Facile purification of rare cucurbiturils by affinity chromatography

A practical method for the separation and purification of cucurbituril (CB) hexamers was developed on the basis of affinity chromatography using aminopentylaminomethylated polystyrene beads. This recyclable resin, which can be used repeatedly, facilitates the general preparation of cucurbituril derivatives and compensates for the usually moderate yields and mixed products that characterize the acid-catalyzed synthesis of CB derivatives. This technique allows convenient, rapid isolation of rare substituted cucurbiturils, including hexacyclohexanocucurbit[6]uril and dodecamethylcucurbit[6]uril. [reaction: see text]     

Repulsive interaction can be a key design element of molecular rotary motors

Low-barrier molecular rotary motors having rotaxane architecture can be constructed using a cucurbituril host and a polyyne guest serving as stator and rotator, respectively. The repulsive interaction between these components is supported by molecular mechanics calculations with model systems and experimentally verified by X-ray crystallography with several synthetic host-guest complexes, all suggesting that the diyne rod floats at the center of the macrocyclic host with no apparent van der Waals contacts between them. Further support for these interactions is suggested by microcalorimetry measurements.     

Asymmetric synthesis of hexapropionate synthons by sequential enantiotopic group selective enolization of meso diketones

Meso 1,9-diketones (six to seven stereocenters) are readily obtained by stepwise or simultaneous two-directional aldol reactions of tetrahydro-4H-thiopyran-4-one with a thiopyran-derived aldehyde or dialdehyde. Enantioselective enolizations of these diketones with the lithium amide from (R,R)-bis(1-phenylethyl)amine occur with simultaneous kinetic resolution to give the mono-TMS enol ethers in >90% yields (BORSM) and >95% ee. The products are applicable to polypropionate synthesis. [reaction: see text]     

Magnetic exchange interactions and magneto-structural correlations in heterobridged μ-phenoxo-μ(1,1)-azide dinickel(II) compounds: a combined experimental and theoretical exploration

This investigation presents the syntheses, crystal structures, magnetic properties, and density functional theoretical modeling of magnetic behavior of two heterobridged μ-phenoxo-μ(1,1)-azido dinickel(II) compounds [Ni(II)(2)(L(1))(2)(μ(1,1)-N(3))(N(3))(H(2)O)]·CH(3)CH(2)OH (1) and [Ni(II)(2)(L(2))(2)(μ(1,1)-N(3))(CH(3)CN)(H(2)O)](ClO(4))·H(2)O·CH(3)CN (2), where HL(1) and HL(2) are the [1+1] condensation products of 3-methoxysalicylaldehyde and 1-(2-aminoethyl)-piperidine (for HL(1))/4-(2-aminoethyl)-morpholine (for HL(2)), along with density functional theoretical magneto-structural correlations of μ-phenoxo-μ(1,1)-azido dinickel(II) systems. Compounds 1 and 2 crystallize in orthorhombic (space group Pbca) and monoclinic (space group P2(1)/c) systems, respectively. The coordination environments of both metal centers are distorted octahedral. The variable-temperature (2-300 K) magnetic susceptibilities at 0.7 T of both compounds have been measured. The interaction between the metal centers is moderately ferromagnetic; J = 16.6 cm(-1), g = 2.2, and D = -7.3 cm(-1) for 1 and J = 16.92 cm(-1), g = 2.2, and D(Ni1) = D(Ni2) = -6.41 cm(-1) for 2. Broken symmetry density functional calculations of exchange interaction have been performed on complexes 1 and 2 and provide a good numerical estimate of J values (15.8 cm(-1) for 1 and 15.35 cm(-1) for 2) compared to experiments. The role of Ni-N bond length asymmetry on the magnetic coupling has been noted by comparing the structures and J values of complexes 1 and 2 together with previously published dimers 3 (Eur. J. Inorg. Chem. 2009, 4982), 4 (Inorg. Chem. 2004, 43, 2427), and 5 (Dalton Trans. 2008, 6539). Our extensive DFT calculations reveal an important clue to the mechanism of coupling where the orientation of the magnetic orbitals seems to differ with asymmetry in the Ni-N bond lengths. This difference in orientation leads to a large change in the overlap integral between the magnetic orbitals and thus the magnetic coupling. DFT calculations have also been extended to develop several magneto-structural correlations in this type of complexes and the correlation aim to focus on the asymmetry of the Ni-N bond lengths reveal that the asymmetry plays a proactive role in governing the magnitude of the coupling. From a completely symmetric Ni-N bond length, two behaviors have been noted: with a decrease in bond length there is an increase in the ferromagnetic coupling, while an increase in the bond lengths leads to a decrease in ferromagnetic interaction. The later correlation is supported by experiments. The magnetic properties of 1, 2, and three previously reported related compounds have been discussed in light of the structural parameters and also in light of the theoretical correlations determined here.     

Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs

We consider a class of two-stage stochastic integer programs with binary variables in the first stage and general integer variables in the second stage. We develop decomposition algorithms akin to the $L$ -shaped or Benders’ methods by utilizing Gomory cuts to obtain iteratively tighter approximations of the second-stage integer programs. We show that the proposed methodology is flexible in that it allows several modes of implementation, all of which lead to finitely convergent algorithms. We illustrate our algorithms using examples from the literature. We report computational results using the stochastic server location problem instances which suggest that our decomposition-based approach scales better with increases in the number of scenarios than a state-of-the art solver which was used to solve the deterministic equivalent formulation.