Discrete Neutral Niobium Cluster Units in Compounds of the Type [Nb6Cl14L4] with L = O or N Donor Ligand

Six new hexanuclear niobium cluster compounds of the general formula [Nb₆Cl₁₄L₄] · x(solvent molecule) [L = neutral O or N donor ligand, x = 0–2.5; pyrimidine ( 1 ), 1‐methyl imidazole ( 2 ), isobutyronitrile ( 3 ), isopropyl alcohol ( 4 ), triphenylphosphine oxide ( 5 ), dimethyl sulfoxide ( 6 )] were prepared. The syntheses were carried out by dehydration of the precursor [Nb₆Cl₁₄(H₂O)₄] · 4H₂O with different water scavangers, like acetic anhydride, trimethyl acetic anhydride and diethylcarbonate in the presence of the corresponding neutral ligand. The structures are determined by single‐crystal X‐ray diffraction. The specific bonding situations of the ligands to the [Nb₆Cl₁₂]²⁺ cluster cores are compared and discussed. The phenomenon of the observed M₆ distortion is explained and interpreted based on the matrix effect and the terminal ligand effect. In addition, other interactions between the cluster units, such as hydrogen bonding and π–π stacking are discussed.     

Structural Investigation of New Lithium Amidinates and Guanidinates

A series of potentially useful lithium amidinates and guanidinates were prepared and fully characterized. Treatment of N,N′‐diisopropylcarbodiimide with phenyllithium in diethyl ether afforded the lithium amidinate [PhC(NiPr)₂Li(OEt₂)]₂ ( 1 ). Similar treatment of N,N′‐diorganocarbodiimides R′–N=C=N–R′ [R′ = iPr, cyclohexyl (Cy)] with secondary lithium amides LiNR₂ [R₂ = Et₂, iPr₂, (CH₂)₄] followed by crystallization from THF or 1,4‐dioxane gave the lithium guanidinates [R₂NC(NR′)₂Li(S)]₂ [ 2 : R = Et, R′ = iPr, S = THF; 3 : R₂ = (CH₂)₄, R′ = iPr, S = THF; 4 : R = R′ = iPr, S = ½ 1,4‐dioxane; 5 : R₂ = (CH₂)₄, R′ = Cy, S = 1,4‐dioxane] as crystalline solids. Reaction of N‐lithioaziridine with the corresponding carbodiimides afforded solvent‐deficient [{C₂H₄NC(NiPr₂)₂}₂Li₂(THF)]₂ ( 6 ), and [C₂H₄NC(NEt)(NtBu)Li(THF)]₂ ( 7 ). Crystal structure determination revealed the presence of common ladder‐type dimeric structures for 1 – 5 . Compound 6 exists as a dimer of two ladder‐type dimers in the crystal, and 7 exhibits an unusual dimeric structure comprising an eight‐membered C₂N₄Li₂ ring.     

Nonintrusive data-based learning of a switched control heating system using POD,DMD and ANN

The aim of this work is to derive an accurate model of two-dimensional switched control heating system from data generated by a Finite Element solver. The nonintrusive approach should be able to capture both temperature fields, dynamics and the underlying switching control rule. To achieve this goal, the algorithm proposed in this paper will make use of three main ingredients: proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and artificial neural networks (ANN). Some numerical results will be presented and compared to the high-fidelity numerical solutions to demonstrate the capability of the method to reproduce the dynamics.     

Finite element modelling of cold drawing for high-precision tubes

Cold tube drawing is a metal forming process that allows manufacturers to produce high-precision tubes. The dimensions of the tube are reduced by pulling it through a conical converging die with or without inner tool. In this study, finite element modelling has been used to give a better understanding of the process.This paper presents a model that predicts the final dimensions of the tube with very high accuracy. It is validated thanks to experimental tests. Moreover, five studies are performed with this model, such as investigating the influence of the die angle on the drawing force or the influence of relative thickness on tube deformation.     

Repdigits as sums of three Pell numbers

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

On Copper(I) Fluorides,the Cuprophilic Interaction,the Preparation of Copper Nitride at Room Temperature,and the Formation Mechanism at Elevated Temperatures

Our attempts to synthesize the hitherto unknown binary copper(I) fluoride have led to first successes and a serendipitious result: By conproportionation of elemental copper and copper(II) fluoride in anhydrous liquid ammonia, two copper(I) fluorides were obtained as simple NH₃ complexes. One of them presents an example of ligand‐unsupported “cuprophilic” interactions in an infinite [Cu₂(NH₃)₄]²⁺ chain with alternating Cu–Cu distances. We discovered that both copper(I) fluorides can easily be converted into Cu₃N at room temperature, just by applying a vacuum. Additionally, we investigated the formation mechanism of the classical synthesis route of Cu₃N that starts with CuF₂ and flowing NH₃ in the temperature range between ambient and 290 °C by means of thermal analysis and in situ neutron diffraction. The reaction proceeds at elevated temperatures through the formation of a blue and amorphous ammoniate Cu(NH₃)₂F₂, the reformation of CuF₂, and finally the redox reaction to form Cu₃N.     

“(Diphosphine)Nickel”‐Catalyzed Negishi Cross‐Coupling: An Experimental and Theoretical Study

The use of a strongly donating “(bis‐dialkylphosphine)Ni” fragment promotes the catalytic coupling of a large range of ArCl and ArZnCl derivatives under mild conditions. Stoichiometric mechanistic investigations and DFT calculations prove that a Ni⁰/Ni^II cycle is operative in this system.