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.     

π-Bindungsbeitrag in Boranen, 2. Mitt.:Ab initio- und Kraftfeld-Rechnungen von Vinyldifluorboran

Ab initio calculations on vinyldifluoroborane yield a -contribution of 23 kJ/mol (5.5 kcal/mol) mainly due to the C=C bond and not to the lone pairs of the fluorine atoms. The rotational barrier was also determined. The force field calculations favour the interpretation of the bond structure derived from the theab initio results.

     

X-ray structure and variable temperature NMR spectra of [meso-triarylcorrolato]copper(III)

The diamagnetic square planar d(8) complexes [meso-arylcorrolato]copper(III) become paramagnetic upon warming, indicative of the equilibrium between the [corrolato]copper(III) and the [corrolato](+)* copper(II) forms of the complex. [meso-Triphenylcorrolato]copper(III) was structurally characterized and found to be saddled.     

Reactions of Molecules with Two Equivalent Functional Groups. 5. Anomalous Reactivity of 1,10-Cyclooctadecanedione. Crystal and Molecular Structures of cis,cis-1,10-Diphenyl-1,10-cyclooctadiene and the Stereoisomers of 1,10-Diphenyl-1,10-cyclooctadecanediol(1)

The reaction of the title diketone (3) with phenyl Grignard produces (with rate constant k(1)) the conjugate base (6-M) of 10-hydroxy-10-phenylcyclooctadecanone (6), which is subsequently converted (with rate constant k(2)) to the conjugate base of the title diol, as a mixture of the cis (7, 55%) and trans (8, 45%) isomers. The ratio k(2)/k(1), 2.2 +/- 0.4, indicates that the carbonyl group in 6-M is 4.4 times as reactive as each carbonyl in 3. Competition experiments further demonstrate that the relative rates (per carbonyl) for addition of phenylmagnesium bromide to 3, 10-methylenecyclooctadecanone (11), and cyclopentadecanone (12) are 1.0:0.60:1.92. Possible reasons for this order of reactivity are discussed. Diols 7 and 8 undergo facile double dehydration to form the title diene 13, which is predicted by molecular mechanics calculations to be the most stable of the four possible symmetrical diene isomers. The structures of 7, 8, and 13 were secured by single-crystal X-ray studies.     

New features in the catalytic cycle of cytochrome P450 during the formation of compound I from compound 0

Density functional theory (DFT) is applied to the dark section of the catalytic cycle of the enzyme cytochrome P450, namely, the formation of the active species, Compound I (Cpd I), from the ferric-hydroperoxide species (Cpd 0) by a protonation-assisted mechanism. The chosen 96-atom model includes the key functionalities deduced from experiment: Asp(251), Thr(252), Glu(366), and the water channels that relay the protons. The DFT model calculations show that (a) Cpd I is not formed spontaneously from Cpd 0 by direct protonation, nor is the process very exothermic. The process is virtually thermoneutral and involves a significant barrier such that formation of Cpd I is not facile on this route. (b) Along the protonation pathway, there exists an intermediate, a protonated Cpd 0, which is a potent oxidant since it is a ferric complex of water oxide. Preliminary quantum mechanical/molecular mechanical calculations confirm that Cpd 0 and Cpd I are of similar energy for the chosen model and that protonated Cpd 0 may exist as an unstable intermediate. The paper also addresses the essential role of Thr(252) as a hydrogen-bond acceptor (in accord with mutation studies of the OH group to OMe).     

Nanostructure investigations with the analytical transmission electron microscope

Concerning the conventional TEM-imaging as well as the analytical procedures the capabilities are pointed out: electron diffraction, energy dispersive X-ray spectroscopy (EDXS) and electron energy loss spectroscopy (EELS). The possibilities of investigation of both nanocrystalline materials and multilayers are discussed, accompanied by examples of current investigations: At alloys, produced by intense milling, at single nanocrystals the imaging by diffraction contrast was successful, the analysis has failed because of the sample thickness. By means of energy spectroscopic imaging multilayers from Fe-SiB/NbCu and Fe/Cr as well as Al₂O₃/TiN have been characterized. Received: 15 July 1997 / Revised: 16 February 1998 / Accepted: 21 February 1998     

Backbonding contributions to small molecule chemisorption in a metal–organic framework with open copper(i) centers

Metal–organic frameworks are promising materials for applications such as gas capture, separation, and storage, due to their ability to selectively adsorb small molecules. The metal–organic framework Cu^I-MFU-4l, which contains coordinatively unsaturated copper(i) centers, can engage in backbonding interactions with various small molecule guests, motivating the design of frameworks that engage in backbonding and other electronic interactions for highly efficient and selective adsorption. Here, we examine several gases expected to bind to the open copper(i) sites in Cu^I-MFU-4l via different electronic interactions, including σ-donation, π-backbonding, and formal electron transfer. We show that in situ Cu L-edge near edge X-ray absorption fine structure (NEXAFS) spectroscopy can elucidate π-backbonding by directly probing excitations to unoccupied backbonding orbitals with Cu d-character, even for gases that participate in other dominant interactions, such as ligand-to-metal σ-donation. First-principles calculations based on density functional theory and time-dependent density functional theory additionally reveal the backbonding molecular orbitals associated with these spectroscopic transitions. The energies of the transitions correlate with the energy levels of the isolated small molecule adsorbates, and the transition intensities are proportional to the binding energies of the guest molecules within Cu^I-MFU-4l. By elucidating the molecular and electronic structure origins of backbonding interactions between electron rich metal centers in metal–organic frameworks and small molecule guests, it is possible to develop guidelines for further molecular-level design of solid-state adsorbents for energy-efficient separations of relevance to industry.

In situ near edge X-ray absorption fine structure spectroscopy directly probes unoccupied states associated with backbonding interactions between the open metal site in a metal–organic framework and various small molecule guests.     

Kinetics of oil saponification by lead salts in ancient preparations of pharmaceutical lead plasters and painting lead mediums

Lead soaps can be found in archaeological cosmetics as well as in oil paintings, as product of interactions of lead salts with oil. In this context, a better understanding of the formation of lead soaps allows a follow-up of the historical evolution of preparation recipes and provides new insights into conservation conditions. First, ancient recipes of both pharmaceutical lead plasters and painting lead mediums, mixtures of oil and lead salts, were reconstructed. The ester saponification by lead salts is determined by the preparation parameters which were quantified by FT-IR spectrometry. In particular, ATR/FT-IR spectrometer was calibrated by the standard addition method to quantitatively follow the kinetics of this reaction. The influence of different parameters such as temperature, presence of water and choice of lead salts was assessed: the saponification is clearly accelerated by water and heating. This analysis provides chemical explanations to the historical evolution of cosmetic and painting preparation recipes.     

Preparative and electrochemical investigations on the electron sponge behavior of cobalt telluride clusters: CO substitution in [Co11Te7(CO)10]n- ions (n=1, 2) by PMe2Ph and crystal structure of [Co11Te7(CO)5(PMe2Ph)5

The reaction of the cluster salts [Cp(2*) Nb(CO)(2)](n)[Co(11)Te(7)(CO)(10)] (Cp*=C(5)Me(5); n=1, 2) with excess PMe(2)Ph gave the neutral, dark brown clusters [Co(11)Te(7)(CO)(6)(PMe(2)Ph)(4)] (5) and [Co(11)Te(7)(CO)(5)(PMe(2)Ph)(5)] (6) with 147 metal valence electrons. The new compounds were characterized by IR spectroscopy, elemental analyses, and mass spectrometry. The molecular structure of 6 was determined by X-ray crystallography. Like its precursor anion, it consists of a pentagonal-prismatic [Co(11)Te(7)] core, but with a ligand sphere composed of five CO and five PMe(2)Ph ligands. Detailed electrochemical studies of both reactions reveal that a stepwise substitution of CO ligands in the initial cluster anions takes place leading to intermediate [Co(11)Te(7)(CO)(10-m)(PMe(2)Ph)(m)](n-) ions (m=1-5; n=1, 2). Each of these intermediates is distinguished by at least one oxidation and two reduction waves, giving rise to a total of 21 redox couples and 27 electroactive species. The electron sponge character of the new compounds is particularly pronounced in 5, which exhibits charges n between +1 and -4 corresponding to metal valence electron counts of between 146 and 151.     

The crystal structure of 4,4′-dipyridinium tetracyanooxothiocyanatorhenate(V)

Summary The light purple crystals of (4,4-dipyridinium) [ReO(NCS)(CN)₄] crystallize in the monoclinic space group P2₁/m witha=6.615(1),b=16.043(1),c=8.405(1) Å,=93.20(1)°,z=2. The anisotropic refinement of the 1770 observed reflections converged to R=0.041.The [ReO(NCS)(CN)₄]^2– ion has a distorted octahedral geometry. The rhenium atom is displaced by 0.30 Å out of the plane formed by the four carbon atoms towards the terminal oxo ligand. Bond distances: Re=0 =1.67(1), Re–N=2.12(1) and Re–C_av=2.11(1)Å. The thiocyanate ion is nitrogen bonded to the rhenium atom.