Secododecahedradienes – Syntheses,Reactivity, in‐Plane Homoconjugated 3C/2e Cations, 4C/3e Radical Cations,and σ‐Bishomoaromatic 4C/2e Dications?

Secodecahedradiene 2a , featuring very proximate, perfectly syn‐periplanar and significantly pyramidalized C=C bonds, was synthesized as testing object for in‐plane(σ)‐homoconjugational electron delocalization, starting from the available pagodane 15b . The response of 2a (and in part its diester 2b ) – in π,π‐distance (average 3.08 Å), olefinic pyramidalization (average 26.9°), and π,π‐split (PE, 1.15 eV) intermediate between disecododecahedradiene 1a and 1,16‐dodecahedradiene 3a – to selected 4π‐reagents, electrophiles, and radicals was explored experimentally and by calculations. Intriguing multistep reaction sequences attest to the ease of competing stabilization pathways for the 3C/2e in‐plane homoconjugated cationic intermediates. PE, CV, and ESR measurements and calculations (DFT) characterize the radical cation generated from 2a as in‐plane homoconjugated 4C/3e‐species 2a ^.+, persistent in a Freon matrix, but only very shortly existent in solution (CIDNP). Consequently, NMR control of the two‐electron oxidation in SbF₅/SO₂ClF did not disclose the σ‐bis‐homoaromatic dication 4C/2e (see 2a ^{2 +} ), but a bis‐allylic dication 75 as persistent species. In support of 2a ^{2 +} as intermediate, evidence is presented for very limited kinetic protection offered by the secododecahedral framework to through H‐cage σ‐homoconjugated cations.     

Evidence for a doubly magic O

The decay energy spectrum for neutron unbound states in ²⁴O (Z=8$Z=8$, N=16$N=16$) has been observed for the first time. The resonance energy of the lowest lying state, interpreted as the ²⁺$2^{+}$ level, has been observed at a decay energy above 600 keV. The resulting excitation energy of the ²⁺$2^{+}$ level above 4.7 MeV, supplies strong evidence that ²⁴O is a doubly magic nucleus. The data is also consistent with the presence of a second excited state around 5.33 MeV which can be interpreted as the ¹⁺$1^{+}$ level.     

Towards perfunctionalized dodecahedranes--en route to C20 fullerene

“One‐pot” substitution of the twenty hydrogen atoms in pentagonal dodecahedrane (C₂₀H₂₀) by OH, F, Cl, and Br atoms is explored. Electrophilic insertion of oxygen atoms with DMDO and TFMDO as oxidizing reagents ended, far off the desired C₂₀(OH)₂₀, in complex polyol mixtures (up to C₂₀H₁₀(OH)₁₀ decols, a trace of C₂₀H(OH)₁₉?). Perfluorination was successful in a NaF matrix but (nearly pure) C₂₀F₂₀ could be secured only in very low yield. “Brute‐force” photochlorination (heat, light, pressure, time) provided a mixture of hydrogen‐free, barely soluble C₂₀Cl₁₆ dienes in high yield and C₂₀Cl₂₀ as a trace component. Upon electron‐impact ionization of the C₂₀Cl₁₆ material sequential loss of the chlorine atoms was the major fragmentation pathway furnishing, however, only minor amounts of chlorine‐free C₂₀⁺ ions. “Brute‐force” photobrominations delivered an extremely complex mixture of polybromides with C₂₀HBr₁₃ trienes as the highest masses. The MS spectra exhibited exclusive loss of the Br substituents ending in rather intense singly, doubly, and triply charged C₂₀H_4–0^+(2+)(3+) ions. The insoluble ～C₂₀HBr₁₃ fraction (C₂₀Br₁₄ trienes as highest masses) obtained along a modified bromination protocol, ultimately allowed the neat mass selection of C₂₀^? ions. The C₂₀Cl₁₆ dienes and C₂₀H_0–3Br_14–12 tri‐/tetraenes, in spite of their very high olefinic pyramidalization, proved resistant to oxygen and dimerization (polymerization) but added CH₂N₂ smoothly. Dehalogenation of the respective cycloaddition products through electron‐impact ionization resulted in C_22–24H_4–8⁺⁽²⁺⁾ ions possibly constituting bis‐/tris‐/tetrakis‐methano‐C₂₀ fullerenes or partly hydrogenated C₂₂, C₂₃, and C₂₄ cages.     

Circular grating waveguide structures for intracavity generation of azimuthal polarization in a thin-disk laser

We report on the generation of beams with azimuthal polarization using resonant grating waveguide structures (GWSs) inside an Yb:YAG thin-disk laser (TDL) oscillator. Two different GWS concepts were used to select the polarization of the emitted beam. The first uses the resonant reflection principle, and the second is based on the leaky-mode approach already reported in our previous work. Up to 93 W and 103 W of output power were extracted from a TDL with an optical efficiency, η(oo), of 36.2% and 40.1% using the first and the second approaches, respectively. In both cases, a pure azimuthal polarization and a beam quality factor, M2, of about 2.2 were measured. The design, fabrication, and different experimental results, as well as the laser performances for both GWSs, are discussed in the present Letter.     

Large-scale Tikhonov regularization via reduction by orthogonal projection

This paper presents a new approach to computing an approximate solution of Tikhonov-regularized large-scale ill-posed least-squares problems with a general regularization matrix. The iterative method applies a sequence of projections onto generalized Krylov subspaces. A suitable value of the regularization parameter is determined by the discrepancy principle.     

Robust expansion of subspaces in iterative projection methods for large eigenvalue problems

The Jacobi–Davidson method is known to converge at least quadratically if the correction equation is solved exactly, and it is common experience that the fast convergence is maintained if the correction equation is solved only approximately. Here we derive the Jacobi–Davidson method in a way that explains this robust behavior. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the shape operator of surfaces in space forms

Necessary and sufficient conditions are studied for the existence of surfaces in space forms with prescribed shape operator S. We consider three cases: that of the non-existence of a solution, the case of a unique solution and that of more than one solution. Examples are given for local and global S-deformations and S-rigidity.     

Numerical simulation of a three dimensional quantum dot

We consider the problem to compute relevant energy states and corresponding wave functions of a three dimensional semiconductor quantum dot. Let Ω_q ⊂ ℝ³ be a domain occupied by the quantum dot, which is embedded in a matrix Ω_m of different material. A typical example is an InAs pyramidal quantum dot embedded in a cuboid GaAs matrix. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exploring the Biocatalytic Potential of Fe/α-Ketoglutarate-Dependent Halogenases

Freestanding Fe/α-ketoglutarate-dependent halogenases are oxidoreductases that catalyze the installation of halogen atoms into unactivated sp³-hybridized carbon centers with high stereo- and regioselectivity. Since their discovery in 2014, a small number of indole alkaloid and amino acid halogenases have been identified and characterized. First enzyme engineering examples suggest that the accessible substrate range of these enzymes may be expanded through the use of rational enzyme design and directed evolution. Structural investigations of non-heme iron halogenases acting on freestanding as well as tethered substrates are beginning to inform about the principles of the underlying halogenation mechanism.