Yang-Mills Detour Complexes and Conformal Geometry

Working over a pseudo-Riemannian manifold, for each vector bundle with connection we construct a sequence of three differential operators which is a complex (termed a Yang-Mills detour complex) if and only if the connection satisfies the full Yang-Mills equations. A special case is a complex controlling the deformation theory of Yang-Mills connections. In the case of Riemannian signature the complex is elliptic. If the connection respects a metric on the bundle then the complex is formally self-adjoint. In dimension 4 the complex is conformally invariant and generalises, to the full Yang-Mills setting, the composition of (two operator) Yang-Mills complexes for (anti-)self-dual Yang-Mills connections. Via a prolonged system and tractor connection a diagram of differential operators is constructed which, when commutative, generates differential complexes of natural operators from the Yang-Mills detour complex. In dimension 4 this construction is conformally invariant and is used to yield two new sequences of conformal operators which are complexes if and only if the Bach tensor vanishes everywhere. In Riemannian signature these complexes are elliptic. In one case the first operator is the twistor operator and in the other sequence it is the operator for Einstein scales. The sequences are detour sequences associated to certain Bernstein-Gelfand-Gelfand sequences.     

Tip-induced reduction of the resonant tunneling current on semiconductor surfaces

We report scanning tunneling microscope measurements showing a substantial decrease of the current, almost to zero, on the Si(111)-(7x7) reconstruction in the near-to-contact region under low bias conditions. First principles simulations for the tip-sample interaction and transport calculations show that this effect is driven by the substantial local modification of the atomic and electronic structure of the surface. The chemical reactivity of the adatom dangling bond states that dominate the electronic density of states close to the Fermi level and their spatial localization result in a strong modification of the electronic current.     

Electrochemical study of the anomalous salt extraction from water to a polar organic solvent

Journal of Solid State Electrochemistry -     

On the defect spectrum of an extension of a Banach space operator

Let T be an operator acting on a Banach space X. We show that between extensions of T to some Banach space Y X which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.     

The electronic structure and adsorption geometry of L-histidine on Cu(110)

The adsorption of L-histidine on clean and oxygen-covered Cu(110) surfaces has been studied by soft X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. The valence band spectra, carbon, nitrogen and oxygen 1 s XPS and N K edge absorption spectra were measured for submonolayer, monolayer, and multilayer films. The spectra provide a detailed picture of the electronic structure and adsorption geometry at each coverage. In the monolayer, the histidine molecules are randomly oriented, in contrast to the submonolayer regime, where the molecules are coordinated to the copper surface with the imidazole functional group nearly parallel to, and strongly interacting with, the surface. The pi*/sigma* intensity ratio in NEXAFS spectra at the nitrogen edge varies strongly with angle, showing the imidazole ring is oriented. Adsorption models are proposed.     

31P chemical shift tensors for canonical and non-canonical conformations of nucleic acids: a DFT study and NMR implications

31P chemical shift anisotropy (CSA) tensors have been calculated for a set of selected DNA and RNA backbone conformations using density functional theory. The set includes canonical A-RNA, A-DNA, BI-DNA, BII-DNA, ZI-DNA, and ZII-DNA as well as four A-RNA-type, seven non-A-RNA-type, and three non-canonical DNA conformations. Hexahydrated dimethyl phosphate has been employed as a model. The 31P chemical shift tensors obtained are discussed in terms of similarities in the behavior observed for gauche-gauche (gg) and gauche-trans (gt) conformations around the P-O bonds. We show that torsion angles alpha and zeta are major determinants of the isotropic chemical shift deltaiso and of the deltaCSA11 component of the traceless chemical shift tensor, which is revealed in separate ranges of both deltaiso and deltaCSA11 for gg- and gt-conformers, respectively. A clear distinction between the two conformation types has not been found for the deltaCSA22 and deltaCSA33 components, which is attributed to their different directional properties. The 31P CSA tensors exhibit considerable variations resulting in large spans of approximately 16 ppm for deltaCSA11 and approximately 22 ppm for deltaCSA22 and deltaCSA33. We examine the consequences of the CSA variations for predicting the chemical shift changes upon partial alignment deltacsa and for the values of CSA order parameters extracted from the analysis of 31P NMR relaxation data. The theoretical 31P CSA tensors as well as the experimental 31P CSA tensor of barium diethyl phosphate (BDEP) are used to calculate deltacsa for two eclipsed orientations of the CSA and molecular alignment tensors. Percentage differences between the CSA order parameters obtained using the theoretical 31P CSA tensors and the experimental 31P CSA tensor of BDEP, respectively, are also determined.     

Dependence of the L-alanyl-L-alanine conformation on molecular charge determined from ab initio computations and NMR spectra

The l-alanyl-l-alanine (AA) molecule behaves differently in acidic, neutral, and basic environments. Because of its molecular flexibility and strong interaction with the aqueous environment, its behavior has to be deduced from the NMR spectra indirectly, using statistical methods and comparison with ab initio predictions of geometric and spectral parameters. In this study, chemical shifts and indirect spin-spin coupling constants of the AA cation, anion, and zwitterion were measured and compared to values obtained by density functional computations for various conformers of the dipeptide. The accuracy and sensitivity of the quantum methods to the molecular charge was also tested on the (mono)-alanine molecule. Probable AA conformers could be identified at two-dimensional potential energy surfaces and verified by the comparison of the computed parameters with measured NMR data. The results indicate that, whereas the main-chain peptide conformations of the cationic (AA+) and zwitterionic (AAZW) forms are similar, the anion (AA-) adopts also another, approximately equally populated conformer in the aqueous solution. Additionally, the NH2 group can rotate in the two main chain conformations of the anionic form AA-. According to a vibrational quantum analysis of the two-dimensional energy surfaces, higher-energy conformers might exist for all three charged AA forms but cannot be detected directly by NMR spectroscopy because of their small populations and short lifetimes. In accord with previous studies, the NMR parameters, particularly the indirect nuclear spin-spin coupling constants, often provided an excellent probe of a local conformation. Generalization to peptides and proteins, however, has to take into account the environment, molecular charge, and flexibility of the peptide chain.     

Electrochemical behaviour of the LiF-(CaF2)-La2O3 system

The electrochemical behaviour of the LiF-La₂O₃ and LiF-CaF₂-La₂O₃ systems was investigated by means of cyclic voltammetry. Several types of working electrodes (spectrographic pure graphite, W, Mo, Ni, Cu) were used. It was found that chemical reactions take place in the system during the dissolution of lanthanum oxide. The reduction of lithium cations occurred at the most positive potential from the species formed in the melt on ‘inert’ cathodes (W, Mo). The reactive cathodes (Cu, Ni) allowed the lanthanum deposition with depolarisation.