due to I.P. Mysovskikh ([5, 6]) which will be derived in a new way as a special case of the general characterization given here. Furthermore, it will be shown how this characterization can be used to construct minimal formulae of even degree.     

Photolyse von 3-Methyl-2, 1-benzisoxazol (3-Methylanthranil) und 2-Azido-acetophenon in Gegenwart von Schwefelsäure und Benzolderivaten

Photolysis of 3-Methyl-2, 1-benzisoxazole (3-Methylanthranil) and 2-Azido-acetophenone in the Presence of Sulfuric Acid and Benzene Derivatives Irradiation of 3-methylanthranil ( 1 ) in acetonitrile in the presence of sulfuric acid and benzene, toluene, p-xylene, mesitylene or anisole with a mercury high-pressure lamp through a pyrex filter yields beside varying amounts of 2-amino-acetophenone ( 3 ) and 2-amino-5-hydroxy- ( 4a ) and 2-amino-3-hydroxy-acetophenone ( 4b ) the corresponding diphenylamine derivatives 5 (see Table 1). In the case of toluene and anisole mixtures of the corresponding ortho- and para-substituted isomers ( 5b, 5d or 5g, 5i respectively), but no meta-substituted isomers ( 5c or 5h ) are obtained. In addition to these products, the irradiation of 1 in the presence of anisole yields also 2-amino-5-(4′-methoxyphenyl)-acetophenone ( 7 ), 2-amino-3-(4′-methoxyphenyl)-acetophenone ( 8 ) and 2-methoxy-9-methyl-acridine ( 6 ; see Scheme 1). The latter product is also formed thermally by acid catalysis from the diphenylamine derivative 5i . Irradiation of 2-azido-acetophenone ( 2 ) in acetonitrile solution in the presence of sulfuric acid and benzene leads to the formation of 1, 3, 4a, 4b, 5a and 9 (see Table 2). Compounds 3, 4a, 4b and 5a are also obtained after acid catalyzed decomposition of 2 in the presence of benzene. Thus, it is concluded that irradiation of 1 or 2 in the presence of sulfuric acid yields 2-acetyl-phenylnitrenium ions 10 in the singlet ground state which will undergo electrophilic substitution of the aromatic compounds, perhaps via the π-complex 11 (see Scheme 2).     

Photochemische Cycloadditionen von 3-Phenyl-2H-azirinen an Carbonsäurechloride. 35. Mitteilung über Photoreaktionen

Irradiation of 2, 3-diphenyl-2H-azirine ( 1a ) and 1-azido-1-phenyl-propene, the precursor of 2-methyl-3-phenyl-2H-azirine ( 1b ), in benzene, with a high pressure mercury lamp (pyrex filter) in the presence of acid chlorides yields the oxazoles 5a–d (Scheme 2). Photolysis of 2, 2-dimethyl-3-phenyl-2H-azirine ( 1c ) under the same conditions gives after methanolysis the 5-methoxy-2, 2-dimethyl-4-phenyl-3-oxazolines 7a, b, d , while hydrolysis of the reaction mixture leads to the formation of the 1, 2-diketones 8a, c, d (Scheme 4). The suggested reaction path for all these reactions is a 1, 3-dipolar cycloaddition of the photochemically generated benzonitrilemethylides 2 to the carbonyl double bond of the acid chlorides to give the intermediates 4 , followed by either elimination of hydrogen chloride or solvolysis (Schemes 2 and 4). Irradiation of 1c in the presence of acetic acid anhydride leads via the intermediate 9 to the 5-hydroxy-3-oxazoline 10 and the 5-methylidene-3-oxazoline 11 (Scheme 5).     

Thermisches Verhalten von 1,2-Dipropenylbenzolen

1-cis, 2-cis-Dipropenylbenzene (cis, cis- 1 ) isomerises thermally at 215–235° with 1st order kinetics to give trans, cis- 1 and vice versa. At equilibrium 89% trans, cis- and 11% cis, cis- 1 are present. It is shown by thermal rearrangement of cis, cis-2′, 2″-d₂- 1 that the isomerisation is attributable to aromatic [1, 7a]-sigmatropic H-shifts. trans, trans- 1 rearranges thermally at 225–245° to yield 2, 3-dimethyl-1, 2-dihydronaphthalene ( 2 ). The formation of 2 can be visualized by disrotatory ring closure followed by an aromatic [1, 5s]-sigmatropic H-shift. 2 is also formed when, cis, cis- or trans, cis- 1 are heated for 153 h at 225°. Besides 2 a small amount (3%) of 1-ethyl-1, 2-dihydronaphthalene ( 5 ) is formed. The rearrangement of trans, trans- 1 and trans, trans-2′, 2″-d₂- 1 shows a secondary isotope effect k_H/k_D = 0,90.     

Selective mono,bis, and trisiminoformylation of 2,4,6-trialkyl-1,3,5-triazines - unusual enol acylenamine tautomerism of hydroxyalkenyl-1,3,5-triazines

2,4,6-Trialkyl-1,3,5-triazines 1 can selectively be mono, bis or trisiminoformylated by reaction with trismorpholinomethane 2 or chloromethylene iminium salts 3 (Vilsmeier reagents), with each alkyl substituent reacting with only one molecule of the electrophile. The resulting aminoalkenyltriazines 4, 5 and 6 are partially or fully hydrolysed to corresponding formylation products. The latter exist either in enol or in unusual acylenamine tautomeric structures 10, 12 , and 13 , depending on the number of enamine or enol units found in the molecule. Reaction of triazines 1 with chlorobenzylidene iminium salts 16 gives monoiminobenzoylation to enaminotriazines 17 .     

Highly selective palladium catalyzed kinetic resolution and enantioselective substitution of racemic allylic carbonates with sulfur nucleophiles: asymmetric synthesis of allylic sulfides,allylic sulfones,and allylic alcohols

We describe the highly selective palladium catalyzed kinetic resolutions of the racemic cyclic allylic carbonates rac-1 a-c and racemic acyclic allylic carbonates rac-3 aa and rac-3 ba through reaction with tert-butylsulfinate, tolylsulfinate, phenylsulfinate anions and 2-pyrimidinethiol by using N,N'-(1R,2R)-1,2-cyclohexanediylbis[2-(diphenylphosphino)-benzamide] (BPA) as ligand. Selectivities are expressed in yields and ee values of recovered substrate and product and in selectivity factors S. The reaction of the cyclohexenyl carbonate 1 a (>/=99 % ee) with 2-pyrimidinethiol in the presence of BPA was shown to exhibit, under the conditions used, an overall pseudo-zero order kinetics in regard to the allylic substrate. Also described are the highly selective palladium catalyzed asymmetric syntheses of the cyclic and acyclic allylic tert-butylsulfones 2 aa, 2 b, 2 c, 2 d and 4 a-c, respectively, and of the cyclic and acyclic allylic 2-pyrimidyl-, 2-pyridyl-, and 4-chlorophenylsulfides 5 aa, 5 b, 5 ab, 6 aa-ac, 6 ba and 6 bb, respectively, from the corresponding racemic carbonates and sulfinate anions and thiols, respectively, in the presence of BPA. Synthesis of the E-configured allylic sulfides 6 aa, 6 ab, 6 ac and 6 bb was accompanied by the formation of minor amounts of the corresponding Z isomers. The analogous synthesis of allylic tert-butylsulfides from allylic carbonates and tert-butylthiol by using BPA could not be achieved. Reaction of the cyclopentenyl esters rac-1 da and rac-1 db with 2-pyrimidinethiol gave the allylic sulfide 5 c having only a low ee value. Similar results were obtained in the case of the reaction of the cyclohexenyl carbonate rac-1 a and of the acyclic carbonates rac-3 aa and rac-3 ba with 2-pyridinethiol and lead to the formation of the sulfides 5 ab, 6 ab, and 6 bb, respectively. The low ee values may be ascribed to the operating of a "memory effect", that is, both enantiomers of the substrate give the substitution product with different enantioselectivities. However, in the reaction of the racemic carbonate rac-1 a as well as of the highly enriched enantiomers 1 a (>/=99 % ee) and ent-1 a (>/=99 % ee) with 2-pyrimidinethiol the ee values of the substrates and the substitution product remained constant until complete conversion. Similar results were obtained in the reaction of the cyclic carbonates rac-1 a, ent-1 a (>/=99 % ee) and ent-1 c (>/=99 % ee) with lithium tert-butylsulfinate. Thus, in the case of rac-1 a and 2-pyrimidinthiol and tert-butylsulfinate anion as nucleophiles the enantioselectivity of the substitution step is, under the conditions used, independent of the chirality of the substrate; this shows that no "memory effect" is operating in this case. Hydrolysis of the carbonates ent-1 a-c, ent-3 aa and ent-3 ba, which were obtained through kinetic resolution, afforded the enantiomerically highly enriched cyclic allylic alcohols 9 a-c (>/=99 % ee) and acyclic allylic alcohols 10 a (>/=99 % ee) and 10 b (99 % ee), respectively.     

Totalsynthese von natürlichem α-Tocopherol. 2. Mitteilung. Aufbau der Seitenkette aus (−)-(S)-3-Methyl-γ-butyrolacton

Total Synthesis of Natural α-Tocopherol A short and efficient route to optically pure (+)-(3 R, 7 R)-trimethyldodecanol ( 14 ) is demonstrated, 14 serving as side chain unit in the preparation of natural vitamin E. The synthesis of 14 is based on the concept of using a single optically active C₅-synthon of suitable configuration and functionalization to introduce both asymmetric centres in 14 . (?)-(S)-3-Methyl-γ-butyrolacton ( 1 ) and ethyl (?)-(S)-4-bromo-3-methylbutyrate ( 2 ), respectively, is used in a sequence of either two Grignard C,C-coupling reactions 5 → 8 and 12 → 13 or two Wittig reactions 17a → 18 and 20 → 21 to achieve this goal. 14 is converted to (2 R, 4′R, 8′R)-α-tocopherol (= vitamin E) by coupling with a chroman unit in known manner. Optical purity of products and intermediates is established.     

Die thermische Umlagerung von 2-(Buta-1′,3′-dienyl)-phenolen in 2-Alkyl-2H-chromene; Beispiele für aromatische [1,7a]- und [1,5s]sigmatropische Wasserstoffverschiebungen

2-(1′-cis,3′-cis-)- and 2-(1′-cis,3′-trans-Penta-1′,3′-dienyl)-phenol (cis, cis- 4 and cis, trans- 4 , cf. scheme 1) rearrange thermally at 85–110° via [1,7 a] hydrogen shifts to yield the o-quinomethide 2 (R ? CH₃) which rapidly cyclises to give 2-ethyl-2H-chromene ( 7 ). The trans formation of cis, cis- and cis, trans- 4 into 7 is accompanied by a thermal cis, trans isomerisation of the 3′ double bond in 4. The isomerisation indicates that [1,7 a] hydrogen shifts in 2 compete with the electrocyclic ring closure of 2 . The isomeric phenols, trans, trans- and trans, cis- 4 , are stable at 85–110° but at 190° rearrange also to form 7 . This rearrangement is induced by a thermal cis, trans isomerisation of the 1′ double bond which occurs via [1, 5s] hydrogen shifts. Deuterium labelling experiments show that the chromene 7 is in equilibrium with the o-quinomethide 2 (R ? CH₃), at 210°. Thus, when 2-benzyl-2H-chromene ( 9 ) or 2-(1′-trans,3′-trans,-4′-phenyl-buta1′,3′-dienyl)-phenol (trans, trans- 6 ) is heated in diglyme solution at >200°, an equilibrium mixture of both compounds (～ 55% 9 and 45% 6 ) is obtained.     

Stationary points in the temperature dependence of electron transfer rates

The temperature dependence of the rate of electron transfer is analyzed in the framework of a molecular theory presented recently, characterized by decoupling the total solvent reorganization energy into two contributions featuring reorganizations of permanent dipoles as well as solvent density. The inclusion of the temperature dependence of liquid density reorganization can give rise to a maximum in the Arrhenius coordinates for electron transfer in the inverted region and for exothermic reactions with small activation barriers as well.     

Transition metal complexes in organic synthesis. Part 68: Iron-mediated total synthesis of mukonine and mukonidine by oxidative cyclization with air as the oxidizing agent

The oxidative cyclization of 5-(2-amino-5-methoxycarbonylphenyl)-substituted tricarbonyl[η⁴-cyclohexa-1,3-diene]iron complexes by air in protic medium provides the corresponding tricarbonyl[η⁴-4a,9a-dihydro-9H-carbazole]iron complexes. This procedure is applied to the total synthesis of the 3-methoxycarbonylcarbazole alkaloids mukonine and mukonidine.