Meson properties in an extended nonlocal NJL model

A nonlocal version of the NJL model is investigated. It is based on a separable quark-quark interaction, as suggested by the instanton liquid picture of the QCD vacuum. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Features of the continuation of amplitudes from Euclidean space to Minkowski energies are discussed. These features lead to restrictions on the model parameters as well as on the range of applicability of the model. Conserved currents are constructed, and their consistency with various Ward identities is demonstrated. In particular, the Gell-Mann-Oakes-Renner relation is derived both in the ladder approximation and at meson loop level. The importance of maintaining chiral symmetry in the calculations is stressed throughout. Calculations with the model are performed to all orders in momentum. Meson masses are determined, along with their strong and electromagnetic decay amplitudes. Also calculated are the electromagnetic form factor of the pion and form factors associated with the processes gamma gamma* --> pi0 and omega --> pi0 gamma*. The results are found to lead to a satisfactory phenomenology and demonstrate a possible dynamical origin for vector-meson dominance. In addition, the results produced at meson loop level validate the use of 1/Nc as an expansion parameter and indicate that a light and broad scalar state is inherent in models of the NJL type.

The chemistry of intrinsically chiral surfaces

Intrinsically chiral metal and mineral surfaces show enantioselective behaviour without modifiers. Examples are artificial high-Miller-index surfaces of metal single crystals with cubic bulk lattice symmetry, which have no mirror planes and are therefore chiral, or surfaces of naturally occurring crystallites of some common minerals, such as alpha-quartz or calcite. Recent findings with regards to the surface geometry, reactivity and thermal stability of intrinsically chiral surfaces are discussed. A number of enantioselective effects have been reported in connection with the adsorption of small chiral molecules (e.g. alanine, cysteine) on intrinsically chiral surfaces under well-defined conditions. From a combination of experimental surface science techniques and theoretical ab initio model calculations it emerges that these effects are due to a combination of attractive and repulsive adsorbate-substrate and inter-adsorbate interactions.

Mesonic fluctuations in a nonlocal Nambu–Jona-Lasinio model

The effects of meson fluctuations are studied in a nonlocal generalization of the Nambu–Jona-Lasinio model, by including terms of next-to-leading order (NLO) in 1/Nc. In the model with only scalar and pseudoscalar interactions NLO contributions to the quark condensate are found to be very small. This is a result of cancellation between virtual mesons and Fock terms, which occurs for the parameter sets of most interest. In the quark self-energy, similar cancellations arise in the tadpole diagrams, although not in other NLO pieces which contribute at the 25% level. The effects on pion properties are also found to be small. NLO contributions from real pi-pi intermediate states increase the sigma meson mass by 30%. In an extended model with vector and axial interactions, there are indications that NLO effects could be larger.

Meson properties in an extended nonlocal NJL model

We consider a non-local version of the NJL model, based on a separable quark-quark interaction. The interaction is extended to include terms that bind vector and axial-vector mesons. The non-locality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Working in the ladder approximation, we calculate amplitudes in Euclidean space and discuss features of their continuation to Minkowski energies. Conserved currents are constructed and we demonstrate their consistency with various Ward identities. Various meson masses are calculated, along with their strong and electromagnetic decay amplitudes. We also calculate the electromagnetic form factor of the pion, as well as form factors associated with the processes γγ* → π0 and ω → π0γ*. The results are found to lead to a satisfactory phenomenology and lend some dynamical support to the idea of vector-meson dominance.

Enantiospecific adsorption of alanine on the chiral Cu{531} surface

We have studied enantiospecific differences in the adsorption of (S)- and (R)-alanine on Cu{531}R using low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy, and near edge X-ray absorption fine structure (NEXAFS) spectroscopy. At saturation coverage, alanine adsorbs as alaninate forming a p(1 4) superstructure. LEED shows a significantly higher degree of long-range order for the S than for the R enantiomer. Also carbon K-edge NEXAFS spectra show differences between (S)- and (R)-alanine in the variations of the ð resonance when the linear polarization vector is rotated within the surface plane. This indicates differences in the local adsorption geometries of the molecules, most likely caused by the interaction between the methyl group and the metal surface and/or intermolecular hydrogen bonds. Comparison with model calculations and additional information from LEED and photoelectron spectroscopy suggest that both enantiomers of alaninate adsorb in two different orientations associated with triangular adsorption sites on {110} and {311} microfacets of the Cu{531} surface. The experimental data are ambiguous as to the exact difference between the local geometries of the two enantiomers. In one of two models that fit the data equally well, significantly more (R)-alaninate molecules are adsorbed on {110} sites than on {311} sites whereas for (S)-alaninate the numbers are equal. The enantiospecific differences found in these experiments are much more pronounced than those reported from other ultrahigh vacuum techniques applied to similar systems.

The Structure of the chiral Pt{531} surface: a combined LEED and DFT study

The structure of the chiral kinked Pt{531} surface has been determined by low-energy electron diffraction intensity-versus-energy (LEED-IV) analysis and density functional theory (DFT). Large contractions and expansions of the vertical interlayer distances with respect to the bulk-terminated surface geometry were found for the first six layers (LEED: d(12) = 0.44 angstrom, d(23) = 0.69 angstrom, d(34) = 0.49 angstrom, d(45) = 0.95 angstrom, d(56) = 0.56 angstrom; DFT: d(12) = 0.51 angstrom, d(23) = 0.55 angstrom, d(34) = 0.74 angstrom, d(45) = 0.78 angstrom, d(56) = 0.63 angstrom; d(bulk) = 0.66 angstrom). Energy-dependent cancellations of LEED spots over unusually large energy ranges, up to 100 eV, can be explained by surface roughness and reproduced by applying a model involving 0.25 ML of vacancies and adatoms in the scattering calculations. The agreement between the results from LEED and DFT is not as good as in other cases, which could be due to this roughness of the real surface.

The importance of attractive three-point interaction in enantioselective surface chemistry: stereospecific adsorption of serine on the intrinsically chiral Cu{531} surface

Both enantiomers of serine adsorb on the intrinsically chiral Cu{531} surface in two different adsorption geometries, depending on the coverage. At saturation, substrate bonds are formed through the two oxygen atoms of the carboxylate group and the amino group (μ3 coordination), whereas at lower coverage, an additional bond is formed through the deprotonated β−OH group (μ4 coordination). The latter adsorption geometry involves substrate bonds through three side groups of the chiral center, respectively, which leads to significantly larger enantiomeric differences in adsorption geometries and energies compared to the μ3 coordination, which involves only two side groups. This relatively simple model system demonstrates, in direct comparison, that attractive interactions of three side groups with the substrate are much more effective in inducing strong enantiomeric differences in heterogeneous chiral catalyst systems than hydrogen bonds or repulsive interactions.

Emulation of chiral hydrogenation catalysts by adsorbtion of small molecules onto Ni surfaces

Adsorption of small molecules on the Ni{111} and NiO{111} surfaces is investigated under UHV and elevated pressures (~10-1 mbar) of hydrogen and water. The molecules considered are chosen for their relevance to understanding the mechanism of enantioselective hydrogenation on Raney Nickel modified by chiral molecules. Adsorption of water onto, and its subsequent reaction with, oxygen-covered Ni{111} is dependent on the initial atomic oxygen coverage. An OH species (O1s binding energy 531.5eV), oriented perpendicular to the surface, forms at atomic oxygen coverages <0.25ML. The reaction does not consume all the adsorbed oxygen for coverages ≥0.12ML. The p(2×2) atomic oxygen uperstructure is unreactive, while an OH species is formed on the p(√3×√3) superstructure at binding energy 530.9eV. L-alanine is adsorbed on Ni{111} as a model chiral modifier molecule. At low coverages, alanine forms a presumed tridentate alaninate species for coverages ≥0.11ML at 250K. A minority, bidentate zwitterionic species forms at coverages >0.11ML, but was not observed at 300K. Saturation occurs at 0.25ML. At high alanine coverages (≥0.19ML) and H2 pressure (≥1×10-2 mbar), the tridentate L-alaninate converts to bidentate zwitterionic L-alanine at 300K. Thermal evolution of L-alanine on Ni{111} under varying hydrogen pressures is examined. Adsorption of L-alanine onto hydroxylated NiO{111} at 300K in UHV, mimicking a catalyst surface under aqueous conditions, yields the tridentate alaninate which is immune to the effects of elevated hydrogen pressure. Exposing the L-alanine/Ni{111} adsorption system to water (≤10-1 mbar) oxidises the surface and recreates the L-alanine/hydroxylated NiO{111} system. Pyruvic acid on Ni{111} is examined as a model for hydrogenation substrate adsorption. Behaviour is coverage dependent and several conformations are possible at low coverages (≤0.1ML). Annealing at coverages <0.2ML causes a condensation reaction, releasing water onto the surface. High coverages do not condense and a saturation coverage of ~0.35ML is found.