Probability density in the complex plane

The correspondence principle asserts that quantum mechanics resembles classical mechanics in the high-quantum-number limit. In the past few years, many papers have been published on the extension of both quantum mechanics and classical mechanics into the complex domain. However, the question of whether complex quantum mechanics resembles complex classical mechanics at high energy has not yet been studied. This paper introduces the concept of a local quantum probability density ρ(z) in the complex plane. It is shown that there exist infinitely many complex contours C of infinite length on which ρ(z) dz is real and positive. Furthermore, the probability integral is finite. Demonstrating the existence of such contours is the essential element in establishing the correspondence between complex quantum and classical mechanics. The mathematics needed to analyze these contours is subtle and involves the use of asymptotics beyond all orders.     

On the limit of proton-coupled electronic doping in a Ti(iv)-containing MOF

Ti^IV-containing metal–organic frameworks are known to accumulate electrons in their conduction bands, accompanied by protons, when irradiated in the presence of alcohols. The archetypal system, MIL-125, was recently shown to reach a limit of 2e⁻ per Ti₈ octomeric node. However, the origin of this limit and the broader applicability of this unique chemistry relies not only on the presence of Ti^IV, but also access to inorganic inner-sphere Lewis basic anions in the MOF nodes. Here, we study the loading of protons and electrons in MIL-125, and assess the thermodynamic limit of doping these materials. We find that the limit is determined by the reduction potential of protons: in high charging regimes the MOF exceeds the H⁺/H₂ potential. Generally, we offer the design principle that inorganic anions in MOF nodes can host adatomic protons, which may stabilize meta-stable low valent transition metals. This approach highlights the unique chemistry afforded by MOFs built from inorganic clusters, and provides one avenue to developing novel catalytic scaffolds for hydrogen evolution and transfer hydrogenation.

Photo-promoted doping of MIL-125 is limited by the potential of MOF-bound protons exceeding the hydrogen evolution reaction.     

On‐chip THz spectrometer for bunch compression fingerprinting at fourth‐generation light sources

The layout of an integrated millimetre‐scale on‐chip THz spectrometer is presented and its peformance demonstrated. The device is based on eight Schottky‐diode detectors which are combined with narrowband THz antennas, thereby enabling the simultaneous detection of eight frequencies in the THz range on one chip. The size of the active detector area matches the focal spot size of superradiant THz radiation utilized in bunch compression monitors of modern linear electron accelerators. The 3 dB bandwidth of the on‐chip Schottky‐diode detectors is less than 10% of the center frequency and allows pulse‐resolved detection at up to 5 GHz repetition rates. The performance of a first prototype device is demonstrated at a repetition rate of 100 kHz at the quasi‐cw SRF linear accelerator ELBE operated with electron bunch charges between a few pC and 100 pC.     

Synthesis,Crystal Structure and Bioactivity of Phenazine-1-carboxylic Acylhydrazone Derivatives

A phenazine-1-carboxylic acid intermediate was synthesized from the reaction of aniline and 2-bromo-3-nitro-benzoic acid. It was then esterified and reacted with hydrazine hydrate to afford phenazine-1-carboxylic hydrazine. Finally, 10 new hydrazone compounds 3a–3j were obtained by the condensation reaction of phenazine-1-carboxylic acid hydrazide and the respective aldehyde-containing compound. The structures were characterized by ¹H and ¹³C NMR spectroscopy, MS and single crystal X-ray diffraction. The antitumor activity of the target compounds in vitro (HeLa and A549) was determined by thiazolyl blue tetrazolium bromide. The results showed that compound (E)-N′-(2-hydroxy-4-(2-(piperidine-1-yl) ethoxy) benzyl) phenazine-1-carbonyl hydrazide 3d exhibited good cytotoxic activity.     

Relative angular precision in electron backscatter diffraction: A comparison between cross correlation and Hough transform based analysis

In the present study the relative angular resolution of an electron backscatter diffraction system based on Hough transform analysis has been determined with a silicon single crystal wafer. The resolution is found to be better than 0.1° and can be easily improved by repetition of measurements. A test measurement on a BaFe₂As₂ thin film, where disorientations of 0.1° and less are present, was performed using the cross correlation electron backscatter diffraction technique. The same measurement is evaluated with the Hough transform technique. Comparing both techniques give evidence of a relative resolution of better than 0.1°. However, in specimen areas with strain inhomogeneities a deviation along one rotation axis can be observed.     

Maximizing MR signal for 2D UTE slice selection in the presence of rapid transverse relaxation

Ultrashort TE (UTE) sequences allow direct visualization of tissues with very short T2 relaxation times, such as tendons, ligaments, menisci, and cortical bone. In this work, theoretical calculations, simulations, and phantom studies, as well as in vivo imaging were performed to maximize signal-to-noise ratio (SNR) for slice selective RF excitation for 2D UTE sequences. The theoretical calculations and simulations were based on the Bloch equations, which lead to analytic expressions for the optimal RF pulse duration and amplitude to maximize magnetic resonance signal in the presence of rapid transverse relaxation. In steady state, it was found that the maximum signal amplitude was not obtained at the classical Ernst angle, but at an either lower or higher flip angle, depending on whether the RF pulse duration or amplitude was varied, respectively.     

X-ray photoemission spectra measurements of CeNi2Sb2 and CeCu2Sb2

X-ray photoemission spectra, resistivity and susceptibility of CeNi₂Sb₂ and CeCu₂Sb₂ were measured and are discussed. The results indicate that these alloys are Kondo systems. For comparison of the valence band properties, the spectra of the isostructural alloys of RT₂X₂-type with R = La, Gd, T = Cu, Ni and X = Sn, Sb were investigated, too.     

Clustering of rare earths in GeAs sulfide glass

Clustering of rare-earth dopants in GeAs sulfide glasses was studied by fluorescence spectroscopy of Pr-doped glasses and by EPR measurements of Gd-doped samples. The linewidth of the g  2 resonance of Gd³⁺, as well as the relative intensity of emission from the ¹D₂ level of Pr³⁺, was used as a relative measure of rare-earth clustering. Rare earths were found to have low solubility in uncodoped GeAs sulfide glasses, which also displayed poor fluorescence efficiency due to severe clustering. Codoping such glasses with Ga greatly enhanced rare-earth solubility and dispersal, particularly for Ga:rare earth ratios ≥ 10:1, as evidenced by the narrower EPR resonances and more intense luminescence of Gd- and Pr-doped glasses, respectively. In, P and Sn were also observed to ‘decluster’ rare earths, although less efficiently than Ga, whereas codoping with I was found to have no effect on clustering. These phenomena are explained by a structural model in which (1) rare-earth dopants and codopants are spatially associated and (2) rare-earth dispersal is accomplished by a statistical distribution of codopants in tetrahedral network sites.     

Palladium-catalyzed carbonylative Heck reaction of aryl bromides with vinyl ethers to 3-alkoxy alkenones and pyrazoles

Three COming together: The first carbonylative Heck coupling reaction of aryl bromides and vinyl ethers leading to 1-aryl-3-alkoxy-2-propen-1-ones has been established (see scheme). Based on this coupling methodology, a novel one-pot synthesis of aryl-substituted pyrazoles was also realized.