Electronic structure of Sc2AC (A=Al, Ga, In, Tl)

Using ab initio calculations, we have studied Sc₂AC with A=Al, Ga, In and Tl. We show that C 2p and Sc 3d as well as A p and Sc 3d states are hybridized, but the antibonding states in the vicinity of the Fermi level weaken the overall bonding. In terms of the chemical bonding, the influence of the size of the A element is minute. Furthermore, the bulk modulus of the corresponding binary transition metal carbide is not conserved in these phases. Therefore, Sc₂AC can be classified as weakly coupled MAX phases according to Sun and co-workers [Z. Sun, D. Music, R. Ahuja, S. Li, J.M. Schneider, Phys. Rev. B 70 (2004) 092102]. It is our ambition that these calculations will stimulate experimental research on these compounds.     

Geometric separation and exact solutions for the parameterized independent set problem on disk graphs

We consider the parameterized problem, whether for a given set  of n disks (of bounded radius ratio) in the Euclidean plane there exists a set of k non-intersecting disks. For this problem, we expose an algorithm running in time that is—to our knowledge—the first algorithm with running time bounded by an exponential with a sublinear exponent. For λ-precision disk graphs of bounded radius ratio, we show that the problem is fixed parameter tractable with a running time  . The results are based on problem kernelization and a new “geometric ( -separator) theorem” which holds for all disk graphs of bounded radius ratio. The presented algorithm then performs, in a first step, a “geometric problem kernelization” and, in a second step, uses divide-and-conquer based on our new “geometric separator theorem.”     

The opacity coefficient method—nongray determination of inhomogeneous atmospheric extinction

The computation of radiation transmittance in nongray, inhomogeneous atmospheric models is frequently complicated by complex bands of line spectra which range in value over many orders of magnitudes and depend strongly on either or both of pressure and temperature. We present here a new opacity sampling technique which is shown to determine correctly the wavelength-averaged extinction due to path-dependent realizations of banded line spectra. The technique is easy to implement computationally and is applicable to a wide variety of atmospheric problems in which frequent iteration of the radiative transfer model is required. We consider two such instances: modeling of solar flux attenuation for use in a time-dependent planetary ionosphere model and retrieval from nadir measurements of backscattered solar irradiance. The power of the new method lies in its straightforward analytical treatment of both atmospheric inhomogeneity and spectral complexity. It is thus relevant for both retrieval and radiative transfer modeling purposes.     

The "invisible" 13C NMR chemical shift of the central carbon atom in [(Ph3PAu)6C]2+: a theoretical investigation

The experimental 13C NMR chemical shift of the central carbon atom in the octahedral [(Ph3PAu)6C]2+ cluster was investigated on the basis of relativistic density functional calculations. In order to arrive at independent model conclusions regarding the value of the chemical shift, a systematic study of the dependence of the cluster structure on the phosphine ligands, the chosen density functionals, and the basis set size was conducted. The best structures obtained were then used in the NMR calculations. Because of the cage-like cluster structure a pronounced deshielding of the central carbon nucleus could have been expected. However, upon comparison with the 13C NMR properties of the related complex [C{Au[P(C6H5)2(p-C6H4NMe2)]}6]2+, Schmidbaur et al. have assigned a signal at delta=135.2 ppm to the interstitial carbon atom. Our calculations confirm this value in the region of the aromatic carbon atoms of the triphenylphosphine ligands. The close-lying signals of the 108 phenyl carbon atoms can explain the difficulties of assigning them experimentally.     

Total Syntheses of the Alkaloids Ipalbidinium and Clathryimine B

 The indolizidinium alkaloid ipalbidinium and the quinolizidinium alkaloid clathryimine B were prepared starting from brominated 2-aminopyridines using two Pd-catalyzed cross-coupling reactions and a Sandmeyer-type diazotation/iodination protocol as the key steps.