Inverse problem in atom-atom scattering in WKB approach

The WKB phase of a scattering problem including high angular momenta can be written as a Jeffreys-Born integral, $${}^{\delta WKB}(\beta ,K) = - \frac{A}{{2K}}\int\limits_\beta ^\infty {\frac{{Q(t,K)tdt}}{{\sqrt {t^2 - \beta ^2 } }}} $$ where β=(l+1/2)/A is the reduced collision parameter. The quasipotential Q(t, K) defined by this formula is connected with the potential in an easily understandable way. Its introduction allows the solution of the inversion problem (in WKB approximation) by treating this formula as an integral equation forQ. It further permits to investigate the relation between potential and phase function. The evaluation of experimental atom-atom-scattering data, using a phase function with seven parameters is given as an example how potential parameters can be used. Potentials leading to observed differential cross sections thus can easily be computed. Computation times are about a factor 50 smaller than in conventional methods.     

Taking detection to the limit with optical microcavities: Recent advances presented at the 560. WE Heraeus Seminar

We provide a review on the applications of whispering gallery mode resonators in sensing, and biosensing in particular. We highlight the most recent developments in this area, which were presented at the 560. WE Heraeus Seminar “Taking Detection to the Limit – Biosensing with Optical Microcavities”.     

One-electron bonds in copper–aluminum and copper–gallium complexes

Odd-electron bonds have unique electronic structures and are often encountered as transiently stable, homonuclear species. In this study, a pair of copper complexes supported by Group 13 metalloligands, M[N((o-C₆H₄)NCH₂PⁱPr₂)₃] (M = Al or Ga), featuring two-center/one-electron (2c/1e) σ-bonds were synthesized by one-electron reduction of the corresponding Cu(i) ⇢ M(III) counterparts. The copper bimetallic complexes were investigated by X-ray diffraction, cyclic voltammetry, electron paramagnetic spectroscopy, and density functional theory calculations. The combined experimental and theoretical data corroborate that the unpaired spin is delocalized across Cu, M, and ancillary atoms, and the singly occupied molecular orbital (SOMO) corresponds to a σ-(Cu–M) bond involving the Cu 4p_z and M ns/np_z atomic orbitals. Collectively, the data suggest the covalent nature of these interactions, which represent the first examples of odd-electron σ-bonds for the heavier Group 13 elements Al and Ga.

Hanging on by a thread. Formally zerovalent copper complexes with an Al(iii) or Ga(iii) support were investigated. The combined experimental and theoretical data corroborate the presence of an odd-electron σ-bond between Cu and the Group 13 center.

Odd-electron σ-bonds, where the electrons are delocalized between two atoms, can occur as two-center/one-electron (2c/1e) or two-center/three-electron (2c/3e) interactions. Proposed by Pauling in 1931,¹ odd-electron σ-bonds have garnered attention because of their fundamental importance to chemical bonding and their relationship to radical species generated during oxidative stress in biological systems.^2–14 Examples of compounds exhibiting odd-electron bonding are typically homonuclear (like H₂⁺, He₂⁺, and alkali metal dimers) and transiently stable, limiting them to spectroscopic characterization.^1,11,15–18The first solid-state structure of a formally one-electron σ-bond was a tetraphosphabenzene species (Fig. 1a) which was formed by the coupling of two diphosphirenyl radicals.¹⁹ Following this discovery, the formation of discrete 2c/1e σ-bonds, where the odd-electron is delocalized between two homonuclear main group centers, was reported for B·B and then extended to P·P.^8,17,20 Of note, the first solid-state structure of a B·B compound was reported in only 2014 (Fig. 1b).²¹ Examples of 2c/1e σ-bonds between the heavier Group 13 congeners are even more lacking because of the greater propensity for their unpaired spins to couple, forming larger more stable clusters.⁸ To our knowledge, there are only three structurally characterized examples of odd-electron bonds for the heavy Group 13 atoms,²² and these examples are all homonuclear π-radicals (Fig. 1c).^23–26Open in a separate windowFig. 1Select examples of structurally characterized molecules (a–d) featuring odd-electron bonds.Heteronuclear odd-electron σ-bonds are also rare. The Cu(TPB) complex, where TPB is a trisphosphinoborane, is the single structural example of a 2c/1e bond between heteroatoms (Fig. 1d).²⁷ The authors described the bonding as Cu·B, where the unpaired electron is heavily polarized toward B. A theoretical study predicted that such a bond would also exist between Cu and Al, but no heavier analogues of Cu(TPB) have been synthesized to date.²⁸ Furthermore, the heavier Group 13 elements by virtue of their lower electronegativity compared to B should facilitate greater covalent interactions with the Cu center.Hence, we sought to target formally zerovalent Cu complexes supported by Al(III) or Ga(III) as an extension of the previously reported isoelectronic nickelate species and Cu(TPB).²⁹ Herein, we describe the synthesis, structure, spectroscopic characterization, and DFT calculations of cationic [CuML]⁺ complexes (L = [N((o-C₆H₄)NCH₂PⁱPr₂)₃]³⁻; M = Al and Ga) as well as their one-electron reduced metalloradical counterparts that feature discrete 2c/1e bonds.     

Korrosion

Ohne Zusammenfassung     

Synthese und Kristallstruktur von Tetraphenylphosphonium-Aquabis(tetrasulfido)thionitrosyl-Osmat,PPh4[Os(NS)(S4)2(H2O)]

Synthesis and Crystal Structure of Tetraphenylphosphonium Aqua-bis(tetrasulfido)thionitrosyl Osmate, PPh₄[Os(NS)(S₄)₂(H₂O)] PPh₄[Os(NS)(S₄)₂(H₂O)] has been prepared as redbrown crystals by reacting PPh₄[OsNCl₄] with a solution of excess disodium tetrasulfide in dimethylformamide/H₂O and characterized by IR spectroscopy and by a crystal structure determination. Space group P2₁/n, Z = 4, structure solution with 4162 independent reflections, R = 0.059 for reflections with I > 2σ(I). Lattice dimensions at ?40°C: a = 1138.9(5), b = 1301.4(4), c = 2092.7(7) pm, β = 104.74(3)º. Os? N, Os? O, and Os? S distances are 175.2(12), 219.8(12), and 237.5(4)?239.1(4) pm, respectively. The Os?N?S moiety is approximately linear, with an OsNS angle of 171.2(7)º.     

Interactions of ionic liquids with polysaccharides 9. Hydroxyalkylation of cellulose without additional inorganic bases

Water-soluble hydroxyalkyl cellulose with a molar degree of substitution of up to 2.79 was prepared under completely homogeneous reaction conditions in various ionic liquids without addition of inorganic bases. In acetate containing solvents the IL acts as a catalyst. The substitution patterns of the cellulose ethers were analyzed by ¹³C NMR spectroscopy, ¹H NMR spectroscopy after peracetylation and GLC/MS after permethylation and depolymerization. A diminished tendency towards the formation of side chains compared to heterogeneously prepared hydroxyalkyl celluloses in the presence of inorganic bases was found.     

Toward the characterization of peptidoglycan structure and protein-peptidoglycan interactions by solid-state NMR spectroscopy

Solid-state NMR spectroscopy is applied to intact peptidoglycan sacculi of the Gram-negative bacterium Escherichia coli. High-quality solid-state NMR spectra allow atom-resolved investigation of the peptidoglycan structure and dynamics as well as the study of protein-peptidoglycan interactions.     

Solution of a laser Fokker-Planck equation for intensity and inversion

In the commonly used laser model (two levels, homogeneously broadened, one running mode, no detuning) the polarization can be eliminated adiabatically, if the dephasing time is much shorter than the other time constants. We thus arrive at a Fokker-Planck equation for inversion and light intensity, which does not fulfill the detailed balance condition. By a suitable expansion of the distribution function it is shown that the Fokker-Planck equation is equivalent to a tridiagonal recurrence relation for the coefficient vectors, which can be solved by matrix continued fractions. In this way all moments and two-time correlations can be obtained. Especially the correlation coefficients between inversion and intensity, the photon counting coefficient [<(n–<n>)²>–<n>]/<n>² for the stationary state as well as the eigenvalues of the Fokker-Planck equation are presented in the threshold region.     

Brownian motion in periodic potentials; nonlinear response to an external force

The Brownian motion of particles in a periodic potential in response to a constant external force is investigated. By expanding the distribution function into Hermite-functions and into a Fourier-series, the Fokker-Planck-equation is transformed into a set of coupled equations for the expansion coefficients. These equations are solved by a continued fraction method for matrices. This continued fraction for the matrices converges for large, intermediate and even for very small damping constants. The mobility, the kinetic and potential energy for various damping constants and external forces are given for a cos-potential. The current-voltagecharacteristic of the Josephson tunneling junction is also shown.