Solution set splitting at low energy levels in Schrödinger equations with periodic and symmetric potential

The time-independent superlinear Schrödinger equation with spatially periodic and positive potential admits sign-changing two-bump solutions if the set of positive solutions at the minimal nontrivial energy level is the disjoint union of period translates of a compact set. Assuming a reflection symmetric potential we give a condition on the equation that ensures this splitting property for the solution set. Moreover, we provide a recipe to explicitly verify the condition, and we carry out the calculation in dimension one for a specific class of potentials.     

Laser-induced local dehydroxylation on surface-oxidized silicon substrates: mechanistic aspects and prospects in nanofabrication

Processing of silicon oxide surfaces with a focused laser beam at a wavelength of 514 nm has been investigated. Laser processing of native silicon samples (d _ox=1–2 nm) allows the fabrication of reactive templates with laterally varying hydroxyl group density. Very similar results were also obtained on thermally oxidized silicon samples (d _ox≈100 nm), whereas respective experiments on quartz plates have failed. These results support a photothermal mechanism where laser irradiation causes a local temperature rise and initiates dehydroxylation. In agreement with a photothermally induced dehydroxylation reaction, a thermokinetic analysis of the experimental data points to a highly activated process. In conjunction with site-selective functionalization routines this opens up an avenue towards functional surface structures with lateral dimensions significantly below the optical diffraction limit.     

The Averaged Dynamics of the Hydrogen Atom in Crossed Electric and Magnetic Fields as a Perturbed Kepler Problem

We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action–angle variables, we separate the different time scales of the motion. The method of averaging then allows us to reduce the system to two degrees of freedom, and to classify the most important periodic orbits.     

Biocatalytic Reduction of 2‐Monosubstituted 3‐Thiazolines Using Imine Reductases

The application of a straightforward biocatalytic technology for the reduction of racemic 2‐monosubstituted 3‐thiazolines, which are easily prepared via Asinger‐multicomponent reaction, is reported. The biocatalytic reduction yields racemic 2‐monosubstituted 3‐thiazolidines, which are difficult to be prepared by means of classic chemical routes, in moderate to high yields. Moreover, our study clarifies the stereochemical reaction course of the biocatalytic reduction. Furthermore, the efficiency of this biocatalytic technology is demonstrated in an experiment at an elevated substrate concentration of 60 mM leading to 96% conversion.     

Difluoro(aryl)(perfluoroalkyl)‐λ4‐sulfanes and Selanes: Missing Links of Trichloroisocyanuric Acid/Potassium Fluoride Chemistry

The TCICA/KF approach to oxidative fluorination of heteroatoms has emerged as a surprisingly simple, safe, and versatile surrogate to classically challenging fluorination reactions. Although polyfluorination (or chlorofluorination) of diaryl disulfides, diaryl diselenides, diaryl ditellurides, aryl iodides, and aryl(perfluoroalkyl)tellanes has been described, the application of this TCICA/KF methodology to aryl(perfluoroalkyl)sulfanes and selanes remains an area of unexplored chemical space. Accordingly, to address the “missing links” in the developing series of chalcogen‐based substrate reactivity, we report mild syntheses of metastable difluoro(aryl)(perfluoroalkyl)‐λ⁴‐sulfanes and selanes. As only limited examples of these species exist in the current literature (accessible only by using F₂ or XeF₂/HF), we have carried out detailed structural analyses, primarily using NMR and SC‐XRD data. In addition, we investigate the effect of the perfluoroalkyl chain on the outcome of oxidative fluorination, and, finally, we provide preliminary evidence that difluoro(aryl)(trifluoro‐methyl)‐λ⁴‐sulfanes may act as fluorinating reagents.     

Electrochemical N2 splitting at well-defined metal complexes

In this short review, we discuss recent examples of well-defined metal complexes capable to split dinitrogen electrochemically. Large progress has been made in the chemical dinitrogen splitting with molecular complexes during the last couple of years; however, electrochemical N₂ splitting remains scarce. Herein, three distinct examples, which were investigated in depth, are discussed. The iron complex 2⁺ converts N₂ to ammonia via an associative mechanism. With the rhenium pincer complex 3, N₂ is cleaved via a dissociative mechanism forming a very stable Re^V-nitride complex. The aluminium complex 6 also converts N₂ electrochemically to ammonia; however, the mechanism is distinctly different to that in 2⁺ or 3, as there is no evidence for a metal–N₂ interaction and likely the ligand acts as a hydride donor.