A class of means and related inequalities

The aim of this paper is two-fold: First we describe a certain class of strictly positive, continuous functions u:I defined on certain intervals I]0,+[, and demonstrate that each function u of this class permits the definition of an associated mean M_u (a₁,...,a_n) for any finite number a₁,...,a_n of numbers in I. The arithmetic and the geometric mean are special cases of these u-means M_u. -Thereafter, we improve the classical inequality between the geometric and the arithmetic mean and derive from it a corresponding inequality between certain u-means and the arithmetic mean.     

Dynamic Fourier transform infrared spectroscopy in polymer research

The rapid-scanning capability of FTIR instrumentation has revitalized the field of vibrational spectroscopy in polymer research and will be discussed with reference to the study of polyurethane kinetics, the temperature dependence of hydrogen bonding in polyamide 6 and strain-induced crystallization in a polydimethylsiloxane elastomer.     

Binding Ensembles of p53-MDM2 Peptide Inhibitors by Combining Bayesian Inference and Atomistic Simulations

Designing peptide inhibitors of the p53-MDM2 interaction against cancer is of wide interest. Computational modeling and virtual screening are a well established step in the rational design of small molecules. But they face challenges for binding flexible peptide molecules that fold upon binding. We look at the ability of five different peptides, three of which are intrinsically disordered, to bind to MDM2 with a new Bayesian inference approach (MELD × MD). The method is able to capture the folding upon binding mechanism and differentiate binding preferences between the five peptides. Processing the ensembles with statistical mechanics tools depicts the most likely bound conformations and hints at differences in the binding mechanism. Finally, the study shows the importance of capturing two driving forces to binding in this system: the ability of peptides to adopt bound conformations (ΔGconformation) and the interaction between interface residues (ΔGinteraction).     

Rate-equilibrium relationships in hydride transfer reactions: the role of intrinsic barriers

A literature survey on the kinetics of hydride abstractions from CH-groups by carbocations reveals a general phenomenon: Variation of the hydride acceptor affects the rates of hydride transfer to a considerably greater extent than an equal change of the thermodynamic driving force caused by variation of the hydride donor. The origin of this relationship was investigated by quantum chemical calculations on various levels of ab initio and DFT theory for the transfer of an allylic hydrogen from 1-mono- and 1,1-disubstituted propenes (XYC=CH-CH(3)) to the 3-position of 1-mono- and 1,1-disubstituted allyl cations (XYC=CH-CH(2)(+)). The discussion is based on the results of the MP2/6-31+G(d,p)//RHF/6-31+G(d,p) calculations. Electron-releasing substituents X and Y in the hydride donors increase the exothermicity of the reaction, while electron-releasing substituents in the hydride acceptors decrease exothermicity. In line with Hammond's postulate, increasing exothermicity shifts the transition states on the reaction coordinate toward reactants, as revealed by the geometry parameters and the charge distribution in the activated complexes. Independent of the location of the transition state on the reaction coordinate, a value of 0.72 is found for Hammond-Leffler's alpha = deltaDeltaG/deltaDelta(r)G degrees when the hydride acceptor is varied, while alpha = 0.28 when the hydride donor is varied. The value of alpha thus cannot be related with the position of the transition state. Investigation of the degenerate reactions XYC=CH-CH(3) + XYC=CH-CH(2)(+) indicates that the migrating hydrogen carries a partial positive charge in the transition state and that the intrinsic barriers increase with increasing electron-releasing abilities of X and Y. Substituent variation in the donor thus influences reaction enthalpy and intrinsic barriers in the opposite sense, while substituent variation in the acceptor affects both terms in the same sense, in accord with the experimental findings. Marcus theory is employed to treat these effects quantitatively.     

1-Methoxycarbonyl-substituiertes 2,3-Dihydropyridin-4(1H)-on (= Methyl-1,2,3,4-tetrahydro-4-oxopyridin-1-carboxylat) als Chromophor für die photochemische [2 + 2]-Cycloaddition

1-Methoxycarbonyl-Substituted 2,3-Dihydropyridin-4(1H)-one(= Methyl 1,2,3,4-Tetrahydro-4-oxopyridine-1-carboxylate) as Chromophore for Photochemical [2 + 2]-Cycloadditions With olefins having an electron-acceptor as well as with olefins having an electron-donor substituent, 1-methoxycarbonyl-substituted dihydropyridinone 12 undergoes [2 + 2] cycloaddition in good preparative yields. The photochemical cycloaddition is highly regioselective. For preparative purposes, the ring junction can be equilibrated to the thermodynamically more stable cis-junction. Only the ‘endo’/‘exo’ selectivity at the C-atom bearing the olefin substituent cannot be controlled. The photodimerization of 12 is the only side reaction. Using a slight excess of the olefin, the photodimerization can be suppressed. The protecting group at the N-atom of the dihydropyridinone can be varied in order to introduce an internal sensitizer, as shown with 1-acyl-substituted compound 29 , which underwent the cycloaddition process even with sunlight.     

Reaction of a stable aminoarylcarbene with 2-chloroacrylonitrile: dearomatizing cyclization rather than cyclopropanation

The reaction of a stable aminoarylcarbene with 2-chloroacrylonitrile is reported. The resulting 1/1 adduct has been spectroscopically and structurally characterized. The initial Michael addition is not followed by cyclopropane formation but by a dearomatizing cyclization affording an original bicyclic structure.     

Reaktionen von komplexliganden : XIX. Einschiebung von inaminen in chrom-alkenylcarben- und chrom-aminocarber-bindungen

1-Diethylaminopropyne reacts with pentacarbonyl[methoxy(2,2-diphenylethenyl)carbene]chromium in a stereoselective way to give pentacarbonyl-[diethylamino-E-(2-methoxy-1-methyl-4,4-diphenyl-1,3-butadienyl)carbene]-chromium via insertion of the alkyne into the metal-carbene bond. The reaction of the ynamine with pentacarbonyl[methylamino(phenyl)carbene]chromium results in insertion of the alkyne and loss of carbon monoxide to give cis-tetracarbonyl[3-aza-1-methyl-2-phenyl-2-butenyl)diethylaminocarbene]-chromium. Its structure was established by oxidative degradation in an aqueous medium to give 2-benzoyl-N,N-diethylpropanamide and finally confirmed by an X-ray analysis. The new compounds are characterized spectroscopically.     

The Chemistry of Dichloromethylenammonium Salts (“Phosgenimonium Salts”)

Dichloromethylenammonium salts, particularly dichloromethylenedimethylammonium chloride, occupy a unique place as stable but reactive building blocks for synthesis. They contain three mobile chlorine atoms activated by an amino group on the same carbon atom. These salts can be regarded as chlorinated Vilsmeier or Mannich reagents and are thus at a higher oxidation level. As in the Mannich or Vilsmeier reaction, the carbon condenses here as an electrophile with formation of C? C or C? hetero atom bonds in a variety that is still far from being exhausted.