Concise synthesis of complicated polypropionates through one-pot dissymmetrical two-directional chain elongation

Herein, a major breakthrough in a sulfur dioxide-mediated oxyallylation cascade reaction is reported that allows the preparation of complex long-chain polyketide fragments with more than ten stereogenic centers through a carefully designed desymmetrization process. An allylbissilane is combined, under the appropriate reaction conditions, with two different 1,3-dioxy-1,3-dienes permitting the construction of a 13-membered polypropionate precursor in one pot. Four stereocenters are selectively created during this process. The so-obtained pseudo-C(2)- or -C(S)-symmetric products are desymmetrized through selective deprotection and can be selectively elongated in both directions using aldol chemistry.     

Approximations of Quantum-Graph Vertex Couplings by Singularly Scaled Rank-One Operators

We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex couplings, generalizing the δ′-interaction on the line, and show that with a suitable choice of the parameters they can be approximated in this way in the norm-resolvent sense. We also analyze spectral properties of the involved operators and demonstrate the convergence of the corresponding on-shell scattering matrices.     

Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees

In this paper, we prove that the existence of absolutely continuous spectrum of the Kirchhoff Laplacian on a radial metric tree graph together with a finite complexity of the geometry of the tree implies that the tree is in fact eventually periodic. This complements the results by Breuer and Frank in (Rev Math Phys 21(7):929–945, 2009) in the discrete case as well as for sparse trees in the metric case.     

Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction

Letters in Mathematical Physics - We discuss the spectral properties of singular Schrödinger operators in three dimensions with the interaction supported by an equilateral star, finite or...     

Hydrogen electrocatalysis revisited: Weak bonding of adsorbed hydrogen as the design principle for active electrode materials

Hydrogen electrocatalysis has been spurred by theoretical predictions, using simple ab initio thermodynamic considerations, in that the free-binding energy of adsorbed hydrogen has been applied in a heuristic fashion to search for sustainable electrocatalysts as a replacement for scarce platinum in electrolyzers and fuel cells. The original volcano model of Nørskov et al. is given in [14] purports that the optimum hydrogen-evolution catalyst binds adsorbed hydrogen thermoneutrally at zero overpotential, a paradigm based on pure thermodynamic considerations. Recently, the Sabatier principle was revisited by factoring the applied overpotential and kinetics into the analysis. The extended Sabatier principle suggests that the optimum hydrogen-evolution catalyst binds adsorbed hydrogen weakly rather than thermoneutrally. This notion is corroborated by the fact that the most active hydrogen-evolution catalysts, Pt, MoS₂, or Mo₂C, indeed bind hydrogen weakly by about (100–200) meV rather than thermoneutrally at zero overpotential.     

Does a Thermoneutral Electrocatalyst Correspond to the Apex of a Volcano Plot for a Simple Two-Electron Process?

Volcano analyses have been established as a standard tool in the field of electrocatalysis for assessing the performance of electrodes in a class of materials. The apex of the volcano curve, where the most active electrocatalysts are situated, is commonly defined by a hypothetical ideal material that binds its reaction intermediates thermoneutrally at zero overpotential, in accordance with Sabatier's principle. However, recent studies report a right shift of the apex in a volcano curve, in which the most active electrocatalysts bind their reaction intermediates endergonically rather than thermoneutrally at zero overpotential. Focusing on two-electron process, this Viewpoint addresses the question of how the definition of an optimum catalyst needs to be modified with respect to the requirements of Sabatier's principle when kinetic effects and the applied overpotential are included in the analysis.     

Improvements in the generalized hybrid orbital method

In a previous paper, we described the adaptation of the generalized hybrid orbital (GHO) method for the use in fragment based quantum chemical approaches for large molecules like the field‐adapted adjustable density matrix assembler (FA‐ADMA). It soon became evident that the limitations of the available implementation strongly restrict its use. Therefore, in the article presented here, we describe new developments to circumvent these limitations. These include new construction algorithms of the GHO hybrid orbitals for sp³‐ as well as sp²‐hybridized carbon and nitrogen, different distributions of electrons in the auxiliary orbitals, and the separation from the CHARMM program, which was needed to provide partial charges and bonding information. The results demonstrate an excellent improvement in accuracy of the obtained electron densities compared to capping hydrogen atoms. Additionally, the calculation of gradients opens the possibility to use FA‐ADMA for geometry optimization of large molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Quantum graphs with vertices of a preferred orientation

Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the corresponding band spectra of lattices with square and hexagonal elementary cells showing that they depend heavily on the network topology, in particular, on the degrees of the vertices involved.     

Herstellung radioaktiv markierter ?thylen/Propylen-Copolymerer. Berechnung der Prim?rstruktur aus kinetischen Daten

Ohne Zusammenfassung     

Unstable systems and repeated measurements

In this part of the paper we treat two examples. In the first one the chamber structure is assumed only to be periodic andP(t) is an exponential. In the second example no specific assumption is made about the primary decay law and the measuring device is structured as an idealized spark chamber. This example contains results ofBeskow andNilsson as a special case.We follow the program formulated in the first part of this paper (referred hereafter as [I]). In the introduction of [I] we mentioned three examples; here we give two of them.