Amorphous silicon hexaboride at high pressure

ABSTRACT

We investigate the pressure-induced structural phase transformation of amorphous silicon hexaboride (a-SiB₆) using a constant pressure first principles approach. a-SiB₆ is found to undergo a gradual phase transformation to a high-density amorphous phase (HDA) in which the average coordination number of both B and Si atoms is about 6. The HDA phase consists of differently coordinated motifs ranging from 4 to 8. B₁₂ icosahedra are found to persist during compression of a-SiB₆ and the structural modifications primarily occur around Si atoms and in the regions linking pentagonal pyramid-like configurations to each other. Upon pressure release, an amorphous structure, similar to the uncompressed one, is recovered, indicating a reversible amorphous-to-amorphous phase change in a-SiB_6. When the electronic structure is considered, the HDA phase is perceived to have a wider forbidden band gap than the uncompressed one.     

Hierarchical Assembly of an Interlocked M8L16 Container

The self‐assembly of eight Pd^II cations and sixteen phenanthrene‐derived bridging ligands with 60° bite angles yielded a novel M₈L₁₆ metallosupramolecular architecture composed of two interlocked D_4h‐symmetric barrel‐shaped containers. Mass spectrometry, NMR spectroscopy, and X‐ray analysis revealed this self‐assembled structure to be a very large “Hopf link” catenane featuring channel‐like cavities, which are occupied by NO₃⁻ anions. The importance of the anions as catenation templates became imminent when we observed the nitrate‐triggered structural rearrangement of a mixture of M₃L₆ and M₄L₈ assemblies formed in the presence of BF₄⁻ anions into the same interlocked molecule. Furthermore, the densely packed structure of the M₈L₁₆ catenane was exploited in the preparation of a hexyloxy‐functionalized analogue, which further self‐assembled into vesicle‐like aggregates in a reversible manner.     

Conditioned Diffusions which are Brownian Bridges

Let X _t be a one-dimensional diffusion of the form dX _t=dB _t+(X _t)dt. Let Tbe a fixed positive number and let be the diffusion process which is X _t conditioned so that X ₀=X _T=x. If the drift is constant, i.e., , then the conditioned diffusion process is a Brownian bridge. In this paper, we show the converse is false. There is a two parameter family of nonlinear drifts with this property.     

The Trotter-Kato theorem and approximation of PDEs

We present formulations of the Trotter-Kato theorem for approximation of linear C-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes' equation as illustrative examples.

     

Internal and external eigenvalue problems of Hermitian operators and their use in electronic structure theory

Within the fragment resolution of molecular systems the conceptual and interpretative advantages of using the separate eigenvalue problems for the internal and external part of the Hermitian matrix representing a physical quantity in quantum mechanics are examined. By definition, these two parts accordingly combine only the diagonal and off-diagonal subsystem-resolved blocks of matrix elements. These two partial eigenvalue problems bring about the matrix internal or external decouplings, respectively, which have recently been used in several interpretations of the molecular electronic structure. A character and structure of the external eigensolutions is examined in some detail and their recent applications in the Charge Sensitivity Analysis—to extract the most important electron-transfer effects between constituent atoms of model chemisorption systems, and in the Molecular-Orbital theory—to precisely identify the inter-orbital flows of electrons, are summarized and commented upon. The grouping relation, for combining the external/internal eigensolutions into those for the whole matrix, is derived in the context of the complementary “rotations” of the basis set vectors.     

Skeletal transformations of perfluorinated 2,2-diethyl- and 2-ethyl-2-phenyl-benzocyclobutenones under the action of antimony pentafluoride

Perfluoro-2-ethyl-2-phenylbenzocyclobutenone heated with SbF₅ at 70 °C and then treated with water, forms perfluoro-3-ethyl-3-phenylphthalide. In contrast to this, heating of perfluoro-2,2-diethylbenzo-cyclobutenone with SbF₅ at 70 °C gives, after treatment of the reaction mixture with water, perfluoro-2-(pent-2-en-3-yl)benzoic acid. When the reaction temperature is raised to 125 °C, a solution of a salt of perfluoro-4-ethyl-3-methylisochromenyl cation is obtained. Hydrolysis of the solution of the salt gives perfluoro-4-ethyl-3-methylisochromen-1-one.     

SHAH: SHape-Adaptive Haar Wavelets for Image Processing

We propose the shape-adaptive Haar (SHAH) transform for images, which results in an orthonormal, adaptive decomposition of the image into Haar-wavelet-like components, arranged hierarchically according to decreasing importance, whose shapes reflect the features present in the image. The decomposition is as sparse as it can be for piecewise-constant images. It is performed via a stepwise bottom-up algorithm with quadratic computational complexity; however, nearly linear variants also exist. SHAH is rapidly invertible. We show how to use SHAH for image denoising. Having performed the SHAH transform, the coefficients are hard- or soft-thresholded, and the inverse transform taken. The SHAH image denoising algorithm compares favorably to the state of the art for piecewise-constant images. A clear asset of the methodology is its very general scope: it can be used with any images or more generally with any data that can be represented as graphs or networks.     

Divergent and Stereoselective Synthesis of β‐Silyl‐α‐Amino Acids through Palladium‐Catalyzed Intermolecular Silylation of Unactivated Primary and Secondary C−H Bonds

A general and practical Pd^II‐catalyzed intermolecular silylation of primary and secondary C?H bonds of α‐amino acids and simple aliphatic acids is reported. This method provides divergent and stereoselective access to a variety of optical pure β‐silyl‐α‐amino acids, which are useful for genetic technologies and proteomics. It can also be readily performed on a gram scale and the auxiliary can be easily removed with retention of configuration. The synthetic importance of this method is further demonstrated by the late‐stage functionalization of biological small molecules, such as (?)‐santonin and β‐cholic acid. Moreover, several key palladacycles were successfully isolated and characterized to elucidate the mechanism of this β?C(sp³)‐H silylation process.