The multipliers‐free domain decomposition methods

This article concludes the development and summarizes a new approach to dual‐primal domain decomposition methods (DDM), generally referred to as “the multipliers‐free dual‐primal method.” Contrary to standard approaches, these new dual‐primal methods are formulated without recourse to Lagrange‐multipliers. In this manner, simple and unified matrix‐expressions, which include the most important dual‐primal methods that exist at present are obtained, which can be effectively applied to floating subdomains, as well. The derivation of such general matrix‐formulas is independent of the partial differential equations that originate them and of the number of dimensions of the problem. This yields robust and easy‐to‐construct computer codes. In particular, 2D codes can be easily transformed into 3D codes. The systematic use of the average and jump matrices, which are introduced in this approach as generalizations of the “average” and “jump” of a function, can be effectively applied not only at internal‐boundary‐nodes but also at edges and corners. Their use yields significant advantages because of their superior algebraic and computational properties. Furthermore, it is shown that some well‐known difficulties that occur when primal nodes are introduced are efficiently handled by the multipliers‐free dual‐primal method. The concept of the Steklov–Poincaré operator for matrices is revised by our theory and a new version of it, which has clear advantages over standard definitions, is given. Extensive numerical experiments that confirm the efficiency of the multipliers‐free dual‐primal methods are also reported here. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Dual Gold‐Catalyzed Cycloaromatization of Unconjugated (E)‐Enediynes

A synthesis of unconjugated (E)‐enediynes from allenyl amino alcohols is reported and their gold‐catalyzed cascade cycloaromatization to a broad range of enantioenriched substituted isoindolinones has been developed. Experimental and computational studies support the reaction proceeding via a dual‐gold σ,π‐activation mode, involving a key gold‐vinylidene‐ and allenyl‐gold‐containing intermediate.     

Evidence for Multiple Binding Modes in the Initial Contact Between SARS-CoV-2 Spike S1 Protein and Cell Surface Glycans**

Infection of host cells by SARS-CoV-2 begins with recognition by the virus S (spike) protein of cell surface heparan sulfate (HS), tethering the virus to the extracellular matrix environment, and causing the subunit S1-RBD to undergo a conformational change into the ‘open’ conformation. These two events promote the binding of S1-RBD to the angiotensin converting enzyme 2 (ACE2) receptor, a preliminary step toward viral-cell membrane fusion. Combining ligand-based NMR spectroscopy with molecular dynamics, oligosaccharide analogues were used to explore the interactions between S1-RBD of SARS CoV-2 and HS, revealing several low-specificity binding modes and previously unidentified potential sites for the binding of extended HS polysaccharide chains. The evidence for multiple binding modes also suggest that highly specific inhibitors will not be optimal against protein S but, rather, diverse HS-based structures, characterized by high affinity and including multi-valent compounds, may be required.     

A molecular orbital rationalization of ligand effects in N2 activation

Molecular orbital theory has been used to study a series of [(micro-N2){ML3}2] complexes as models for dinitrogen activation, with M=Mo, Ta, W, Re and L=NH2, PH2, AsH2, SbH2 and N(BH2)2. The main aims of this study have been to provide a thorough electronic analysis of the complexes and to extend previous work involving molecular orbital analyses. Molecular orbital diagrams have been used to rationalize why for L=NH2 ligand rotation is important for the singlet state but not the triplet, to confirm the effect of ligand pi donation, and to rationalize the importance of the metal d-electron configuration. The outcomes of this study will assist with a more in-depth understanding of the electronic basis for N2 activation and allow clearer predictions to be made about the structure and multiplicity of systems involved in transition-metal catalysis.     

IR spectroscopic observation of molecular transport through Pt@CoO yolk-shell nanostructures

FTIR spectroscopy has been used to monitor the transport of CO to the Pt cores of Pt@CoO nanoparticles forming CO/Pt species. It was found that external Pt sites are not present on the outer surfaces of the approximately 10 nm diameter nanostructures and that CO transports to Pt adsorption sites by an activated surface diffusion process through the CoO shells surrounding approximately 2 nm diameter Pt cores. The CO transport process is not due to gas-phase transport below 300 K. The weakly bound adsorbed CO/CoO species responsible for transport was directly observed at approximately 2147 cm(-1) during transport through the CoO shells.     

Photochemistry on TiO2: Mechanisms behind the surface chemistry

Photochemistry from TiO₂ surfaces is described for two cases: The UV-induced photodesorption of O₂ from TiO₂(1 1 0) – 1 × 1; and the hydrophilic effect caused by UV irradiation on TiO₂. In both cases fundamental information about how these processes occur has been found. In the case of the O₂ photodesorption kinetics, it has been found that the rate of the process is proportional to the square root of the UV flux, showing that second-order electron–hole pair recombination is dominant in governing the photodesorption rate. In addition these measurements provide an estimate of the concentration of hole traps in the TiO₂ crystal. In other measurements of the UV-induced hydrophilicity, starting with the atomically-clean TiO₂ surface, it has been shown that the effect occurs suddenly at a critical point during irradiation as a result of photooxidation of a monolayer of hydrocarbon (n-hexane) at equilibrium with ppm concentration of n-hexane in O₂ at 1 atmosphere pressure.