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.     

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.     

Synthesis and photochemical reaction of novel p-alkylcalix[n]arene derivatives containing cationically polymerizable groups

New photoreactive p-methylcalix[6]arene (MCA) derivatives containing cationically polymerizable groups such as propargyl ether (calixarene 1), allyl ether (calixarene 2), and ethoxy vinyl ether (calixarene 3) groups were synthesized with 80, 74, and 84% yields by the substitution reaction of MCA with propargyl bromide, allyl bromide, and 2-chloroethyl vinyl ether (CEVE), respectively, in the presence of either potassium hydroxide or sodium hydride by using tetrabutylammonium bromide (TBAB) as a phase transfer catalyst (PTC). The p-tert-butylcalix[8]arene (BCA) derivative containing ethoxy vinyl ether groups (calixarene 4) was also synthesized in 83% yield by the substitution reaction of BCA with CEVE by using sodium hydride as a base and TBAB as a PTC. The MCA derivative containing 1-propenyl ether groups (calixarene 5) was synthesized in 80% yield by the isomerization of calixarene 2, which contained allyl ether groups, by using potassium tert-buthoxide as a catalyst. The photochemical reactions of carixarene 1, 3, 4, 5, and 6 were examined with certain photoacid generators in the film state. In this reaction system, calixarene 3 containing ethoxy vinyl ether groups showed the highest photochemical reactivity when bis-[4-(diphenylsulfonio)phenyl]sulfide bis(hexafluorophosphate) (DPSP) was used as the catalyst. On the other hand, calixarene 1 containing propargyl ether groups had the highest photochemical reactivity when 4-morpholino-2,5-dibuthoxybenzenediazonium hexafluorophosphate (MDBZ) was used as the catalyst. It was also found that the prepared carixarene derivatives containing cationically polymerizable groups such as propargyl, allyl, vinyl, and also 1-propenyl ethers have good thermal stability. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1805–1814, 1999     

Evolutionary Algorithm Directed Synthesis of Mixed Anion Compounds LaF2X (X=Br,I) and LaFI2

Mixed-anion compounds have attracted growing attentions, but their synthesis is challenging, making a rational search desirable. Here, we explored LaF₃-LaX₃ (X=Cl, Br, I) system using ab initio structure searches based on evolutionary algorithms, and predicted LaF₂X and LaFX₂ (X=Br, I), which are respectively isostructural with LaHBr₂ and YH₂I, consisting of layered La-F blocks with single and double ordered honeycomb lattices, separated by van der Waals gaps. We successfully synthesized these compounds: LaF₂Br and LaFI₂ crystallize in the predicted structure, while LaF₂I is similar to the predicted one but with different layer stacking. LaF₂I exhibits fluoride ion conductivity comparable to that of non-doped LaF₃, and has the potential to show better ionic conductivity upon appropriate doping, given the theoretically lower diffusion energy barrier and the presence of soft iodine anions. This study shows the structure prediction using evolutionary algorithms will accelerate the discovery of mixed-anion compounds in future, in particular those with an ordered anion arrangement.     

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.