Novel synthesis and functionalization of ortho-ortho disubstituted biphenyls and a highly condensed novel heterocycle using radical cyclization reaction

This paper describes a novel synthetic route for the preparation of ortho-ortho disubstituted biphenyls and compounds possessing highly condensed ring system represented by structures X and Y, respectively. Several approaches, such as intermolecular Grubb's olefin metathesis, Heck and, Suzuki reactions were incorporated to functionalize the core structures of X and Y making it suitable for the preparation of a library of compounds.     

A new synthetic route for axially chiral secondary amines with binaphthyl backbone and their applications in asymmetric Michael reaction of aldehydes to nitroalkenes

A new synthetic route for binaphthyl-based secondary amines has been developed. The key features of this route include the selective direct esterification of the binaphthyl structure at the 3- or 3,3'-position and the methylation by a Negishi cross-coupling reaction. Based on the new approach, a series of 3-monosubstituted and 3,3'-disubstituted chiral secondary amines with a binaphthyl backbone were synthesized and screened in the Michael reaction of aldehydes to various nitroalkenes. 3-Monosubstituted secondary amine 7c was proved to be the best catalyst, affording high yields (up to 95%), good to excellent enantioselectivities (up to 99%) and diastereoselectivities (syn/anti up to 99:1) under the optimized conditions.     

Pairs of partitions without repeated odd parts

We prove two identities related to overpartition pairs. One of them gives a generalization of an identity due to Lovejoy, which was used in a joint work by Bringmann and Lovejoy to derive congruences for overpartition pairs. We apply our two identities on pairs of partitions where each partition has no repeated odd parts. We also present three partition statistics that give combinatorial explanations to a congruence modulo 3 satisfied by these partition pairs.     

On linear and semidefinite programming relaxations for hypergraph matching

The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph. This is a well-studied problem in combinatorial optimization and graph theory with various applications. The best known approximation algorithms for this problem are all local search algorithms. In this paper we analyze different linear and semidefinite programming relaxations for the hypergraph matching problem, and study their connections to the local search method. Our main results are the following:

We consider the standard linear programming relaxation of the problem. We provide an algorithmic proof of a result of Füredi, Kahn and Seymour, showing that the integrality gap is exactly ${k-1+\frac{1}{k}}$ for k-uniform hypergraphs, and is exactly k ? 1 for k-partite hypergraphs. This yields an improved approximation algorithm for the weighted 3-dimensional matching problem. Our algorithm combines the use of the iterative rounding method and the fractional local ratio method, showing a new way to round linear programming solutions for packing problems.

We study the strengthening of the standard LP relaxation by local constraints. We show that, even after linear number of rounds of the Sherali-Adams lift-and-project procedure on the standard LP relaxation, there are k-uniform hypergraphs with integrality gap at least k ? 2. On the other hand, we prove that for every constant k, there is a strengthening of the standard LP relaxation by only a polynomial number of constraints, with integrality gap at most ${\frac{k+1}{2}}$ for k-uniform hypergraphs. The construction uses a result in extremal combinatorics.

We consider the standard semidefinite programming relaxation of the problem. We prove that the Lovász ${\vartheta}$ -function provides an SDP relaxation with integrality gap at most ${\frac{k+1}{2}}$ . The proof gives an indirect way (not by a rounding algorithm) to bound the ratio between any local optimal solution and any optimal SDP solution. This shows a new connection between local search and linear and semidefinite programming relaxations.

     

Synthesis and structure characterization of ladder-like polymethylsilsesquioxane (PMSQ) by isolation of stereoisomer

The stereo cyclic siloxane compounds having tetra hydroxyl and tetra methyl group were synthesized by hydrolysis of tetrahydrido tetramethyl cyclosiloxane consisting of four stereoisomers. Among the stereo cyclic isomers, cis-trans-cis tetrahydroxyl tetramethyl cyclosiloxane (2) was separated by recrystallization and was used as a monomer species for preparation of ladder-like polymethylsilsesquioxane (PMSQ). The isolated isomer was directly polymerized in THF with potassium carbonate (K₂CO₃) by systematic ring condensation. The hydrolyzed stereoisomers were characterized by ¹H and ²⁹Si NMR, and HPLC. The structure of the synthesized PMSQs were characterized by size exclusion chromatography (SEC), MALDI-TOF mass, ²⁹Si NMR, and small angle X-ray scattering (SAXS).     

Crystal growth, structure, and physical properties of LnCu2(Al,Si)5 (Ln = La and Ce)

LnCu(2)(Al,Si)(5) (Ln = La and Ce) were synthesized and characterized. These compounds adopt the SrAu(2)Ga(5) structure type and crystallize in the tetragonal space group P4/mmm with unit cell dimensions of a ≈ 4.2 ? and c ≈ 7.9 ?. Herein, we report the structure as obtained from single crystal X-ray diffraction. Additionally, we report the magnetic susceptibility, magnetization, resistivity, and specific heat capacity data obtained for polycrystalline samples of LnCu(2)(Al,Si)(5) (Ln = La and Ce).     

Spin-adapted density matrix renormalization group algorithms for quantum chemistry

We extend the spin-adapted density matrix renormalization group (DMRG) algorithm of McCulloch and Gulacsi [Europhys. Lett. 57, 852 (2002)] to quantum chemical Hamiltonians. This involves using a quasi-density matrix, to ensure that the renormalized DMRG states are eigenfunctions of S?(2), and the Wigner-Eckart theorem, to reduce overall storage and computational costs. We argue that the spin-adapted DMRG algorithm is most advantageous for low spin states. Consequently, we also implement a singlet-embedding strategy due to Tatsuaki [Phys. Rev. E 61, 3199 (2000)] where we target high spin states as a component of a larger fictitious singlet system. Finally, we present an efficient algorithm to calculate one- and two-body reduced density matrices from the spin-adapted wavefunctions. We evaluate our developments with benchmark calculations on transition metal system active space models. These include the Fe(2)S(2), [Fe(2)S(2)(SCH(3))(4)](2-), and Cr(2) systems. In the case of Fe(2)S(2), the spin-ladder spacing is on the microHartree scale, and here we show that we can target such very closely spaced states. In [Fe(2)S(2)(SCH(3))(4)](2-), we calculate particle and spin correlation functions, to examine the role of sulfur bridging orbitals in the electronic structure. In Cr(2) we demonstrate that spin-adaptation with the Wigner-Eckart theorem and using singlet embedding can yield up to an order of magnitude increase in computational efficiency. Overall, these calculations demonstrate the potential of using spin-adaptation to extend the range of DMRG calculations in complex transition metal problems.     

Selective surface reactions for Janus ORMOSIL particles with multiple functional groups using an ordered monolayer film at liquid-liquid interface

Monodispersed, submicron-sized Janus ORMOSIL particles with multiple functional groups were prepared by the selective surface reaction of a monolayer film formed at a hexane-water interface. A well-ordered monolayer film was obtained by self-assembly of ORMOSIL particles with multiple functional groups at hexane-water interface. The photopolymerization of an ordered monolayer containing ORMOSIL particles yields a rigid film strong enough to maintain its integrity for transfer and further chemical reaction. The chemical reaction of this ordered film with organic and inorganic functional groups produced Janus ORMOSIL particles with multiple functional groups. The morphologies, structures, and chemical compositions of monolayer films and Janus ORMOSIL particles were characterized by FT-IR, solid state NMR, X-ray diffraction (XRD), optical microscopy (OM), electron microscopies (SEM and TEM), and confocal laser scanning microscopy.     

Measurement and analysis of forces in bubble and droplet systems using AFM

The use of atomic force microscopy to measure and understand the interactions between deformable colloids - particularly bubbles and drops - has grown to prominence over the last decade. Insight into surface and structural forces, hydrodynamic drainage and coalescence events has been obtained, aiding in the understanding of emulsions, foams and other soft matter systems. This article provides information on experimental techniques and considerations unique to performing such measurements. The theoretical modelling frameworks which have proven crucial to quantitative analysis are presented briefly, along with a summary of the most significant results from drop and bubble AFM measurements. The advantages and limitations of such measurements are noted in the context of other experimental force measurement techniques.     

Mechanism for the reaction of 2-naphthol with N-methyl-N-phenyl-hydrazine suggested by the density functional theory investigations

For the first time the computed mechanisms for the novel reaction of 2-naphthol with N-methyl-N-phenylhydrazine, leading to 1-amino-2-naphthol (Tang et al., J Am Chem Soc 2008, 130, 5840), have been investigated using the density functional theory. Four distinct possible pathways were evaluated: two amination mechanisms with the attack of NH(2) group respectively at the α-position C1 and β-position C3 atoms of 2-naphthol (pathways 1 and 2) as well as two rearrangement processes with displacement of the phenolic hydroxyl group followed by the benzidine-like rearrangement at the α-position C1 and β-position C3 atoms of 2-naphthol, respectively (pathways 3 and 4). Solvent effect has been tested based on the optimized geometries of the stationary points in solution at the B3LYP/PCM/6-31+G(d,p) level of theory with an averaged dielectric constant of binary solvent. Single-point energies of the optimized structures have been calculated using three hybrid density functionals, B3LYP, MPW3LYP, and B3PW91 with the 6-311++G(3df,2p) basis set. Our computed results clearly manifest that pathway 1 (α-amination) has the highest possibility to occur, with the Gibbs free energies being lower by 6 to 20 kcal/mol compared with the other three pathways, which leads to 1-amino-2-naphthol and N-methylaniline as products. It is in excellent agreement with the experimental observation.