Mechanistic Aspects of a Highly Active Dinuclear Zinc Catalyst for the Co‐polymerization of Epoxides and CO2

The dinuclear zinc complex reported by us is to date the most active zinc catalyst for the co‐polymerization of cyclohexene oxide (CHO) and carbon dioxide. However, co‐polymerization experiments with propylene oxide (PO) and CO₂ revealed surprisingly low conversions. Within this work, we focused on clarification of this behavior through experimental results and quantum chemical studies. The combination of both results indicated the formation of an energetically highly stable intermediate in the presence of propylene oxide and carbon dioxide. A similar species in the case of cyclohexene oxide/CO₂ co‐polymerization was not stable enough to deactivate the catalyst due to steric repulsion.     

Aryl Boronic Acid Catalysed Dehydrative Substitution of Benzylic Alcohols for C−O Bond Formation

A combination of pentafluorophenylboronic acid and oxalic acid catalyses the dehydrative substitution of benzylic alcohols with a second alcohol to form new C−O bonds. This method has been applied to the intermolecular substitution of benzylic alcohols to form symmetrical ethers, intramolecular cyclisations of diols to form aryl-substituted tetrahydrofuran and tetrahydropyran derivatives, and intermolecular crossed-etherification reactions between two different alcohols. Mechanistic control experiments have identified a potential catalytic intermediate formed between the aryl boronic acid and oxalic acid.     

Defining Integrality at Prime Sets of High Density over Function Fields

 Let F be a function field of characteristic over a finite field . Then for any finite set of F-primes S and any , there exists a set of F-primes W of density greater than such that and has a Diophantine definition over . (Here and is defined analogously.)     

Continuous modified Newton’s-type method for nonlinear operator equations

A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point x ₀ and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated. Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003 This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks DAAD for support     

Diophantine Undecidability of Function Fields of Characteristic Greater than 2, Finitely Generated over Fields Algebraic over a Finite Field

Let F be a function field of characteristic p > 2, finitely generated over a field C algebraic over a finite field C _p and such that it has an extension of degree p. Then Hilbert's Tenth Problem is not decidable over F.     

Hydrogen-bonded block mesogens derived from semiperfluorinated benzoic acids and the non-mesogenic 1,2-bis(4-pyridyl)ethylene

Thermal properties of benzoic acids carrying one or two semiperfluorinated alkoxy tails on the aromatic core have been investigated in binary mixtures with the non-liquid crystalline bidirectional trans-1,2-bis(4-pyridyl)ethylene. The hydrogen bonded complexes built from the complementary molecular species show a significantly enhanced mesophase stability compared with the fluorinated acids in their pure states. The mesophase morphologies of the complexes are governed mainly by the number of the partially fluorinated chains grafted to the acid component. Mixed systems comprising the one-chain acids exhibit a smectic C phase followed by a smectic A phase at more elevated temperatures. Incorporation of a second semiperfluorinated chain into the acid leads to the formation of columnar mesophases. These columnar phases of the H-bonded complexes should represent ribbon phases resulting from the collapse of the smectic layers.     

Synthesen von Mannich-Basen von Hydroxy-indolen. 3. Mitteilung über synthetische Indol-Verbindungen [1]

The reactivity of hydroxy-indoles under the conditions of the Mannich-reaction has been studied. The electrophilic side-chain enters in each case in a position ortho to the phenolic group. 4-Hydroxy-indole is substituted in the 5-, 5-hydroxy-indole in the 4-, 6-hydroxy-indole in the 7-, and 7-hydroxy-indole probably in the 6-position. The structures of the Mannich bases from 4-, 5- and 6-hydroxy-indole have been confirmed by comparison of the hydroxy-methyl-indoles obtained by reductive desamination with hydroxy-methyl-indoles prepared by unambiguous total synthesis.     

The observation of a large gauche preference when 2-fluoroethylamine and 2-fluoroethanol become protonated

The energies of the gauche and anti conformers of 2-fluoroethylamine, 2-fluoroethanol and their protonated analogues are calculated using density functional theory. Unlike the non protonated systems, the protonated systems show a strong gauche effect where the C-F and the C-(+)NH(3) or C-F and C-(+)OH(2) bonds are gauche rather than anti to each other. Single crystal X-ray diffraction studies of 2-fluoroethylammonium compounds identify the same conformational preference.     

Substituent effects on the rate constants for the photo-Claisen rearrangement of allyl aryl ethers

The photochemistry of 11 substituted allyl 4-X- and 3-X-aryl ethers 3 (ArOCH2-CH=CH2) has been examined in both methanol and cyclohexane as solvents. The ethers react by the photo-Claisen rearrangement to give allyl substituted phenols as the major primary photoproducts, as expected from the well-established radical pair mechanism. The excited singlet state properties (absorption spectra, fluorescence spectra, fluorescence quantum yields, and singlet lifetimes) were compared with a parallel set of unreactive 4-X- and 3-X-anisoles 4. The excited-state properties of three substituted 4-X-aryl 4-(1-butenyl) ethers 14 (ArOCH2CH2-CH=CH2) were also examined. The model compounds 4 and the reactive allyl ethers 3 have essentially identical rate constants for the excited-state processes with the exception of, the rate constant for homolytic cleavage from S(1) of the allyl ethers to give the radical pair. The difference between the fluorescence quantum yields and/or singlet lifetimes for 3 and 4 were used to obtain values of for all of the allyl ethers. These values exhibit a large substituent effect, spanning almost 2 orders of magnitude with electron-donating groups (CH3O, CH3) accelerating the reaction and electron-withdrawing ones (CN, CF3) slowing it down. The parallel range of rate constants observed in both methanol and cyclohexane indicates that ion pairs are not important intermediates in these rearrangements. Quantum yields of reaction (Phi(r)) for several of the more reactive ethers demonstrate that neither these values nor rate constants of reaction derived from them are reliable measures of the actual excited-state process. In fact, the values are significantly lower than the ones, indicating that the radical pairs undergo recombination to generate starting material. Finally, the rate constants were found to parallel a trend for the change in bond dissociation energy (deltaBDE) for the O-C (allyl) bond of the allyl ethers, indicating that other possible substituent effects are of minor importance.