Vibrational Raman Optical Activity Comes of Age

It is almost precisely 20 years since the first recording of an entire vibrational Raman optical activity (VROA) spectrum was accomplished. We describe some of the developments which by now have allowed the measurement of carbohydrates, peptides and even proteins, and nucleic acids. While we outline the enormous general potential of VROA for structural determinations of chiral molecules, our emphasis is on the particular potential the separate determination of the isotropic and anisotropic invariants of the optical activity scattering tensor has for the interpretation of VROA data

Characterizing vibrational motion beyond internal coordinates

We present a procedure for the decomposition of the normal modes of a composite system, including its rotations and translations, into those of fragments. The method permits—by the cross-contraction of dyads of mass-weighted displacement vectors, without recourse to valence coordinates—the direct comparison of nuclear motions of structurally similar but otherwise arbitrary fragments of molecules, and it leads to a quantitative definition of the similarity and the overlap of nuclear motions. We illustrate its usefulness by the quantification of the mixing of the normal modes of formic acid monomers upon the formation of a dimer, by the comparison of the overlap of the intermolecular normal vibrations of the water dimer computed with different ab initio schemes, and by the comparison of similarity and overlap of vibrations of (4S,7R)-galaxolide and (4S)-4-methylisochromane. The approach is expected to become a standard tool in vibrational analysi

Raman Optical Activity: A Reliable Chiroptical Technique

Vibrational optical activity (VOA) is a research field in full expansion. The two main areas where VOA is used are the determination of absolute configurations and the investigation of the secondary and tertiary solution structures of biopolymers. Commercial instrumentation is available since some time for vibrational circular dichroism (VCD) and, more recently, also Raman optical activity (ROA). Here, we describe a recent instrumental implementation of forward scattering, advances in the computational interpretation of ROA, and the determination of the mechanistically important absolute configuration of (4E)-3,3-dimethyl-5-[(2R,3R)-3-methyloxiran-2-yl]pent-4-en-2-one (1)

Computational interpretation of vibrational optical activity: The ROA spectra of (4<i>S</i>)-4-Methylisochromane and the (4<i>S</i>)-Isomers of <i>Galaxolide</i>®

The reliable computation of Raman-optical-activity (ROA) spectra of molecules of the size of the title compounds has, until now, not been possible. We show that our rarefied basis sets yield results in good agreement with the experimental data for (4S)-4-methylisochromane (=(4S)-3,4-dihydro-4-methyl-1H-2-benzopyran; 1), provided the equilibrium between the pseudo-equatorial and the pseudo-axial conformers is taken into account. Comparison between the measured and the computed ROA back-scattering spectra allows the unequivocal assignment of the absolute configuration of the molecule. Comparison with more-approximate calculations for the larger (4S)-isomers of Galaxolide® (2), which contain the (4S)-4-methylisochromane moiety, shows large-scale group frequencies on the same chiral fragments of the two molecules. The data confirm that ROA can be generated by interactions extending over several bonds, i.e., over larger distances than can be probed by NMR spectroscopy. Thus, the absolute configuration at C(7) of Galaxolide® is assignable independently of that at C(4). The computation of ROA for forward-scattering, which will soon be measurable for Galaxolide®, suggests that this scattering geometry provides additional stereochemical information that will be valuable in situations where absolute configurations at several stereogenic centers have to be assigned

Tractable Identification of Electric Distribution Networks

The identification of distribution network topology and parameters is a critical problem that lays the foundation for improving network efficiency, enhancing reliability, and increasing its capacity to host distributed energy resources. Network identification problems often involve estimating a large number of parameters based on highly correlated measurements, resulting in an ill-conditioned and computationally demanding estimation process. We address these challenges by proposing two admittance matrix estimation methods. In the first method, we use the eigendecomposition of the admittance matrix to generalize the notion of stationarity to electrical signals and demonstrate how the stationarity property can be used to facilitate a maximum a posteriori estimation procedure. We relax the stationarity assumption in the second proposed method by employing Linear Minimum Mean Square Error (LMMSE) estimation. Since LMMSE estimation is often ill-conditioned, we introduce an approximate well-conditioned solution based on eigenvalue truncation. Our quantitative results demonstrate the improvement in computational efficiency compared to the state-of-the-art methods while preserving the estimation accuracy

Reductive Transformations of Anthropogenic Chemicals in Natural and Technical Systems

Reductive transformation reactions of chemical pollutants (e.g., polyhalogenated hydrocarbons, aromatic azo and nitro compounds, chromium(VI) species) in the environment are important both from an ecotoxicological and from an environmental technology point of view. Using well-defined model reactors as well as more complex 'real world' systems, several groups at EAWAG are trying to unravel compound- and system-specific factors that control the reduction of a variety of anthropogenic chemicals under different conditions in the environment. The examples presented in this article include the reduction of nitroaromatic compounds under iron- and sulfate-reducing conditions, the reductive dehalogenation of chlorinated ethenes by cob(I)alamin and by a bacterium that uses such compounds as terminal electron acceptors, and the reduction of chromium(VI) by various reduced iron species. The link between microbial and abiotic (chemical) processes involved in reductive transformations of pollutants is emphasized. The major goal of this article is to illustrate the approaches taken to elucidate the mechanisms and kinetics of environmentally relevant reduction reactions of pollutants, and to discuss how the results of such studies can be used 1) to gain insight into what is actually happening in the environment, and 2) to develop methods for the treatment of chemical wastes or contaminated sites

General affine surface areas

Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for $L_{\phi}$ affine surface areas are established.Comment: Next version; minor change

New LpL_p Affine Isoperimetric Inequalities

We prove new $L_p$ affine isoperimetric inequalities for all $p \in [-\infty,1)$. We establish, for all $p\neq -n$, a duality formula which shows that $L_p$ affine surface area of a convex body $K$ equals $L_\frac{n^2}{p}$ affine surface area of the polar body $K^\circ$

Electron scattering in atomic force microscopy experiments

It has been shown that electron transitions, as measured in a scanning tunnelling microscope (STM), are related to chemical interactions in a tunnelling barrier. Here, we show that the shape and apparent height of subatomic features in an atomic force microscopy (AFM) experiment on Si(111) depend directly on the available electron states of the silicon surface and the silicon AFM tip. Simulations and experiments confirm that forces and currents show similar subatomic variations for tip-sample distances approaching the bulk bonding length.Comment: 5 pages and 4 figure