On the recognition problem of quasi-homogeneous locally nilpotent derivations in dimension three

We give a criterion to decide if a given w-homogeneous derivation on A?k[X₁,X₂,X₃] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation.     

Calculation of the infrared spectrum and density of the vibrational states of an SiO2 melt by molecular dynamics

The density of the vibrational states of an SiO₂ melt under various PT conditions, the distributions of the Si-O-Si and O-Si-O angles in it, and its IR absorption spectra have been calculated by molecular dynamics with the use of a pairwise additive Born-Mayer potential. A comparison with the experimental data reveals that the ionic approximation selected is capable of basically reproducing the structural and spectroscopic properties of the melt, but the distributions of the bond angles are considerably broader than the experimentally determined distributions, and the absorption band caused by the stretching vibrations is not displayed in the calculated spectrum. The disparities indicated are apparently due to the isotropic nature of the potential of the interparticle interactions.V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 467–470, July–August, 1991. Original article submitted October 12, 1990.     

The preparation and X-ray structural study of complexes that catalyze isocyanate cyclotrimerization

A 11-complex of trinitrophenol with benzyldimethylamine (1) and a 111-complex, the product of the interaction of benzyldimethylamine, glycidyl phenyl ether, and phenol (2), have been synthesized and characterized by means of X-ray analysis. Complex1 is a precursor for the catalysts of selective isocyanate cyclotrimerization, while complex2 is one of those catalysts. In the crystal structure complex1 forms H-bonded cationic-anionic aggregates with proton transfer from phenol to the N-atom of the tertiary amine. Complex2 crystallizes as a monohydrate (2a) with a strong H-bond between the quaternary ammonium and phenolic components, and exists in crystals in the form of globular H-bonded dimeric hydrates. Possible pathways of dissociation of complex2a are discussed. The data obtained may be used as a basis for further interpretation of the regularities of cyclotrimerization of isocyanates catalyzed by complexes of this type.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No 1, pp. 92–97, January, 1993.     

Large effect of polydispersity on defect concentrations in colloidal crystals

We compute the equilibrium concentration of stacking faults and point defects in polydisperse hard-sphere crystals. We find that, while the concentration of stacking faults remains similar to that of monodisperse hard-sphere crystals, the concentration of vacancies decreases by about a factor of 2. Most strikingly, the concentration of interstitials in the maximally polydisperse crystal may be some six orders of magnitude larger than in a monodisperse crystal. We show that this dramatic increase in interstitial concentration is due to the increased probability of finding small particles and that the small-particle tail of the particle size distribution is crucial for the interstitial concentration in a colloidal crystal.     

Modification of Non-Hydrolytic Sol-Gel Derived Alumina by Solvent Treatments

The effect of wetting non-hydrolytic derived alumina xerogels with water and organic solvents in the 20–70°C range on the alumina's properties was investigated. Wetting with organic solvents does not affect the alumina. However, contact with water was found to change the sharp crystallization at 800°C to a continuous crystallization starting at 450°C. Water treatment for a day at room temperature (RT) followed by second calcination decreased the surface area by 10%. This decrease in surface area is less pronounced with increasing wetting periods. On the other hand water treatment at 50–70°C followed by a second calcination resulted in a surface area increase of up to 15%. Upon water treatment the total pore volume has decreased from 0.65 (cm³/gr) to 0.48 (cm³/gr) and the average pore size decreased from 6.8 nm to 4.1 nm. The Cl content was found to be uneffected by the water treatment, remaining at 2.5% wt. Wetting with water at elevated temperature (70°C) accelerated the morphological changes, eliminating the crystallization peak at 800°C in one hour. A dissolution-reprecipitation mechanism is suggested to explain the results. In addition, Mass-Spectroscopy of the effluent gas during heat treatment revealed the emission of CO₂ and water upon phase transition into -Al₂O₃, at 1150–1300°C.     

The effect of (natural) polyols on the initial colour of heavy metal- and zinc-free poly(vinyl chloride)

The propensity of (natural) polyols dispersed in heavy metal- and zinc-free PVC sheets to improve the initial colour, e.g. the colour during the first minutes of exposure to high processing temperatures (short-term stability), has been investigated. It is shown using W(Lab) values that the initial colour improves upon addition of polyols containing primary hydroxyl groups. The polyols act as HCl scavengers, presumably via an acid-catalysed S_N2 substitution of the primary hydroxyl groups by chloride ions. In contrast, polyols with only secondary or tertiary hydroxyl groups accelerate the thermal degradation of PVC. Notwithstanding, the efficacy of the (natural) polyols containing primary hydroxyl groups will be reduced if the polyol is susceptible to competitive acid-catalysed intramolecular cyclodehydration reactions under the processing conditions. This is substantiated by a comparison of the behaviour of mannitol and 3,4-di-O-methyl-d-mannitol. The methylated derivative, which is less prone to undergo intramolecular cyclodehydration, improves the initial colour of heavy metal- and zinc-free PVC sheets more significantly than mannitol itself.     

The reaction of propane sultone with cuanosine,adenosine, and related compounds

Propane sultone (3-hydroxypropanesulfonic acid-γ-lactone) which is a monofunctional directacting alkylating carcinogen, has been shown to react irreversibly with DNA from various sources in vitro. It reacts with guanosine in DMSO to yield the N-7 alkyl nucleoside, while reaction with 2′-deoxyguanosine yields the corresponding N-7 alkyl purine. Evidence for the structure of these products and of one formed when adenosine and propane sultone react is presented.     

Oxidative addition of the ethane C-C bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.