Evolution of the electronic properties of metallic single-walled carbon nanotubes with the degree of CCl2 covalent functionalization

The changes in energetic, structural, and electronic properties of the metallic (5,5) single-walled carbon nanotube (SWNT) with the degree of sidewall covalent functionalization of CCl(2) are investigated extensively by using density functional theory calculations. The saturation concentration of CCl(2) covalent functionalization is predicted to be 33.3%. The cycloadducts always adopt an open structure. A band gap opens as the functionalization concentration reaches 11% and then basically increases with increasing functionalization concentration. These results are in agreement with available experiments and can be applied to accurately predict the band gap of metallic SWNTs produced by the HiPco method at a given CCl(2) functionalization concentration.     

A facile and clean direct cyanation of heteroaromatic compounds using a recyclable hypervalent iodine(III) reagent

The facile and clean direct cyanating reaction of pyrroles and thiophenes has been achieved using a recyclable hypervalent iodine(III) reagent 1b by a simple solid-liquid separation of the products and the reagent.     

The Bingel monoadducts of La@C82: synthesis, characterization, and electrochemistry

The reaction of La@C82 with diethyl bromomalonate in the presence of base (the Bingel reaction) generated five monoadducts which have been fully characterized. It was found that four of them (mono-A, -B, -C, and -D) are ESR-inactive, suggesting singly bonded regioisomers. In contrast, the fifth product (mono-E) is ESR-active, indicating that it possesses a cyclic moiety between the appended malonate group and the fullerene cage, analogous to conventional Bingel adducts. The differences in the molecular structures of mono-A, -B, -C, and -E result in varying thermal stabilities and electrochemical behavior. In particular, the singly bonded monoadducts undergo the retro-Bingel reaction either under thermal treatment or during electron transfer on the cyclic voltammetric timescale. However, mono-E shows remarkable thermal stability and perfect reversibility under the same experimental conditions.     

13C NMR spectroscopic study of scandium dimetallofullerene, Sc2@C84 vs. Sc2C2@C82

Although Sc2C84 has been widely believed to have the form Sc2@C84, the present 13C NMR study reveals that it is a scandium carbide metallofullerene, Sc2C2@C82, which has a C82(C(3v)) cage.     

Supramolecular complexes of La@C82 with unsaturated thiacrown ethers

The paramagnetic La@C82-A(C2v) with unsaturated thiacrown ethers forms 1 : 1 host-guest complexes of [La@C82-A(C2v)]-[D]+ in solution as a result of electron transfer.     

Synthesis of substituted anthracenes, pentaphenes and trinaphthylenes via alkyne-cyclotrimerization reaction

The [2+2+2] cycloaddition reaction of 1,6-diynes 3 with 4-aryl-2-butyn-1-ols 4 and the following oxidation of the resulting benzylic alcohols to the aldehydes 1 and then treatment with an acid catalyst provided annulated anthracenes 2 in good yields.     

Fermionic solutions of chiral Gross–Neveu and Bogoliubov–de Gennes systems in nonlinear Schrödinger hierarchy

The chiral Gross–Neveu model or equivalently the linearized Bogoliubov–de Gennes equation has been mapped to the nonlinear Schrödinger (NLS) hierarchy in the Ablowitz–Kaup–Newell–Segur formalism by Correa, Dunne and Plyushchay. We derive the general expression for exact fermionic solutions for all gap functions in the arbitrary order of the NLS hierarchy. We also find that the energy spectrum of the n  -th NLS hierarchy generally has n+1$n+1$ gaps. As an illustration, we present the self-consistent two-complex-kink solution with four real parameters and two fermion bound states. The two kinks can be placed at any position and have phase shifts. When the two kinks are well separated, the fermion bound states are localized around each kink in most parameter region. When two kinks with phase shifts close to each other are placed at distance as short as possible, the both fermion bound states have two peaks at the two kinks, i.e., the delocalization of the bound states occurs.     

A limiting analysis on regularization of singular SDP and its implication to infeasible interior-point algorithms

We consider primal-dual pairs of semidefinite programs and assume that they are singular, i.e., both primal and dual are either weakly feasible or weakly infeasible. Under such circumstances, strong duality may break down and the primal and dual might have a nonzero duality gap. Nevertheless, there are arbitrary small perturbations to the problem data which would make them strongly feasible thus zeroing the duality gap. In this paper, we conduct an asymptotic analysis of the optimal value as the perturbation for regularization is driven to zero. Specifically, we fix two positive definite matrices, \(I_p\) and \(I_d\), say, (typically the identity matrices), and regularize the primal and dual problems by shifting their associated affine space by \(\eta I_p\) and \(\varepsilon I_d\), respectively, to recover interior feasibility of both problems, where \(\varepsilon \) and \(\eta \) are positive numbers. Then we analyze the behavior of the optimal value of the regularized problem when the perturbation is reduced to zero keeping the ratio between \(\eta \) and \(\varepsilon \) constant. A key feature of our analysis is that no further assumptions such as compactness or constraint qualifications are ever made. It will be shown that the optimal value of the perturbed problem converges to a value between the primal and dual optimal values of the original problems. Furthermore, the limiting optimal value changes “monotonically” from the primal optimal value to the dual optimal value as a function of \(\theta \), if we parametrize \((\varepsilon , \eta )\) as \((\varepsilon , \eta )=t(\cos \theta , \sin \theta )\) and let \(t\rightarrow 0\). Finally, the analysis leads us to the relatively surprising consequence that some representative infeasible interior-point algorithms for SDP generate sequences converging to a number between the primal and dual optimal values, even in the presence of a nonzero duality gap. Though this result is more of theoretical interest at this point, it might be of some value in the development of infeasible interior-point algorithms that can handle singular problems.