Stability and accuracy of time discretizations for initial value problems

Summary This paper continues earlier work by the same authors concerning the shape and size of the stability regions of general linear discretization methods for initial value problems. Here the treatment is extended to cover also implicit schemes, and by placing the accuracy of the schemes into a more central position in the discussion general method-free statements are again obtained. More specialized results are additionally given for linear multistep methods and for the Taylor series method.This research has been supported by Swiss National Foundation, Grant No. 82-524.077This research has been supported by the Heinrich-Hertz-Stiftung, B 32 No. 203/79     

Photochemistry of 3-Substituted 1-Iminopyridinium Ylides. Regiospecific versus non-regiospecific photoisomerization patterns [1]

3-Substituted 1-iminopyridinium ylides 1 undergo photo-induced ring enlargement to 1H-1,2-diazepines. With strongly electron-withdrawing substituents the ring expansion process is regiospecific and leads exclusively to 4-substituted 1 H-1, 2-diazepines. Weak electron-donating substituents, like a methyl group and halogen atoms, do not have any directing effect since both 4- and 6-substituted 1 H -1,2-diazepines are obtained. With strong electron-donating substituents no diazepines are formed; instead one observes photo-induced isomerization to the 2-aminopyridine derivatives, the process being non-regiospecific. Regiospecific photo-induced ring expansion processes are explained in terms of a simple HMO model.     

Aristoserratin,ein neues Indolalkaloid aus Aristotelia serrata W.R.B. OLIVER und A. peduncularis (LABILL.) HOOK. F. 178. Mitteilung über organische Naturstoffe

Aristoserratine, a New Indole Alkaloid from Aristotelia serrata W.R.B. OLIVER and from A. peduncularis (LABILL .) HOOK . F. The new indole alkaloid aristoserratine (2) has been isolated from Aristotelia. Its structure and absolute configuration were elucidated on the basis of spectroscopic data.     

The Structure of the Alkaloid Peduncularine. Communication no. 172 on organic natural products

The revised structure 1 is put forward for peduncularine, the main alkaloid of Aristotelia peduncularis (Labill.) HOOK. F. (Elaeocarpaceae), on the basis of its spectroscopic properties and those of its degradation products, the Hofmann base 3 and the hydrogenation product 4 . Structure 1 represents the relative configuration of the alkaloid. Peduncularine belongs to the class of indole alkaloids with a monoterpene unit as the aliphatic portion. To our knowledge it constitutes the first example in which an isopropyl group has become detached from the terpene unit and occurs as a substituent on nitrogen.     

Sensitized photo-oxidation of methylcyclohexane as a thin film on seawater by irradiation with natural sunlight

Methylcyclohexane dissolved in and forming a thin film on purified seawater with traces of anthraquinone added as triplet sensitizer was exposed to natural sunlight in a quartz flask. The water was circulated through a glass cartridge filled with Amberlite XAD-2 for the concentration of reaction products which were identified by GC/MS after elution and silica gel chromatography. They included isomeric methylcyclohexanols as the principal components, primary hydroperoxides, a tentatively identified secondary peroxide, methylcyclohexanones, and acyclic ketones. Mass spectra and mechanisms are discussed as well as possible biological consequences of the formation of these compounds.     

Kurze Totalsynthesen von (±)-Sativen und (±)-cis-Sativendiol

Short Total Syntheses of (±)-Sativene and (±)-cis-Sativenediol Our approach to (±)-sativene (7) and (±)-cis-sdtivenediol (9) involves: (a) reaction of 3-methylbutanoyl chloride with Et₃N/cyclopentadiene to give the endo-isopropyl-ketone 1 (here improved to 71%), (b) NBS bromination of 1 to a 5:1 mixture (87%) of the bromo-ketones 2 and 3 , (c) NFD-reaction sequence initiated by the attack of 1,2-butadienyl titanate (complex of 15 , obtained from 2-butine) on 2/3 to afford 52% of the brexenone derivative 4 (along with 8% of its epimer 16 ), (d) addition of dibromomethane to 4 forming 63% of the diene-alcohol 5 (along with 13% of the diene-carbaldehyde 38 ), and (e) carbenoid ring-expansion with MeLi applied to 5 resulting in 41% the diene-ketone 6 (along with 15% of a 1:3 mixture of the diene-ketones 32 and 33 ). Wolff-Kishner reduction of 6 led to 81% of (±)-sativene (7), when enough O₂ was present, but to 97% of the diene 8 in the strict absence of O₂. (±)-cis-Sativenediol (9) was obrained (86%) by OsO₄ hydroxylation of 8 . The brexenone derivatives 4 and 16 (6:1, 50%) were also produced when the NFD-reaction sequence was applied to the isomeric bromo-ketone mixture 13/13 (1:3). The latter was obtained by NBS bromination of 10 , which in turn was available by base epimerization of 1 , followed by destructive removal of unreacted 1 by repeated gas-flow thermolysis. An analogous (less convenient) route to (±)-sativene (7) passed through a series of dihydro compounds (the ene series) it started with the methylidene-ketone 36 , which was the product (97%) of a partial hydrogenation of 4 . Addition of dibromomethane to 36 led t 62% of the methylidene-alcohol 39 (along with a little tetracyclic ether 40 ). Carbenoid ring expansion of 39 with MeLi afforded ca. 42% of the methylidene-ketone 41 (along with 7% of the methylidene-ketone 43 or, under slightly different condition, along with 9% of the methylidene-ketone 42 and 10% of the methylidene-carabaldehyde 44 ). The methylidene-alcohol 39 and the methylidene-ketone 43 were also obtained by partial hydrogenation of 5 and 33 , respectively. Wolff-Kisher reduction converted 41 into (±)-sativene ( 7 99%); the same conditons applied to 42 afforded only ca. 8% 7 (along with three other hydrocarbons, one of them (ca. 21%) probably being (±)-copacamphene (45)). In the diene series, the two succeeding reactions ( 4→5 and 5→6 ) competed with the same side reaction, a rearrangement leading to the brendene-aldehyde 38. In the ene series, the corresponding dihydro-by-product 44 was found in the reacton 39→41 , but not during 36→39. These side reactons could largely be suppressed by keeping the reaction temperature low. An explanation is proposed.     

Self-assembly of tetrahedral and trigonal antiprismatic clusters [Fe4(L4)4] and [Fe6(L5)6] on the basis of trigonal tris-bidentate chelators

In a one-pot reaction, the tetranuclear iron chelate complex [Fe4(L4)4] 6 was generated from benzene-1,3,5-tricarboxylic acid trichloride (4), bis-tert-butyl malonate (5a), methyllithium, and iron(II) dichloride under aerobic conditions. Alternatively, hexanuclear iron chelate complex [Fe(L5)6] 7 was formed starting from bis-para-tolyl malonate (5b) by employing identical reaction conditions to those applied for the synthesis of 6. The clusters 6 and 7 are present as racemic mixtures of homoconfigurational (delta,delta,delta,delta)/(lambda,lambda,lambda,lambda)-fac or (delta,delta,delta,delta,delta,delta)/(lambda,lambda,lambda,lambda,lambda,lambda)-fac stereoisomers. The structures of 6 and 7 were unequivocally resolved by single-crystal X-ray analyses. The all-iron(III) character of 6 and 7 was determined by M?ssbauer spectroscopy.     

Solvothermal Synthesis and Characterization of the New Iron Thioantimonates(III) [Fe(C6H18N4)]FeSbS4 and [Fe(C4H13N3)2]Fe2Sb4S10 Containing FeII and FeIII and Protein‐Analogous [2FeIII‐2S]2+ Clusters

The two new compounds [Fe(tren)]FeSbS₄ ( 1 ) (tren = tris(2‐aminoethyl)amine) and [Fe(dien)₂]Fe₂Sb₄S₁₀ ( 2 ) (dien = diethylendiamine) were prepared under solvothermal conditions and represent the first thioantimonates(III) with iron cations integrated into the anionic network. In both compounds Fe³⁺ is part of a [2Fe^III‐2S] cluster which is often found in ferredoxines. In addition, Fe²⁺ ions are present which are surrounded by the organic ligands. In ( 1 ) the Fe²⁺ ion is also part of the thioantimonate(III) network whereas in ( 2 ) the Fe²⁺ ion is isolated. In both compounds the primary SbS₃ units are interconnected into one‐dimensional chains. The mixed‐valent character of [Fe(tren)]FeSbS₄ was unambiguously determined with Mössbauer spectroscopy. Both compounds exhibit paramagnetic behaviour and for ( 1 ) a deviation from linearity is observed due to a strong zero‐field splitting. Both compounds decompose in one single step.