Toeplitz Operators with Uniformly Continuous Symbols

Let T _f be a Toeplitz operator on the Segal–Bargmann space or the standard weighted Bergman space over a bounded symmetric domain \({\Omega \subset {\bf C}^n}\) with possibly unbounded symbol f. Combining recent results in Bauer et al. (J. Funct. Anal. 259:57–78, 2010), Bauer et al. (J. reine angew. Math. doi: 10.1515/crelle-2015-0016), Issa (Integr. Equ. Oper. Theory 70:569–582, 2011) we show that in the case of uniformly continuous symbols f with respect to the Euclidean metric on C ⁿ and the Bergman metric on \({\Omega}\), respectively, the operator T _f is bounded if and only if f is bounded. Moreover, T _f is compact if and only if f vanishes at the boundary of \({\Omega.}\) This observation substantially extends a result in Coburn (Indiana Univ. Math. J. 23:433–439, 1973).     

A Novel Bismuth‐Based Metal–Organic Framework for High Volumetric Methane and Carbon Dioxide Adsorption

Solvothermal reaction of H₄L (L=biphenyl‐3,3′,5,5′‐tetracarboxylate) and Bi(NO₃)₃ ? (H₂O)₅ in a mixture of DMF/MeCN/H₂O in the presence of piperazine and nitric acid at 100 °C for 10 h affords the solvated metal–organic polymer [Bi₂(L)_1.5(H₂O)₂] ? (DMF)_3.5 ? (H₂O)₃ (NOTT‐220‐solv). A single crystal X‐ray structure determination confirms that it crystallises in space group P2/c and has a neutral and non‐interpenetrated structure comprising binuclear {Bi₂} centres bridged by tetracarboxylate ligands. NOTT‐220‐solv shows a 3,6‐connected network having a framework topology with a {4 ? 6²}₂{4² ? 6⁵ ? 8⁸}{6² ? 8} point symbol. The desolvated material NOTT‐220a shows exceptionally high adsorption uptakes for CH₄ and CO₂ on a volumetric basis at moderate pressures and temperatures with a CO₂ uptake of 553 g L^?1 (20 bar, 293 K) with a saturation uptake of 688 g L^?1 (1 bar, 195 K). The corresponding CH₄ uptake was measured as 165 V(STP)/V (20 bar, 293 K) and 189 V(STP/V) (35 bar, 293 K) with a maximum CH₄ uptake for NOTT‐220a recorded at 20 bar and 195 K to be 287 V(STP)/V, while H₂ uptake of NOTT‐220a at 20 bar, 77 K is 42 g L^?1. These gas uptakes have been modelled by grand canonical Monte Carlo (GCMC) and density functional theory (DFT) calculations, which confirm the experimental data and give insights into the nature of the binding sites of CH₄ and CO₂ in this porous hybrid material.     

The Ketimide Ligand is Not Just an Inert Spectator: Heteroallene Insertion Reactivity of an Actinide–Ketimide Linkage in a Thorium Carbene Amide Ketimide Complex

The ketimide anion R₂C?N^? is an important class of chemically robust ligand that binds strongly to metal ions and is considered ideal for supporting reactive metal fragments due to its inert spectator nature; this contrasts with R₂N^? amides that exhibit a wide range of reactivities. Here, we report the synthesis and characterization of a rare example of an actinide ketimide complex [Th(BIPM^TMS){N(SiMe₃)₂}(N?CPh₂)] [ 2 , BIPM^TMS=C(PPh₂NSiMe₃)₂]. Complex 2 contains Th?C_carbene, Th? N_amide and Th? N_ketimide linkages, thereby presenting the opportunity to probe the preferential reactivity of these linkages. Importantly, reactivity studies of 2 with unsaturated substrates shows that insertion reactions occur preferentially at the Th? N_ketimide bond rather than at the Th?C_carbene or Th? N_amide bonds. This overturns the established view that metal‐ketimide linkages are purely inert spectators.     

D3R grand challenge 4: blind prediction of protein–ligand poses,affinity rankings,and relative binding free energies

Journal of Computer-Aided Molecular Design - The Drug Design Data Resource (D3R) aims to identify best practice methods for computer aided drug design through blinded ligand pose prediction and...     

Controlling the optical and catalytic properties of artificial metalloenzyme photocatalysts using chemogenetic engineering

Visible light photocatalysis enables a broad range of organic transformations that proceed via single electron or energy transfer. Metal polypyridyl complexes are among the most commonly employed visible light photocatalysts. The photophysical properties of these complexes have been extensively studied and can be tuned by modifying the substituents on the pyridine ligands. On the other hand, ligand modifications that enable substrate binding to control reaction selectivity remain rare. Given the exquisite control that enzymes exert over electron and energy transfer processes in nature, we envisioned that artificial metalloenzymes (ArMs) created by incorporating Ru(ii) polypyridyl complexes into a suitable protein scaffold could provide a means to control photocatalyst properties. This study describes approaches to create covalent and non-covalent ArMs from a variety of Ru(ii) polypyridyl cofactors and a prolyl oligopeptidase scaffold. A panel of ArMs with enhanced photophysical properties were engineered, and the nature of the scaffold/cofactor interactions in these systems was investigated. These ArMs provided higher yields and rates than Ru(Bpy)₃²⁺ for the reductive cyclization of dienones and the [2 + 2] photocycloaddition between C-cinnamoyl imidazole and 4-methoxystyrene, suggesting that protein scaffolds could provide a means to improve the efficiency of visible light photocatalysts.

Artificial metalloenzyme visible light photocatalysts possess enhanced optical properties and are competent towards single electron and energy transfer organic transformations.     

Synthesis of mesocyclic and macrocyclic polythioethers using the cesium dithiolate technique

The mesocyclic trithioethers, 1,4,7-trithiacyclodecane, 1,4,7-trithiacycloundecane, 1,4,8-trithiacycloundecane, and 1,5,9-trithiacyclododecane; the mesocyclic trithioether ketones, 1,4,7-trithiacyclodecan-9-one; 1,4,8-trithiacycloundecan-6-one, and 1,5,9-trithiacyclododecan-3-one; and the mesocyclic trithioether alcohols, 1,4,7-trithiacyclodecan-9-ol, 1,4,8-trithiacycloundecan-6-ol, and 1,5,9-trithiacyclododecan-3-ol, have been synthesized using the cesium dithiolate technique. In some cases, the corresponding macrocyclic hexathioether was isolated from the reaction mixture in addition to the mesocyclic trithioether; 1,4,7,11,14,17-hexathiacycloeicosane, 1,4,7,11,14,17-hexathiacycloeicosan-9,19-dione, 1,4,7,12,15,18-hexathiacyclodocosane, and 1,5,9,13,17,21-hexathiacyclotetracosane. Single-crystal X-ray structures have been determined for 1,5,9-trithiacyclododecan-3-ol and 1,4,7,12,15,18-hexathiacyclodocosane. For 1,5,9-trithiacyclododecane-3-ol, the compound crystallizes in the monoclinic space group, C2/c, with a = 10.5926( 9 ) Å, b = 15.582(2) Å, c = 13.6015(8) Å, β = 98.186(6)⁰, Z = 8, and R = 0.038. The macrocycle, 1,4,7,12,15,18-hexathiacyclodocosane, crystallizes in the orthorhombic space group, Pbca, with a = 21.406(5) Å, b = 9.810(2) Å, c = 10.225(2) Å, Z = 4, and R = 0.020.     

Finite element modelling of natural-convection-controlled change of phase

The problem of phase change in the presence of natural convection has been investigated. A model has been proposed based on the treatment of the release/absorption of latent heat as a heat source/sink in combination with the standard Galerkin finite element method with a primitive variable formulation on a fixed grid. To demonstrate the capabilities of the model, three cases of phase change of an aluminium alloy in the presence of natural convection arc considered, i.e. solidification, melting and combined solidification and melting. The solidification of water in a square cavity is modelled as another example, taking into account the density extremum, and the results are compared with a previously published work.     

An Analytical Model for Flow of Seawater Adjacent to an Igneous Wall

Transport in Porous Media - We develop an analytical model describing the flow of NaCl– $$\hbox {H}_2\hbox {O}$$ in a saturated porous medium adjacent to a hot vertical wall and apply the...     

Gas hydrate single-crystal structure analyses

The first single-crystal diffraction studies on methane, propane, methane/propane, and adamantane gas hydrates SI, SII, and SH have been performed. To circumvent the problem of very slow crystal growth, a novel technique of in situ cocrystallization of gases and liquids resulting in oligocrystalline material in a capillary has been developed. With special data treatment, termed oligo diffractometry, structural data of the gas hydrates of methane, acetylene, propane, a propane/ethanol/methane-mixture and an adamantane/methane-mixture were obtained. Cell parameters are in accord with reported values. Host network and guest are subject to extensive disorder, reducing the reliability of structural information. It was found that most cages are fully occupied by a guest molecule with the exception of the dodecahedral cage in the acetylene hydrate which is only filled to 60%. For adamantane in the icosahedral cage a disordered model is proposed.