Eta1 and eta2 complexes of lambda3-1,2,4,6-thiatriazinyls with CpCr(CO)x

The title heterocyclic radicals coordinate to either 17e CpCr(CO)3 or 15e CpCr(CO)2 moieties as one-electron or as three-electron donors, respectively; in the former the bonding is via the perpendicular p orbital of the sulfur atom, while in the latter bonding is via p(pi) orbitals on both sulfur and nitrogen.     

A nonclassical LIL for geometrically weighted series in Banach space

Let {X, Xn ; n ≥ 0} be a sequence of independent and identically distributed random variables, taking values in a separable Banach space (B,||·||) with topological dual B* . Considering the geometrically weighted series ξ(β) =∑∞n=0βnXn for 0 β 1, and a sequence of positive constants {h(n), n ≥ 1}, which is monotonically approaching infinity and not asymptotically equivalent to log log n, a limit result for(1-β2)1/2||ξ(β)||/(2h(1/(1-β2)))1/2 is achieved.     

Special Green’s function boundary element approach for steady-state axisymmetric heat conduction across low and high conducting planar interfaces

The problem of determining the steady-state axisymmetric temperature distribution in a bimaterial with a planar interface is considered here. The interface is either low or high conducting. Special Green’s functions satisfying the thermal conditions on the interface are derived and employed to obtain boundary integral equations whose path of integration does not include the interface. Boundary element procedures that do not require the interface to be discretized into elements are proposed for solving the problem under consideration.     

On properties of discrete (r, q) and (s, T) inventory systems

We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that these properties no longer hold in the discrete space, in the sense of linear interpolation extension and L^?-convexity. This nonconvexity can lead to failure of optimization techniques based on local optimality to obtain the optimal inventory policies. It can also make certain comparative properties established previously using continuous variables invalid. We revise these properties in the discrete space.     

An All‐Alkynyl Protected 74‐Nuclei Silver(I)–Copper(I)‐Oxo Nanocluster: Oxo‐Induced Hierarchical Bimetal Aggregation and Anisotropic Surface Ligand Orientation

The hardness of oxo ions (O^2?) means that coinage‐metal (Cu, Ag, Au) clusters supported by oxo ions (O^2?) are rare. Herein, a novel μ₄‐oxo supported all‐alkynyl‐protected silver(I)–copper(I) nanocluster [Ag_74?xCu_xO₁₂(PhC≡C)₅₀] ( NC‐1 , avg. x=37.9) is characterized. NC‐1 is the highest nuclearity silver–copper heterometallic cluster and contains an unprecedented twelve interstitial μ₄‐oxo ions. The oxo ions originate from the reduction of nitrate ions by NaBH₄. The oxo ions induce the hierarchical aggregation of Cu^I and Ag^I ions in the cluster, forming the unique regioselective distribution of two different metal ions. The anisotropic ligand coverage on the surface is caused by the jigsaw‐puzzle‐like cluster packing incorporating rare intermolecular C?H???metal agostic interactions and solvent molecules. This work not only reveals a new category of high‐nuclearity coinage‐metal clusters but shows the special clustering effect of oxo ions in the assembly of coinage‐metal clusters.     

Solvent‐Induced Cluster‐to‐Cluster Transformation of Homoleptic Gold(I) Thiolates between Catenane and Ring‐in‐Ring Structures

Supramolecular ensembles adopting ring‐in‐ring structures are less developed compared with catenanes featuring interlocked rings. While catenanes with inter‐ring closed‐shell metallophilic interactions, such as d¹⁰–d¹⁰ Au^I–Au^I interactions, have been well‐documented, the ring‐in‐ring complexes featuring such metallophilic interactions remain underdeveloped. Herein is described an unprecedented ring‐in‐ring structure of a Au^I‐thiolate Au₁₂ cluster formed by recrystallization of a Au^I‐thiolate Au₁₀ [2]catenane from alkane solvents such as hexane, with use of a bulky dibutylfluorene‐2‐thiolate ligand. The ring‐in‐ring Au^I‐thiolate Au₁₂ cluster features inter‐ring Au^I–Au^I interactions and underwent cluster core change to form the thermodynamically more stable Au₁₀ [2]catenane structure upon dissolving in, or recrystallization from, other solvents such as CH₂Cl₂, CHCl₃, and CH₂Cl₂/MeCN. The cluster‐to‐cluster transformation process was monitored by ¹H NMR and ESI‐MS measurements. Density functional theory (DFT) calculations were performed to provide insight into the mechanism of the “ring‐in‐ring? [2]catenane” interconversions.     

Modeling halogen bonding with planewave density functional theory: Accuracy and challenges

Inspired by the recent interest of halogen bonding (XB) in the solid state, we detail a comprehensive benchmark study of planewave DFT geometry and interaction energy of lone-pair (LP) type and aromatic (AR) type halogen bonded complexes, using PAW and USPP pseudopotentials. For LP-type XB dimers, PBE-PAW generally agrees with PBE/aug-cc-pVQZ(−pp) geometries but significantly overbinds compared to CCSD(T)/aug-cc-pVQZ(-pp). Grimme's D3 dispersion corrections to PBE-PAW gives better agreement to the MP2/cc-pVTZ(-pp) results for AR-type dimers. For interaction energies, PBE-PAW may overbind or underbind for weaker XBs but clearly overbinds for stronger XBs. D3 dispersion corrections exacerbate the overbinding problem for LP-type complexes but significantly improves agreement for AR-type complexes compared to CCSD(T)/CBS. Finally, for periodic XB crystals, planewave PBE methods slightly underestimate the XB lengths by 0.03 to 0.05 Å. © 2019 Wiley Periodicals, Inc.     

Three silver coordination polymers constructed from 4,4′-bipyridine-like ligands and 2,5-thiophenedicarboxylic acid: crystal structures and photocatalytic performances

Transition Metal Chemistry - Three coordination polymers (CPs), formulated as [Ag(bpy)]2(tdc)·4H2O (BUC-78), [Ag(bpe)]2(tdc)·6H2O (BUC-79) and [Ag(bpp)]2(tdc)·8H2O (BUC-80) have been...