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.     

Analysis of spin states, spin barriers, and trans-effects involved in the coordination and stabilization of dinitrogen by biomimetic iron complexes

Coordination of dinitrogen to Sellmann-type iron (II) complexes in a sulfur-dominated coordination sphere, which emulates the environment of iron centers in the FeMo-cofactor of nitrogenase, is analyzed with respect to spin states, spin barriers, and the effect of trans-ligands. Such detailed investigations became only recently feasible when the reliability of density functional methods, which are the only quantum chemical methods capable of describing large transition metal complexes, could significantly be improved for the calculation of energies for states of different spin. It is found that the actual binding energy of dinitrogen is of sufficient magnitude for a reasonably strong fixation of N₂ by Sellmann-type coordination compounds. However, potential fixation is determined by additional factors which reduce the binding energy. One factor is the change in spin state of the N₂-free metal fragment, which lowers the total energy and quenches the thermodynamic stabilization effect of the binding energy. In addition, the metal fragment rearranges and gains even more stabilization energy for the un-coordinated state. Apart from these thermodynamical effects, the existence of spin barriers, which must be overcome upon binding of dinitrogen, leads to kinetical effects, which cannot be neglected.     

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.     

Thermodynamic and kinetic data for adduct formation, cis-trans isomerization and redox reactions of ML4 complexes: a case study with rhodium- and iridium-tropp complexes in d8, d9 and d10 valence electron configurations (tropp=dibenzotropylidene phosphanes)

The formation of adducts of the square-planar 16-electron complexes trans-[M(tropp(ph))(2)](+) and cis-[M(tropp(ph))(2)](+) (M=Rh, Ir; tropp(Ph)=5-diphenylphosphanyldibenzo[a,d]cycloheptene) with acetonitrile (acn) and Cl(-), and the redox chemistry of these complexes was investigated by various physical methods (NMR and UV-visible spectroscopy, square-wave voltammetry), in order to obtain some fundamental thermodynamic and kinetic data for these systems. A trans/cis isomerization cannot be detected for [M(tropp(ph))(2)](+) in non-coordinating solvents. However, both isomers are connected through equilibria of the type trans-[M(tropp(ph))(2)](+)+L<==>[ML(tropp(ph))(2)](n)<==>cis-[M(tropp(ph))(2)](+)+L, involving five-coordinate intermediates [ML(tropp(ph))(2)](n) (L=acn, n=+1; L=Cl(-), n=0). Values for K(d) (K(f)), that is, the dissociation (formation) equilibrium constant, and k(d) (k(f)), that is, the dissociation (formation) rate constant, were obtained. The formation reactions are fast, especially with the trans isomers (k(f)>1x10(5) m(-1) s(-1)). The reaction with the sterically more hindered cis isomers is at least one order of magnitude slower. The stability of the five-coordinate complexes [ML(tropp(ph))(2)](n) increases with Ir>Rh and Cl(-)>acn. The dissociation reaction has a pronounced influence on the square-wave (SW) voltammograms of trans/cis-[Ir(tropp(ph))(2)](+). With the help of the thermodynamic and kinetic data independently determined by other physical means, these reactions could be simulated and allowed the setting up of a reaction sequence. Examination of the data obtained showed that the trans/cis isomerization is a process with a low activation barrier for the four-coordinate 17-electron complexes [M(tropp(ph))(2)](0) and especially that a disproportionation reaction 2 trans/cis-[M(tropp(ph))(2)](0)-->[M(tropp(ph))(2)](+)+[M(tropp(ph))(2)](-) may be sufficiently fast to mask the true reactivity of the paramagnetic species, which are probably less reactive than their diamagnetic equilibrium partners.     

Optimization of auxiliary basis sets for the LEDO expansion and a projection technique for LEDO-DFT

We present a systematic procedure for the optimization of the expansion basis for the limited expansion of diatomic overlap density functional theory (LEDO-DFT) and report on optimized auxiliary orbitals for the Ahlrichs split valence plus polarization basis set (SVP) for the elements H, Li--F, and Na--Cl. A new method to deal with near-linear dependences in the LEDO expansion basis is introduced, which greatly reduces the computational effort of LEDO-DFT calculations. Numerical results for a test set of small molecules demonstrate the accuracy of electronic energies, structural parameters, dipole moments, and harmonic frequencies. For larger molecular systems the numerical errors introduced by the LEDO approximation can lead to an uncontrollable behavior of the self-consistent field (SCF) process. A projection technique suggested by L?wdin is presented in the framework of LEDO-DFT, which guarantees for SCF convergence. Numerical results on some critical test molecules suggest the general applicability of the auxiliary orbitals presented in combination with this projection technique. Timing results indicate that LEDO-DFT is competitive with conventional density fitting methods.