Dispersion terms and analysis of size- and charge dependence in an enhanced Poisson-Boltzmann approach

We implement a well-established concept to consider dispersion effects within a Poisson-Boltzmann approach of continuum solvation of proteins. The theoretical framework is particularly suited for boundary element methods. Free parameters are determined by comparison to experimental data as well as high-level quantum mechanical reference calculations. The method is general and can be easily extended in several directions. The model is tested on various chemical substances and found to yield good-quality estimates of the solvation free energy without obvious indication of any introduced bias. Once optimized, the model is applied to a series of proteins, and factors such as protein size or partial charge assignments are studied.     

Side-chain and backbone ordering in a polypeptide

We report results from multicanonical simulations of polyglutamic acid chains of length of ten residues. For this simple polypeptide we observe a decoupling of backbone and side-chain ordering in the folding process. While the details of the two transitions vary between the peptide in gas phase and in an implicit solvent, our results indicate that, independent of the specific surroundings, upon continuously lowering the temperature side-chain ordering occurs only after the backbone topology is completely formed.     

Palladium-catalyzed alkylation of 1,4-dienes by C-H activation

Activated: the title reaction proceeds with a broad range of nucleophiles and variously substituted 1,4-dienes under mild conditions, and provides direct access to the corresponding 1,3-diene-containing products with high regio- and stereocontrol (see scheme; 2,6-DMBQ=2,6-dimethylbenzoquinone, EWG=electron-withdrawing group). This is the first catalytic allylic C-H alkylation that proceeds in the absence of sulfoxide ligands.     

Energy landscape paving simulations of the trp-cage protein

We evaluate the efficiency of multiple variants of energy landscape paving in all-atom simulations of the trp-cage protein using a recently developed new force field. Especially, we introduce a temperature-free variant of the method and demonstrate that it allows a fast scanning of the energy landscape. Nativelike structures are found in less time than by other techniques. The sampled low-energy configurations indicate a funnel-like energy landscape.     

Properties of interfaces in the two and three dimensional Ising model

To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the 2D and 3D Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability density. Stringent tests of the numerical methods are performed by reproducing with high precision exact 2D results. In the physically more interesting 3D case we estimate the amplitudeF ₀ ^s of the critical interfacial tensionF ³=F ₀ ^s t to beF ₀ ^s =1.52±0.05. This result is in good agreement with a previous MC calculation by Mon, as well as with experimental results for related amplitude ratios. In addition, we study in some details the shape of the magnetic probability density for temperatures below the Curie point.     

Lieb–Thirring Type Inequalities for Schrödinger Operators with a Complex-Valued Potential

We present a possible generalization of the Lieb–Thirring inequalities for eigenvalues of Schrödinger operators to the case of complex potentials. We ask for a proof or disproof of this generalization. Some weaker results which have been obtained are reviewed.     

Correction to: On the strong universal consistency of local averaging regression estimates

A general result concerning the strong universal consistency of local averaging regression estimates is presented, which is used to extend previously known results on the strong universal consistency of kernel and partitioning regression estimates. The proof is based on ideas from Etemadi’s proof of the strong law of large numbers, which shows that these ideas are also useful in the context of strong laws of large numbers for conditional expectations in \(L_2\).

     

On the discrete spectrum of non-selfadjoint operators

We prove quantitative bounds on the eigenvalues of non-selfadjoint unbounded operators obtained from selfadjoint operators by a perturbation that is relatively-Schatten. These bounds are applied to obtain new results on the distribution of eigenvalues of Schrödinger operators with complex potentials.     

Bulk electronic structure of metals resolved with scanning tunneling microscopy

We demonstrate that bulk band structure can have a strong influence in scanning tunneling microscopy measurements by resolving electronic interference patterns associated with scattering phenomena of bulk states at a metal surface and reconstructing the bulk band topology. Our data reveal that bulk information can be detected because states at the edge of the surface-projected bulk band have a predominant role on the scattering patterns. With the aid of density functional calculations, we associate this effect with an intrinsic increase in the projected density of states of edge states. This enhancement is characteristic of the three-dimensional bulk band curvature, a phenomenon analog to a van Hove singularity.