Zn(II) Robson macrocycles as templates for chelating diphosphines

Chelating diphosphines were constructed using dinuclear Zn(II) complexes of Robson macrocycles (Zn-RMCs) as templates. The assembly process is driven by the interaction between the metal centers (Lewis acids) with anionic and neutral Lewis base-functionalized monophosphines. The stability of the final structure depends on the geometry and the affinity of the functional groups of the ditopic phosphines and on the structure of the RMC. In the free ligand the ditopic phosphines coordinate at opposite faces of the pseudo-planar macrocycle as is shown in the molecular structure of several of the assemblies, according to X-ray diffraction. Pre-organization of the system by coordinating the phosphorus atoms to a transition metal center enforced coordination of the functional groups at the same face of the RMC. For several templated diphosphines cis-PtCl(2) complexes were identified by NMR. The in situ assembled diphosphines showed a chelating effect in the rhodium catalyzed hydroformylation of 1-octene. Combination of Zn-RMC 3 and phosphine A gave the highest l/b ratio (13) in acetonitrile.     

Enantioselective supramolecular catalysis induced by remote chiral diols

A new method of creating libraries of chiral diphosphines is presented. Supramolecular coordination compounds based on Ti, Rh, achiral ditopic ligands, and chiral diols were synthesized by in situ mixing and used as catalysts in the asymmetric hydrogenation of (Z)-methyl 2-acetamido-3-phenylacrylate, giving ee's of up to 92%. The ditopic ligands contain a Schiff base that coordinates to the assembly metal Ti and a phosphine as a ligand for Rh. Chirality is introduced by coordination of the chiral diols to Ti. The controlling chiral center and the substrate are separated by as much as 13 ?.     

Relationship between conformational flexibility and chelate cooperativity

A family of four biscarbamates (AA) and four bisphenols (DD) were synthesized, and H-bonding interactions between all AA?DD combinations were characterized using (1)H NMR titrations in carbon tetrachloride. A chemical double mutant cycle analysis shows that there are no secondary electrostatic interactions or allosteric cooperativity in these systems, and the system therefore provides an ideal platform for investigating the relationship between chemical structure and chelate cooperativity. Effective molarities (EMs) were measured for 12 different systems, where the number of rotors in the chains connecting the two H-bond sites was varied from 5 to 20. The association constants vary by less than an order of magnitude for all 12 complexes, and the variation in EM is remarkably small (0.1-0.9 M). The results provide a relationship between EM and the number of rotors in the connecting chains (r): EM ≈ 10r(-3/2). The value of 10 M is the upper limit for the value of EM for a noncovalent intramolecular interaction. Introduction of rotors reduces the value of EM from this maximum in accord with a random walk analysis of the encounter probability of the chain ends (r(-3/2)). Noncovalent EMs never reach the very high values observed for covalent processes, which places limitations on the magnitudes of the effects that one is likely to achieve through the use of chelate cooperativity in supramolecular assembly and catalysis. On the other hand, the decrease in EM due to the introduction of conformational flexibility is less dramatic than one might expect based on the behavior of covalent systems, which limits the losses in binding affinity caused by poor preorganization of the interaction sites.     

Synthesis of 3-methoxyazetidines via an aziridine to azetidine rearrangement and theoretical rationalization of the reaction mechanism

The synthetic utility of N-alkylidene-(2,3-dibromo-2-methylpropyl)amines and N-(2,3-dibromo-2-methylpropylidene)benzylamines was demonstrated by the unexpected synthesis of 3-methoxy-3-methylazetidines upon treatment with sodium borohydride in methanol under reflux through a rare aziridine to azetidine rearrangement. These findings stand in contrast to the known reactivity of the closely related N-alkylidene-(2,3-dibromopropyl)amines, which are easily converted into 2-(bromomethyl)aziridines under the same reaction conditions. A thorough insight into the reaction mechanism was provided by both experimental study and theoretical rationalization.     

Limit theorems for convex hulls

It is shown that the process of vertices of the convex hull of a uniform sample from the interior of a convex polygon converges locally, after rescaling, to a strongly mixing Markov process, as the sample size tends to infinity. The structure of the limiting Markov process is determined explicitly, and from this a central limit theorem for the number of vertices of the convex hull is derived. Similar results are given for uniform samples from the unit disk.     

The mean square error of a randomly discounted sequence of uncertain payments

Expressions are developed for the mean square deviation between a discounted sequence of uncertain payments and the estimated present value. These formulas incorporate random variation from four sources: (1) from the fact that expected values of individual payments are estimated, (2) from the fact that future discount factors are estimated, (3) random variation in the events that give rise to future payments, and (4) random variation in future discount rates. The results extend and encompass existing expressions based on the assumed constancy of one or more of the random vectors.     

Comparison of three sequential extraction procedures to describe metal fractionation in anaerobic granular sludges

In the last few decades, several sequential extraction procedures have been developed to quantify the chemical status of metals in the solid phase. In this study, three extraction techniques (modified [A. Tessier, P.G.C. Campbell, M. Bisson, Anal. Chem. 51 (1979) 844]; [R.C. Stover, L.E. Sommers, D.J. Silvera, J. Water Pollut. Con. F. 48 (1976) 2165]; and the Bureau Communautaire de Reference (BCR) [K.F. Mossop, C.M. Davidson, Anal. Chim. Acta 478 (2003) 111]) were applied to study the distribution of trace (Co, Ni, Zn and Cu) and major (Mn and Fe) elements in two different anaerobic granular sludges from full-scale methanogenic wastewater treatment plants. The Stover scheme displayed a higher number of fractions that induces a poor recovery compared to the other schemes. The sequential extraction scheme recommended by BCR and the modified Tessier scheme gave similar trends and are sufficiently repeatable and reproducible for application in fractionation studies. However, the BCR scheme seems to be of limited utilisation to study anaerobic matrixes because the extraction stage for its reducible fraction may release substantial amounts of trace elements bound to the organic/sulfides fraction, and consequently, the recovery of trace elements in the oxide fraction may be overestimated at the expense of the oxidisable fraction. As a final conclusion, the modified Tessier scheme seems to be the most suitable scheme to study the metal partitioning in anaerobic granular sludges.