The Taming of Redox-Labile Phosphidotitanocene Cations

Tame d⁰ phosphidotitanocene cations stabilized with a pendant tertiary phosphane arm are reported. These compounds were obtained by one-electron oxidation of d¹ precursors with [Cp₂Fe][BPh₄]. The electronic structure of these compounds was studied experimentally (EPR, UV/Vis, and NMR spectroscopy, X-ray diffraction analysis) and through DFT calculations. The theoretical analysis of the bonding situation by using the electron localization function (ELF) shows the presence of π-interactions between the phosphido ligand and Ti in the d⁰ complexes, whereas dπ–pπ repulsion prevents such interactions in the d¹ complexes. In addition, CH–π interactions were observed in several complexes, both in solution and in the solid state, between the phosphido ligand and the phosphane arm. The d⁰ complexes were found to be light sensitive, and decompose through Ti−P bond homolysis to give Ti^III species. A naked d⁰ phosphidotitanocene cation has been trapped by reaction with diphenylacetylene, yielding a Ti/P frustrated Lewis pair (FLP), which was found to be less reactive than a previously reported Zr analog.     

A Probabilistic Analysis of the Power of Arithmetic Filters

The assumption of real-number arithmetic, which is at the basis of conventional geometric algorithms, has been seriously challenged in recent years, since digital computers do not exhibit such capability. A geometric predicate usually consists of evaluating the sign of some algebraic expression. In most cases, rounded computations yield a reliable result, but sometimes rounded arithmetic introduces errors which may invalidate the algorithms. The rounded arithmetic may produce an incorrect result only if the exact absolute value of the algebraic expression is smaller than some (small) ε , which represents the largest error that may arise in the evaluation of the expression. The threshold ε depends on the structure of the expression and on the adopted computer arithmetic, assuming that the input operands are error-free. A pair (arithmetic engine, threshold) is an arithmetic filter. In this paper we develop a general technique for assessing the efficacy of an arithmetic filter. The analysis consists of evaluating both the threshold and the probability of failure of the filter. To exemplify the approach, under the assumption that the input points be chosen randomly in a unit ball or unit cube with uniform density, we analyze the two important predicates ``which-side' and ``insphere.' We show that the probability that the absolute values of the corresponding determinants be no larger than some positive value V , with emphasis on small V , is Θ(V) for the which-side predicate, while for the insphere predicate it is Θ(V ^2/3 ) in dimension 1, O(V ^1/2 ) in dimension 2, and O(V ^1/2 ln (1/V)) in higher dimensions. Constants are small, and are given in the paper. Received September 15, 1996, and in revised form September 9, 1997.     

Nonlinear Multivariate SAR of Lepidoptera Pheromones

Abstract The combined use of the nonlinear mapping method with correspondence factor analysis allowed to derive interesting structure-chemoreception relationships in Lepidoptera. A chemotaxonomy of insects based on their responses to pheromones was also proposed.     

The role of bismuth as promoter in Pd–Bi catalysts for the selective oxidation of glucose to gluconate

Bismuth is a well-established promoter of noble metal-based catalysts for the selective liquid phase oxidation of alcohols, aldehydes and carbohydrates with molecular oxygen. Experiments were carried out to improve the understanding of the promoting role of bismuth in bimetallic Pd–Bi catalysts used for the selective oxidation of glucose to gluconate. In relationship with the fact that these catalysts undergo substantial bismuth leaching under the reaction conditions, particular attention was paid to the possible role played by the soluble fraction of bismuth in the oxidative process. Carbon-supported Pd–Bi/C catalysts characterized by various Bi–Pd compositions (0.33≤Bi/Pd≤3.0,10 wt.%Pd+Bi) were prepared from acetate-type precursors, tested under various experimental conditions and analyzed by X-ray diffractometry and X-ray photoelectron spectroscopy (XPS). Whatever the initial catalyst composition, the surface intensity ratio measured by XPS in used catalysts lies in the range 0.4–0.6, suggesting that the dynamic state of the catalyst involves the association of one Bi and two to three Pd atoms. The leaching process and the promoting effect itself are discussed in line with the formation of Bi–glucose and Bi–gluconate complexes present in solution but also as adsorbed species at the catalyst surface. The performances of a monometallic Pd/C catalyst are significantly improved in the presence of adequate amounts of soluble Bi. The involvement of the soluble fraction of bismuth in the overall mechanistic scheme of glucose oxidative dehydrogenation is suggested. The detrimental effect of large amounts of soluble bismuth is attributed to a too extensive adsorption of Bi–glucose complexes on the surface Pd atoms.     

Crystallographic,spectroscopic and electrochemical characterization of pyridine adducts of magnesium(II) and zinc(II) porphine complexes

A new purification method of magnesium(II) and zinc(II) porphine complexes (MgP and ZnP, respectively) by crystallization of their respective pyridine adducts is described. Pure MgP and ZnP can be regenerated by removal of the coordinated pyridine ligands by heating at 200 °C under vacuum. X-ray crystallographic structures of the pyridine adducts are presented for the first time. NMR analyses of the adducts reveal the coordination of two pyridine molecules. Electrochemical as well as UV-vis absorption spectroscopy analyses in DMF of MgP·(Py)₂, ZnP·(Py)₂, MgP and ZnP indicate that pyridine adducts are totally dissociated. Besides, oxidation peaks of these complexes are totally irreversible, revealing a high reactivity of the oxidized species. Electrolyses at the first oxidation potential lead to the formation of the meso-meso (ZnP)₂ and (MgP)₂ dimers, oligomers and polymers on the electrode surface, as attested by MALDI-TOF mass spectrometry and UV-vis absorption spectroscopy analyses of the crude solution.     

Delandtsheer–Doyen parameters for block-transitive point-imprimitive 2-designs

Designs, Codes and Cryptography - Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two...     

Oja centers and centers of gravity

Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.