Solvable Model of a Generic Driven Mixture of Trapped Bose–Einstein Condensates and Properties of a Many-Boson Floquet State at the Limit of an Infinite Number of Particles

A solvable model of a periodically driven trapped mixture of Bose–Einstein condensates, consisting of N1 interacting bosons of mass m1 driven by a force of amplitude fL,1 and N2 interacting bosons of mass m2 driven by a force of amplitude fL,2, is presented. The model generalizes the harmonic-interaction model for mixtures to the time-dependent domain. The resulting many-particle ground Floquet wavefunction and quasienergy, as well as the time-dependent densities and reduced density matrices, are prescribed explicitly and analyzed at the many-body and mean-field levels of theory for finite systems and at the limit of an infinite number of particles. We prove that the time-dependent densities per particle are given at the limit of an infinite number of particles by their respective mean-field quantities, and that the time-dependent reduced one-particle and two-particle density matrices per particle of the driven mixture are 100% condensed. Interestingly, the quasienergy per particle does not coincide with the mean-field value at this limit, unless the relative center-of-mass coordinate of the two Bose–Einstein condensates is not activated by the driving forces fL,1 and fL,2. As an application, we investigate the imprinting of angular momentum and its fluctuations when steering a Bose–Einstein condensate by an interacting bosonic impurity and the resulting modes of rotations. Whereas the expectation values per particle of the angular-momentum operator for the many-body and mean-field solutions coincide at the limit of an infinite number of particles, the respective fluctuations can differ substantially. The results are analyzed in terms of the transformation properties of the angular-momentum operator under translations and boosts, and as a function of the interactions between the particles. Implications are briefly discussed.     

Transition Metal-Catalyzed Enantioselective C−H Functionalization via Chiral Transient Directing Group Strategies

Transition metal-catalyzed enantioselective functionalization of C−H bond, the most abundant functionality in organic molecules, has emerged as an expedient synthetic approach to streamline the synthesis of complex chiral molecules. Despite significant progress, traditional directing group-enabled strategies require additional steps for the installation and removal of directing groups from the target molecule. The recently developed asymmetric C−H functionalization using chiral transient directing groups (cTDGs) offers a promising alternative that can circumvent this obstacle and therefore simplify the process. In this Minireview, we briefly discuss the advent and recent advances of this emerging concept, with an emphasis on discussing the creation of various stereogenic centers and the developments of cTDGs. Applications in natural product synthesis and ligand derivatizations are also discussed. We hope this Minireview will highlight the great potential of this strategy and help to inspire further endeavors.     

On one-relator products induced by generalized triangle groups II

This is the second of two papers in which we study a group which is the quotient of a free product of groups by the normal closure of a single word that is contained in a subgroup which has the form of a free product of two cyclic groups. We use known properties of generalized triangle groups, together with detailed analysis of pictures and of words in free monoids, to prove a number of results such as a Freiheitssatz and the existence of Mayer-Vietoris sequences for such groups under suitable hypotheses. The results generalize those in an earlier article of the second author and Shwartz.     

Group 6 Oxyfluoro-Anion Salts of [XeF5]+ and [Xe2F11]+: Syntheses and Structures of [XeF5][M2O2F9] (M=Mo,W), [Xe2F11][M′OF5] (M′=Cr,Mo, W), [XeF5][HF2]⋅CrOF4, and [XeF5][WOF5]⋅XeOF4

The reactions of the fluoride-ion donor, XeF₆, with the fluoride-ion acceptors, M′OF₄ (M′=Cr, Mo, W), yield [XeF₅]⁺ and [Xe₂F₁₁]⁺ salts of [M′OF₅]⁻ and [M₂O₂F₉]⁻ (M=Mo, W). Xenon hexafluoride and MOF₄ react in anhydrous hydrogen fluoride (aHF) to give equilibrium mixtures of [Xe₂F₁₁]⁺, [XeF₅]⁺, [(HF)_nF]⁻, [MOF₅]⁻, and [M₂O₂F₉]⁻ from which the title salts were crystallized. The [XeF₅][CrOF₅] and [Xe₂F₁₁][CrOF₅] salts could not be formed from mixtures of CrOF₄ and XeF₆ in aHF at low temperature (LT) owing to the low fluoride-ion affinity of CrOF₄, but yielded [XeF₅][HF₂]⋅CrOF₄ instead. In contrast, MoOF₄ and WOF₄ are sufficiently Lewis acidic to abstract F⁻ ion from [(HF)_nF]⁻ in aHF to give the [MOF₅]⁻ and [M₂O₂F₉]⁻ salts of [XeF₅]⁺ and [Xe₂F₁₁]⁺. To circumvent [(HF)_nF]⁻ formation, [Xe₂F₁₁][CrOF₅] was synthesized at LT in CF₂ClCF₂Cl solvent. The salts were characterized by LT Raman spectroscopy and LT single-crystal X-ray diffraction, which provided the first X-ray crystal structure of the [CrOF₅]⁻ anion and high-precision geometric parameters for [MOF₅]⁻ and [M₂O₂F₉]⁻. Hydrolysis of [Xe₂F₁₁][WOF₅] by water contaminant in HF solvent yielded [XeF₅][WOF₅]⋅XeOF₄. Quantum-chemical calculations were carried out for M′OF₄, [M′OF₅]⁻, [M′₂O₂F₉]⁻, {[Xe₂F₁₁][CrOF₅]}₂, [Xe₂F₁₁][MOF₅], and {[XeF₅][M₂O₂F₉]}₂ to obtain their gas-phase geometries and vibrational frequencies to aid in their vibrational mode assignments and to assess chemical bonding.     

Unravelling the Time Scale of Conformational Plasticity and Allostery in Glycan Recognition by Human Galectin-1

The interaction of human galectin-1 with a variety of oligosaccharides, from di-(N-acetyllactosamine) to tetra-saccharides (blood B type-II antigen) has been scrutinized by using a combined approach of different NMR experiments, molecular dynamics (MD) simulations, and isothermal titration calorimetry. Ligand- and receptor-based NMR experiments assisted by computational methods allowed proposing three-dimensional structures for the different complexes, which explained the lack of enthalpy gain when increasing the chemical complexity of the glycan. Interestingly, and independently of the glycan ligand, the entropy term does not oppose the binding event, a rather unusual feature for protein-sugar interactions. CLEANEX-PM and relaxation dispersion experiments revealed that sugar binding affected residues far from the binding site and described significant changes in the dynamics of the protein. In particular, motions in the microsecond-millisecond timescale in residues at the protein dimer interface were identified in the presence of high affinity ligands. The dynamic process was further explored by extensive MD simulations, which provided additional support for the existence of allostery in glycan recognition by human galectin-1.     

Cyclic Bis-alkylidene Complexes of Titanium and Zirconium: Synthesis,Characterization, and Reaction

Transition-metal alkylidenes have exhibited wide applications in organometallic chemistry and synthetic organic chemistry, however, cyclic Schrock-carbene-like bis-alkylidenes of group 4 metals with a four-electron donor from an alkylidene have not been reported. Herein, the synthesis and characterization of five-membered cyclic bis-alkylidenes of titanium ( 4 a , b ) and zirconium ( 5 a , b ) are reported, as the first well-defined group 4 metallacyclopentatrienes, by two-electron reduction of their corresponding titana- and zirconacyclopentadienes. DFT analyses of 4 a show a four-electron donor (σ-donation and π-donation) from an alkylidene carbon to the metal center. The reaction of 4 a with N,N′-diisopropylcarbodiimide (DIC) leads to the [2+2]-cycloaddition product 6 . Compound 4 a reacted with CO, affording the oxycyclopentadienyl titanium complex 7 . These reactivities demonstrate the multiple metal–carbon bond character. The reactions of 4 a or 5 a with cyclooctatetraene (COT) or azobenzene afforded sandwich titanium complex 8 or diphenylhydrazine-coordinated zirconacyclopentadiene 9 , respectively, which exhibit two-electron reductive ability.     

TEMPO-mediated radical polymerization in the synthesis of poly(methyl methacrylate) macromonomer

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Parabolic subgroups in FC-type Artin groups

Parabolic subgroups are the building blocks of Artin groups. This paper extends previous results of Cumplido, Gebhardt, Gonzales-Meneses and Wiest, known only for parabolic subgroups of finite type Artin groups, to parabolic subgroups of FC-type Artin groups. We show that the class of finite type parabolic subgroups is closed under intersection. We also study an analog of the curve complex for mapping class group constructed by Cumplido et al. using parabolic subgroups. We extend the construction of this complex, called the complex of parabolic subgroups, to FC-type Artin groups. We show that this simplicial complex is, in most cases, infinite diameter and conjecture that it is δ-hyperbolic.