Non-empirical CI potential curves for the ground and excited states of PH and its positive ion

A series of calculated potential curves is reported for the low lying valence and (selected) Rydberg states of the PH molecule by employing the multi-reference (single- and) double-excitation CI method. A large AO basis including f functions on phosphorous is chosen for this study and up to twenty main configurations are used to generate a given MRD-CI space in the accompanying theoretical treatment. Very good agreement is obtained between calculation and experiment for a variety of spectroscopic constants and a number of predictions for electronically excited states of PH are made for cases in which no comparable empirical data are yet available. The repulsive ⁵∑^- state is shown to be responsible for the predissociation of several states of the neutral system and is also thought to explain the failure to detect a number of low lying Rydberg states experimentally. Analogous calculations for the PH⁺ molecular ion have also been carried out and spectroscopic constants for this system are reported. In this case the ⁴Π state plays much the same role as the neutral ⁵∑^- species in bringing about predissociation in its electronic spectrum. Finally a comparison is made throughout between the results for PH and PH⁺ and a number of isovalent systems, especially NH and NH⁺ and also SiH.     

Control of the Discotic to Isotropic Transition in Alkoxy-Substituted Silicondihydroxo-Phthalocyanines by Axial Substituents

The synthesis of a homologous series of octaalkoxy-substituted silicondihydroxo-phthalocyanines is described. The mesomorphic properties of these new materials were studied by DSC, optical microscopy and X-ray investigations. Compounds with n ≤ 4 (n is the number of carbon atoms in a single alkoxy side chain) show a discotic mesophase transition. A transition to the isotropic state is only observed when n ≤ 8. X-ray diffraction patterns of the mesophases confirm that all compounds form a hexagonal columnar mesophase of the type D_hd.     

The impact of taking a college pre-calculus course on students’ college calculus performance

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.     

Some Poincaré type inequalities for quadratic matrix fields

We present some Poincaré type inequalities for quadratic matrix fields with applications e.g. in gradient plasticity or fluid dynamics. In particular, an application to the pseudostress-velocity formulation of the stationary Stokes problem is discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Algebraic Riccati Equation for Quaternions

We will present the general solution of the algebraic Riccati equation for the quaternionic case, where also one additional variation is treated. For computational purpose a very simple form of the exact Jacobi matrix for Riccati polynomials is presented. There are several examples.     

Atomic force microscopy study of ferroelectric films of P(VDF-TrFE) copolymer and composites based on it

The surface structure and local piezoelectric response of film samples of P(VDF-TrFE) copolymer and composites based on it were studied by atomic and piezoelectric force microscopy. Lamellar crystals 2.0 × 0.6 μm in size were detected in nominally pure P(VDF-TrFE) samples. Introduction of crystalline ferroelectrics increases the crystalline phase fraction in the polymer matrix and changes the shape and sizes of lamellar crystallites. Hysteresis loops of the local piezoelectric response for composite regions corresponding to the polymer matrix and crystalline ferroelectric inclusions were obtained.     

Aggregation Behavior of a Six‐Membered Cyclic Frustrated Phosphane/Borane Lewis Pair: Formation of a Supramolecular Cyclooctameric Macrocyclic Ring System

A new six‐membered cyclic frustrated phosphane/borane Lewis pair was liberated from its HB(C₆F₅)₂ adduct by treatment with vinylcyclohexane. The system is an active frustrated Lewis pair that undergoes cycloaddition reactions with suitable π reagents and it splits dihydrogen. At room temperature in solution the new compound is a monomer, however, in the crystal and in solution at low temperature it aggregates to a thermodynamically favoured supramolecular macrocyclic cyclooctamer.     

Preparation of the Borane (Fmes)BH2 and its Utilization in the FLP Reduction of Carbon Monoxide and Carbon Dioxide

Treatment of 1,3,5‐tris(trifluoromethyl)benzene with n‐BuLi, followed by H₃B?SMe₂ and subsequent hydride removal gave the (Fmes)BH₂ reagent, which was isolated as a SMe₂ stabilized monomer or a ligand free (μ‐H)₂‐bridged dimer. Reaction with Mes₂P(vinyl) gave the respective ethylene‐bridged P/B(Fmes)H FLP. It reduced carbon monoxide to the formyl stage and carbon dioxide to the formaldehyde oxidation state. Most new compounds were characterized by X‐ray diffraction.     

Multi‐Component Synthesis of Rare 1,3‐Dihydro‐1,3‐azaborinine Derivatives: Application of a Bora‐Nazarov Type Reaction

The twofold hydroboration products of (Fmes)BH₂?SMe₂ with a series of alkynes (2‐butyne, arylethynes) react with two molar equiv of 2,6‐dimethylphenyl isocyanide (CN‐Xyl) at 80 °C to give rare examples of 1,3‐azaborinine derivatives. A mechanistic study revealed a reaction course involving insertion of one isonitrile followed by a bora‐Nazarov type ring‐closure reaction and subsequent isonitrile insertion to give the respective 1,3‐dihydro‐1,3‐azaborinines 5 .     

Layering and position-dependent diffusive dynamics of confined fluids

We study the diffusive dynamics of a hard-sphere fluid confined between parallel smooth hard walls. The position-dependent diffusion coefficient normal to the walls is larger in regions of high local packing density. High density regions also have the largest available volume, consistent with the fast local diffusivity. Indeed, local and global diffusivities as a function of the Widom insertion probability approximately collapse onto a master curve. Parallel and average normal diffusivities are strongly coupled at high densities and deviate from bulk fluid behavior.