Static Charge Susceptibility in the <Emphasis Type="Italic">t-J-V</Emphasis> Model

We describe the static charge susceptibility and correlation function of the charge density in the twodimensional t-J-V model based on the method of equations of motion for the relaxation functions of the Hubbard operators. We obtain the dependence of the susceptibility and correlation function on the hole concentration and temperature. Charge density waves can develop if the intersite Coulomb interaction is sufficiently strong.     

Repdigits as sums of three Pell numbers

In this paper, all base 10 repdigits expressible as sums of three Pell numbers are found.     

In Situ Metal-Assisted Ligand Modification Induces Mn4 Cluster-to-Cluster Transformation: A Crystallography,Mass Spectrometry,and DFT Study

Dehydration of (S,S)-1,2-bis(1H-benzo[d]imidazol-2-yl)ethane-1,2-diol (H₄L) to (Z)-1,2-bis(1H-benzo[d]imidazol-2-yl)ethenol) (H₃L′) was found to be metal-assisted, occurs under solvothermal conditions (H₂O/CH₃OH), and leads to [Mn^II₄(H₃L)₄Cl₂]Cl₂ ⋅ 5 H₂O ⋅ 5 CH₃OH ( Mn₄L₄ ) and [Mn^II₄(H₂L′)₆(μ₃-OH)]Cl ⋅ 4 CH₃OH ⋅ H₂O ( Mn₄L′₆ ), respectively. Their structures were determined by single-crystal XRD. Extensive ESI-MS studies on solutions and solids of the reaction led to the proposal consisting of an initial stepwise assembly of Mn₄L₄ from the reactants via [MnL] and [Mn₂L₂] below 80 °C, and then disassembly to [MnL] and [MnL₂] followed by ligand modification before reassembly to Mn₄L′₆ via [MnL′], [MnL′₂], and [Mn₂L′₃] with increasing solvothermal temperature up to 140 °C. Identification of intermediates [Mn₄L_xL′_6−x] (x=5, 4, 3, 2, 1) in the process further suggested an assembly/disassembly/in situ reaction/reassembly transformation mechanism. These results not only reveal that multiple phase transformations are possible even though they were not realized in the crystalline state, but also help to better understand the complex transformation process between coordination clusters during “black-box” reactions.     

Continuous Electrochemical Synthesis of Iso-Coumarin Derivatives from o-(1-Alkynyl) Benzoates under Metal- and Oxidant-Free

A non-oxidant and metal-free strategy for synthesizing iso-coumarin by using a continuous electrochemical microreactor to initiate an oxidative cyclization reaction of o-(1-alkynyl) benzoate and radicals. This efficient and clean continuous electrosynthesis method not only avoids the complicated gas protection operation and production of by-products in the batch processes, but also help to overcome the difficulty that batch metal catalysis and electrocatalysis are difficult to scale up, and has the potential for pilot-scale experiment.     

Precise measurement and control of the pressure-driven flows for microfluidic systems

The pressure-driven device is designed and the flow rates of the microfluidic systems can be supplied by the pressure-driven flows, which can significantly reduce the flow-rate fluctuations coming from the pump source. For pressure-driven flows, the flow rates of the fluids can be predicted by measuring the pressure drop along a polytetrafluoroethylene (PTFE) tubing. Especially, by varying the geometrical parameters of the PTFE tubing, the predicted flow rates of the fluids are compared with the experimental measurements, and the testing precision of the pressure-driven flows can be obtained. Meanwhile, the dynamic characteristics of the open-loop and closed-loop control pressure-driven device are comparatively studied. Particularly, a proportional and integral (PI) controller is integrated with the closed-loop control pressure-driven device, and the effects of the parameters of the PI controller on the dynamic characteristics of the pressure-driven devices are mainly discussed. Most importantly, by improving the dynamic characteristics of the pressure-driven devices, precise measurement and control of the pressure-driven flows can be achieved for microfluidic systems.     

BowtieArene: A Dual Macrocycle Exhibiting Stimuli-Responsive Fluorescence

Although highly useful in supramolecular chemistry, pillararenes lack a fluorophore in their skeleton. Here we present BowtieArene, a novel fluorescent dual macrocycle, featuring a central tetraphenylethylene-derived fluorophore and two pillar-like, pentagon-shaped cavities which are comparable to pillar[5]arene. This concisely prepared, figure-of-eight molecule exhibits vapor absorption and host–guest capabilities, as well as intriguing switchable fluorescence. The fluorochromism of BowtieArene can be triggered by multiple external stimuli including solvent, vapor, and mechanical force, with excellent reversibility and stability. Experimental and theoretical evidence indicate that the fluorochromism should be closely related to molecular packing.     

Stereoselectivity and nonmigratory insertion mechanism of dimethylacetylene dicarboxylate into metallocene-hydride of Cp2M(L)H [Cp = η5-C5H5; M = Nb,V; L = CO,P (OMe)3]: A DFT study

The insertion of an alkyne into transition metal–hydrogen bonds is a key elementary step in catalytic polymerization and hydrogenation processes. It was found that a (Z)- or (E)-type alkyenyl complex can be formed through trans/cis stereospecific processes. In this work, the reaction mechanism of Cp₂M(L)H [Cp = η⁵-C₅H₅; M = Nb, V; L = CO, P (OMe)₃] with dimethylacetylene dicarboxylate (DMAD), and the factors influencing the stereoselectivity have been investigated based on density functional theory calculations. The calculated results show that all of the reactions are exothermic. For L = CO, the Z-isomer product forms first even at low temperatures because of the low Gibbs free energy barrier (ΔG^#). Then the Z-pro converts to E-pro , while for L = P (OMe)₃, the exclusive product is the E-isomer. For different metal centers, the reaction mechanisms of the Cp₂M(CO)H + DMAD (M = Nb and V) reaction are similar, while their products are different at room temperature. For M = Nb, because the energy barrier of the isomerization from Z-pro to E-pro is low and the relative free energies of Z-pro and E-pro are almost equal, both Z-pro and E-pro can be obtained. While for the Cp₂V(CO)H + DMAD reaction, only the Z-pro can be obtained under mild conditions, E-pro can be obtained only at high temperatures. For the Cp₂M(CO)H+DMAD(M=V and Nb) reactions, the formation of E-isomer products proceeds via two five-membered ring transition states. The calculated results provide an reasonable explanation for the experimental results and predict a new insertion reaction.