A ditopic calix[6]arene ligand with N-methylimidazole and 1,2,3-triazole substituents: synthesis and coordination with Zn(II) cations

The first member of a new class of ditopic calix[6]arene has been synthesized, which is decorated with three N-methylimidazoles at the small rim and three 1,4-disubstituted-1,2,3-triazoles at the large rim. The coordination of a first Zn(II) cation selectively takes place at the small rim. Addition of a second equivalent results in the complexation of the three triazoles, providing a rare example of 1,2,3-triazole ligands embedded within a supramolecular system.     

Isotopic labeling for determination of enantiomeric purity by 2H NMR spectroscopy

The use of 2H NMR spectroscopy as a tool for the analysis of enantiomeric purity is reported. Enantiopure isotopically chiral substrates bearing a monodeuterated methylene unit were prepared; introduction of an additional asymmetric center leads to diastereomers which can be distinguished by 2H NMR on a standard spectrometer. The assays allow for simple semiquantitative analysis of asymmetric transformations.     

Synthesis of libraries of thiazole, oxazole and imidazole-based cyclic peptides from azole-based amino acids. A new synthetic approach to bistratamides and didmolamides

Treatment of a 1 : 1 mixture of the thiazole-based amino acids 8a and 8b with FDPP-i-Pr(2)NEt in CH(3)CN gave a mixture of the cyclic trimers 14, 15, 16 and 17 and the cyclic tetramers 19 and 23 in the ratio 2 : 7 : 5 : 8 : 1 : 1 and in a combined yield of 70%. Separate coupling reactions between the bisimidazole amino acid 45 and the thiazole/oxazole amino acids 43a and 42a in the presence of FDPP-i-Pr(2)NEt led to the bisimidazole based cyclic trimers 55 and 57 respectively (54-57%) and to the cyclic tetramer 56 (8-11%). Similar coupling reactions involving the bisthiazole and bisoxazole amino acids 49 and 47 with the imidazole/oxazole/thiazole amino acids 41a, 42a and 43a gave rise to the library of oxazole, thiazole and imidazole-based cyclic peptides 58, 59, 60, 61, 62, 63, 64 and 65. A coupling reaction between the bisthiazole amino acid 49 and the oxazole amino acid 73 led to an efficient (36% overall) synthesis of bistratamide H (67) found in the ascidian Lissoclinum bistratum. Coupling reactions involving oxazolines with thiazole amino acids were less successful. Thus, a coupling reaction between the phenylalanine-based oxazoline amino acid 71a and either the thiazole amino acid 8a or the bisthiazole amino acid 74 gave only a 2% yield of the cyclic hexapeptide didmolamide A (4) found in the ascidian Didemnum molle. Didmolamide B (68) was obtained in 9% yield from a coupling reaction between 74 and the phenylalanine threonine amino acid 72, using either FDPP or DPPA.     

Drastic effects of the second coordination sphere on neutral vs. anionic guest binding to a biomimetic Cu(II) center embedded in a calix[6]aza-cryptand

A calix[6]arene capped by a tmpa unit provides Cu(ii) funnel complexes that, for the first time, accept not only neutral guest ligands but also anionic ones such as a hydroxide, which is due to a small conformational change in the calixarene cone.     

A hydrophilic cyclodextrin duplex forming supramolecular assemblies by physical cross-linking of a biopolymer

New beta-cyclodextrin (beta-CD) dimeric species have been synthesised in which the two CD moieties are connected by one or two hydrophilic oligo(ethylene oxide) spacers. Their complexation with sodium adamantylacetate (free adamantane) and adamantane-grafted chitosan (AD-chitosan) was then studied by different complementary techniques and compared with their hydrophobic counterparts that contain an octamethylene spacer. Isothermal titration calorimetry experiments have demonstrated that the use of hydrophilic spacers between the two CDs instead of aliphatic chains makes almost all of the CD cavities available for the inclusion of free adamantane. Investigation of the interaction of the CDs with AD-chitosan by viscosity measurements strongly suggests that the molecular conformation of the CD dimeric species plays a crucial role in their cross-linking with the biopolymer. The derivative doubly linked with hydrophilic arms, also called a duplex, has been shown to be a more efficient cross-linking agent than its singly bridged counterpart, referred to as a dimer. Hence, only 0.5 molar equivalents of the hydrophilic duplex with respect to adamantane was required to obtain the maximum viscosity, whereas in the case of the duplex with aliphatic spacers, the maximum viscosity was achieved with a [duplex]/[AD] ratio of about 1.7 (corresponding to a [CD]/[AD] ratio of 2.5), but with a higher value. To clarify the relationships between the molecular architecture and complexation properties, computational studies were also performed that clearly confirmed the importance of double bridging.     

Infrared spectrum and structure of thorimine (HN=ThH2)

Laser-ablated thorium atoms react with ammonia to form thorimine (NH=ThH(2)), the first actinide imine to be reported. This work underscores the high reactivity of thorium atoms, particularly for N-H bond activation, reveals a new type of multiple bond to actinide atoms, and shows that this bond is strong for thorium as a result of an important contribution from the f orbitals.     

Synthesis and spectral determination of new derivatives of 1‐[(p‐substituted)phenyl]‐3a‐[(o‐ and p‐substituted)phenyl]‐5‐chloro‐9‐methylthio‐10,3a‐dihydro‐[1,2,4]‐oxadiazolo[2,3‐b][1,4]benzodiazepines

A new synthesis to obtain eight novel derivatives of 1‐[(p‐substituted)phenyl]‐3a‐[(o‐ and p‐substituted)‐phenyl]‐5‐chloro‐9‐methylthio‐10,3a‐dihydro‐[1,2,4]‐oxadiazolo[2,3‐b][1,4]benzodiazepines with possible biological and pharmacological activity as anxiolytics, hypnotics, anticonvulsants in the central nervous system. The final products were obtained by condensation between 2‐methylthio‐5‐[(o‐; p‐substituted)‐phenyl]‐3H‐7‐chloro‐[1,4]benzodiazepine with benzonitrile oxide generated in situ from benzohydroxamoyl chloride in triethylamine. The structure of all products was corroborated by ir, ¹H‐nmr, ¹³C‐nmr, with experiments bidimensional and ms in low and high resolution.     

Stable Marriage and Genetic Algorithms: A Fertile Union

We describe a pair of genetic algorithms for solving two stable matching problems. Both stable matching problems we will consider involve a set of applicants for positions and a set of employers. Each applicant and each employer prepares a rank order list of a subset of the actors in the other set. The goal is to find an assignment of applicants to employers in which if applicant a is not assigned to employer b then either a prefers his assignment to b or b prefers its assignment toa . In other words, no applicant/employer pair can both improve their situations by dropping their current assignments in favor of each other. Our goal will be to enumerate the stable matchings. One of the problems we will consider is the well-known stable marriage problem, in which neither applicant nor employer preference lists are linked. In the other problem, we will allow pairs of applicants who form a couple to submit joint rank order lists of ordered pairs of employers.     

A Class of Integrable Flows on the Space of Symmetric Matrices

For a given skew symmetric real n × n matrix N, the bracket [X, Y] _N = XNY − YNX defines a Lie algebra structure on the space Sym(n, N) of symmetric n × n real matrices and hence a corresponding Lie-Poisson structure. The purpose of this paper is to investigate the geometry, integrability, and linearizability of the Hamiltonian system , or equivalently in Lax form, the equation on this space along with a detailed study of the Poisson geometry itself. If N has distinct eigenvalues, it is proved that this system is integrable on a generic symplectic leaf of the Lie-Poisson structure of Sym(n, N). This is established by finding another compatible Poisson structure. If N is invertible, several remarkable identifications can be implemented. First, (Sym(n, N), [·, ·]) is Lie algebra isomorphic with the symplectic Lie algebra associated to the symplectic form on given by N ⁻¹. In this case, the system is the reduction of the geodesic flow of the left invariant Frobenius metric on the underlying symplectic group Sp(n, N ⁻¹). Second, the trace of the product of matrices defines a non-invariant non-degenerate inner product on Sym(n, N) which identifies it with its dual. Therefore Sym(n, N) carries a natural Lie-Poisson structure as well as a compatible “frozen bracket” structure. The Poisson diffeomorphism from Sym(n, N) to maps our system to a Mischenko-Fomenko system, thereby providing another proof of its integrability if N is invertible with distinct eigenvalues. Third, there is a second ad-invariant inner product on Sym(n, N); using it to identify Sym(n, N) with itself and composing it with the dual of the Lie algebra isomorphism with , our system becomes a Mischenko- Fomenko system directly on Sym(n, N). If N is invertible and has distinct eigenvalues, it is shown that this geodesic flow on Sym(n, N) is linearized on the Prym subvariety of the Jacobian of the spectral curve associated to a Lax pair formulation with parameter of the system. If, on the other hand, N has nullity one and distinct eigenvalues, in spite of the fact that the system is completely integrable, it is shown that the flow does not linearize on the Jacobian of the spectral curve. Research partially supported by NSF grants CMS-0408542 and DMS-0604307. Research partially supported by the Swiss SCOPES grant IB7320-110721/1, 2005-2008, and MEdC Contract 2-CEx 06-11-22/25.07.2006. Research partially supported by the California Institute of Technology and NSF-ITR Grant ACI-0204932. Research partially supported by the Swiss NSF and the Swiss SCOPES grant IB7320-110721/1.