A Peri‐tetracene Diradicaloid: Synthesis and Properties

Peri‐acenes are good model compounds for zigzag graphene nanoribbons, but their synthesis is extremely challenging owing to their intrinsic open‐shell diradical character. Now, the successful synthesis and isolation of a stable peri‐tetracene derivative PT‐2ClPh is reported; four 2,6‐dichlorophenyl groups are attached onto the most reactive sites along the zigzag edges. The structure was confirmed by X‐ray crystallographic analysis and its electronic properties were systematically investigated by both experiments and theoretical calculations. It exhibits an open‐shell singlet ground state with a moderate diradical character (y₀=51.5 % by calculation) and a small singlet–triplet gap (ΔE_S‐T=?2.5 kcal mol^?1 by SQUID measurement). It displays global aromatic character, which is different from the smaller‐size bisanthene analogue BA‐CF3 .     

Single-molecule spectroscopic investigation of energy migration processes in cyclic porphyrin arrays

Covalently linked cyclic porphyrin arrays have been synthesized to mimic natural light-harvesting apparatuses and to investigate the highly efficient energy migration processes occurring in these systems for future applications in molecular photonics. To avoid an ensemble-averaged picture, we performed a single-molecule spectroscopic study on the energy migration processes of cyclic porphyrin arrays and a linear model compound embedded in a rigid polymer matrix by recording fluorescence intensity trajectories, by performing coincidence measurements, and by doing wide-field defocused imaging. Our study demonstrates efficient energy migration within the cyclic porphyrin arrays at the single-molecule level. By comparison with the data of the linear model compound, we could pinpoint the role of the dipole-dipole coupling between diporphyrin subunits and the rigidity of the cyclic structures on the energy transfer processes.     

Optical fibre chemical sensor for trace vanadium(V) determination based on newly synthesized palm based fatty hydroxamic acid immobilized in polyvinyl chloride membrane

Fatty hydroxamic acid (FHA) immobilized in polyvinyl chloride (PVC) has been studied as a sensor element of an optical fibre chemical sensor for V(V). By using this instrument, V(V) in solution has been determined in the log concentration range of 0-2.5 (i.e. 1.0-300 mg/L). The detection limit was 1.0 mg/L. The relative standard deviation (R.S.D.) of the method for the reproducibility study at V(V) concentration of 200 mg/L and 300 mg/L were calculated to be 2.9% and 2.0%, respectively. Interference from foreign ions was also studied at 1:1 mole ratio of V(V):foreign ions. It was found that, Fe(III) ion interfered most in the determination of vanadium(V). Excellent agreement with ICP-AES method was achieved when the proposed method was applied towards determination of V(V).     

Supramolecular cuboctahedra with aggregation-induced emission enhancement and external binding ability

Beyond the AIE (aggregation-induced emission) phenomenon in small molecules, supramolecules with AIE properties have evolved in the AIE family and accelerated the growth of supramolecular application diversity. Inspired by its mechanism, particularly the RIV (restriction of intramolecular vibrations) process, a feasible strategy of constructing an AIE-supramolecular cage based on the oxidation of sulfur atoms and coordination of metals is presented. In contrast to previous strategies that used molecular stacking to limit molecular vibrations, we achieved the desired goal using the synergistic effects of coordination-driven self-assembly and oxidation. Upon assembling with zinc ions, S1 was endowed with a distinct AIE property compared with its ligand L1, while S2 exhibited a remarkable fluorescence enhancement compared to L2. Also, the single cage-sized nanowire structure of supramolecules was obtained via directional electrostatic interactions with multiple anions and rigid-shaped cationic cages. Moreover, the adducts of zinc porphyrin and supramolecules were investigated and characterized by 2D DOSY, ESI-MS, TWIM-MS, UV-vis, and fluorescence spectroscopy. The protocol described here enriches the ongoing research on tunable fluorescence materials and paves the way towards constructing stimuli-responsive luminescent supramolecular cages.

Beyond the AIE (aggregation-induced emission) phenomenon in small molecules, supramolecules with AIE properties have evolved in the AIE family and accelerated the growth of supramolecular application diversity.     

[Cs6Cl][Fe24Se26]: A Host–Guest Compound with Unique Fe–Se Topology

The novel host–guest compound [Cs₆Cl][Fe₂₄Se₂₆] (I4/mmm; a=11.0991(9), c=22.143(2) Å) was obtained by reacting Cs₂Se, CsCl, Fe, and Se in closed ampoules. This is the first member of a family of compounds with unique Fe–Se topology, which consists of edge‐sharing, extended fused cubane [Fe₈Se₆Se_8/3] blocks that host a guest complex ion, [Cs₆Cl]⁵⁺. Thus Fe is tetrahedrally coordinated and divalent with strong exchange couplings, which results in an ordered antiferromagnetic state below T_N=221 K. At low temperatures, a distribution of hyperfine fields in the Mössbauer spectra suggests a structural distortion or a complex spin structure. With its strong Fe–Se covalency, the compound is close to electronic itinerancy and is, therefore, prone to exhibit tunable properties.     

On the polyhedral lift-and-project methods and the fractional stable set polytope

We study two polyhedral lift-and-project operators (originally proposed by Lovász and Schrijver in 1991) applied to the fractional stable set polytopes. First, we provide characterizations of all valid inequalities generated by these operators. Then, we present some seven-node graphs on which the operator enforcing the symmetry of the matrix variable is strictly stronger on the odd-cycle polytope of these graphs than the operator without this symmetry requirement. This disproves a conjecture of Lipták and Tunçel from 2003.     

Approximating the complexity measure of Vavasis-Ye algorithm is NP-hard

Given an m×n integer matrix A of full row rank, we consider the problem of computing the maximum of ∥B ^-1 A∥₂ where B varies over all bases of A. This quantity appears in various places in the mathematical programming literature. More recently, logarithm of this number was the determining factor in the complexity bound of Vavasis and Ye’s primal-dual interior-point algorithm. We prove that the problem of approximating this maximum norm, even within an exponential (in the dimension of A) factor, is NP-hard. Our proof is based on a closely related result of L. Khachiyan [1]. Received November 13, 1998 / Revised version received January 20, 1999? Published online May 12, 1999