ChemInform Abstract: Vibrational Spectrum and Gas-Phase Structure of Disulfur Dinitride (S2N2)

The first gas-phase high-resolution FTIR spectra of S₂N₂ (D_2h) is presented together with a high-level quantum mechanical and experimental study of its molecular ground-state and equilibrium structures.     

Remote Sensing via ℓ 1-Minimization

We consider the problem of detecting the locations of targets in the far field by sending probing signals from an antenna array and recording the reflected echoes. Drawing on key concepts from the area of compressive sensing, we use an ? ₁-based regularization approach to solve this, generally ill-posed, inverse scattering problem. As is common in compressive sensing, we exploit randomness, which in this context comes from choosing the antenna locations at random. With n antennas we obtain n ² measurements of a vector $x \in\mathbb{C}^{N}$ representing the target locations and reflectivities on a discretized grid. It is common to assume that the scene x is sparse due to a limited number of targets. Under a natural condition on the mesh size of the grid, we show that an s-sparse scene can be recovered via ? ₁-minimization with high probability if n ²≥Cslog²(N). The reconstruction is stable under noise and when passing from sparse to approximately sparse vectors. Our theoretical findings are confirmed by numerical simulations.     

Relations between capacity utilization,minimal bin size and bin number

We consider the two-dimensional bin packing problem given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer \({k} \ge 3\) that at most \({k}-1\) bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed \({k}/4\) -times the bin area. Moreover, this bound is tight. Furthermore, we show that only two bins are necessary to pack all items if the total area of items is not larger than the bin area, and if the height of each item is not larger than a third of the bin height and the width of every item does not exceed half of the bin width.     

Vibrational Spectrum and Gas‐Phase Structure of Disulfur Dinitride (S2N2)

Gas‐phase FTIR spectra of the ν₆ (B‐type) and the ν₄ (C‐type) fundamental bands of S₂N₂ (D_2h) were recorded with a resolution of ≤0.004 cm^?1 and the vibrational spectrum of S₂N₂ (D_2h) in solid Ar has been revisited. All IR‐active fundamentals and four combination bands were assigned in excellent agreement with calculated values from anharmonic VPT2 and VCI theory based on (explicitly correlated) coupled‐cluster surfaces. Accurate experimental vibrational ground‐ and excited‐state rotational constants of ³²S₂¹⁴N₂ are obtained from a rovibrational analysis of the ν₆ and ν₄ fundamental bands, and precise zero‐point average r_z (R_z(SN)=1.647694(95) Å, α_z(NSN)=91.1125(33)°) and semi‐experimental equilibrium structures (R_e(SN)=1.64182(33) Å, α_e(NSN)=91.0716(93)°) of S₂N₂ have been established. These are compared to the solid‐state structure of S₂N₂ and structural properties of related sulfur nitrogen compounds and to results of ab initio structure calculations.     

Radial Multiresolution in Dimension Three

We present a construction of a wavelet-type orthonormal basis for the space of radial $L^2$-functions in {\bf R}$^3$ via the concept of a radial multiresolution analysis. The elements of the basis are obtained from a single radial wavelet by usual dilations and generalized translations. Hereby the generalized translation reveals the group convolution of radial functions in {\bf R}$^3$. We provide a simple way to construct a radial scaling function and a radial wavelet from an even classical scaling function on {\bf R}. Furthermore, decomposition and reconstruction algorithms are formulated.     

Generalized coorbit theory, Banach frames, and the relation to {alpha}-modulation spaces

This paper is concerned with generalizations and specific applicationsof the coorbit space theory based on group representations moduloquotients, which has been developed quite recently. We showthat the general theory applied to the affine Weyl–Heisenberggroup gives rise to families of smoothness spaces that can beidentified with -modulation spaces.     

Preparation of functionalized alkylmagnesium derivatives using an I/Mg-exchange

Functionalized alkylmagnesium reagents bearing an acetal, a ketal, an ester, or a pyridine ring were prepared by an I/Mg-exchange using iPr2Mg.LiCl or ClMg(CH2)5MgCl.2LiCl starting from functionalized primary alkyl iodides.     

Quantum chemical rovibrational analysis of aminoborane and its isotopologues

Aminoborane, H₂NBH₂ and its isotopologues, H₂N¹⁰BH₂, D₂NBD₂, and D₂N¹⁰BD₂, have been studied by high-level ab initio methods. All calculations rely on multidimensional potential energy surfaces and dipole moment surfaces including high-order mode coupling terms, which have been obtained from electronic structure calculations at the level of explicitly correlated coupled-cluster theory, CCSD(T)-F12, or the distinguishable cluster approximation, DCSD. Subsequent vibrational structure calculations based on second-order vibrational perturbation theory, VPT2, and vibrational configuration interaction theory, VCI, were used to determine rotational constants, centrifugal distortion constants, vibrationally averaged geometrical parameters and (an)harmonic vibrational frequencies. The impact of core-correlation effects is discussed in detail. Rovibrational VCI calculations were used to simulate the gas phase spectra of these species and an in-depth analysis of the ν₇ band of aminoborane is provided. Color-coding is used to reveal the identity of the individual progressions of the rovibrational transitions for this particular mode.     

Biosynthesis and structure of aeruginoside 126A and 126B, cyanobacterial peptide glycosides bearing a 2-carboxy-6-hydroxyoctahydroindole moiety

Aeruginosins represent a group of peptide metabolites isolated from various cyanobacterial genera and from marine sponges that potently inhibit different types of serine proteases. Members of this family are characterized by the presence of a 2-carboxy-6-hydroxyoctahydroindole (Choi) moiety. We have identified and fully sequenced a NRPS gene cluster in the genome of the cyanobacterium Planktothrix agardhii CYA126/8. Insertional mutagenesis of a NRPS component led to the discovery and structural elucidation of two glycopeptides that were designated aeruginoside 126A and aeruginoside 126B. One variant of the aglycone contains a 1-amino-2-(N-amidino-Delta(3)-pyrrolinyl)ethyl moiety at the C terminus, the other bears an agmatine residue. In silico analyses of the aeruginoside biosynthetic genes aerA-aerI as well as additional mutagenesis and feeding studies allowed the prediction of enzymatic steps leading to the formation of aeruginosides and the unusual Choi moiety.     

Difunctionalisation of arenes and heteroarenes by directed metallation and sulfoxide-magnesium exchange

The aryl sulfoxide moiety allows an expedient two‐step difunctionalisation of readily available diaryl sulfoxides. Highly functionalised 1,2,4‐trisubstituted arenes and difunctionalised heteroarenes (furans, thiophenes, benzofurans and pyridines) were prepared in a two‐step sequence, triggered by an aryl sulfoxide group. In the first step, the sulfoxide moiety acts as a metallation‐directing group, allowing smooth ortho‐magnesiation with TMPMgCl ? LiCl (TMP=tetramethylpiperidine). After a quenching reaction with an electrophile, the resulting sulfoxide is converted into a second magnesium reagent with iPrMgCl ? LiCl (sulfoxide–magnesium exchange), which can be trapped with various electrophiles. Highly chemoselective TMPMgCl ? LiCl and iPrMgCl ? LiCl are compatible with a broad range of functional groups (e.g., F, Cl, CF₃, CN, CO₂tBu, alkynyl, ethers, thioethers). Large‐scale reactions (25–40 mmol) and the preparation of fully functionalised furans and thiophenes are also reported.