A study of the electronic properties of Au nanowires and Au nanoislands on Au(111) surfaces.

By means of ion bombardment of clean Au(111) films, atomically flat nanoparticles of various shapes and sizes were created, ranging from several tens of nm(2) down to only a few nm(2). Both two-dimensional Au islands as well as one-dimensional Au nanowire-like structures have been investigated by means of low-temperature scanning tunneling microscopy and spectroscopy. We were able to probe their local electronic structure in a broad energy range, which was found to be dominated by pronounced size-dependent confinement effects. Mapping of the local density of states revealed complex standing wave patterns that arise due to interference of scattered Au surface state electrons at the edges of the Au nanoparticles. The observed phenomena could be modeled with high accuracy by theoretical particle-in-a-box calculations based on a variational method that can be applied to '2D boxes' of arbitrary polygonal shape and that we have previously successfully applied to explain the electronic wave patterns on Co islands on Au(111). Our findings support the general validity of this particle-in-a-box model.

Vortices and their relation to ring currents and magnetic moments in nanographenes in high magnetic field.

Much attention has been paid to the role of vortices in the magnetic response properties of superconductors, but less so for molecular systems. Here we present a theoretical analysis on nanographenes subject to a strong homogeneous magnetic field. The analysis is based on the simple Hückel-London model, for which we derive the topological definition of vorticity. The results are confirmed by a more elaborate model that includes nonnearest neighbor interaction, the explicit presence of nuclei and all terms due to the magnetic field. We find that due to frontier orbital intersections, large changes in magnetic dipole moments occur. Orbital energy minima and maxima can be related to change of vortex patterns with flux.

Unique definition of the Zeeman-splitting g tensor of a Kramers doublet.

It has been widely accepted in the past that the g tensor describing the Zeeman splitting of a Kramers doublet is not uniquely defined. Here we show that with two basic requirements, (i) the invariance of the Zeeman Hamiltonian under symmetry transformations and (ii) its continuous change with the variations of the parameters of the system (geometry and crystal field), a unique determination of the elements of the g tensor is achieved.

Frontier orbitals of trivalent cages: (3,6) cages and (4,6) cages.

A qualitative molecular-orbital treatment and group-theoretical analysis reveals the nature of the frontier orbitals of (3,6) and (4,6) polyhedral cages, consisting of a hexagonal network with triangular and square defects, respectively. Leapfrog (3,6) cages have two nonbonding filled orbitals. Leapfrog (4,6) cages have a high HOMO-LUMO gap, while nonleapfrog (4,6) cages with octahedral symmetry have a very small HOMO-LUMO gap. The symmetry of the frontier orbitals is determined.

[Mo2(CN)11]:5- A detailed description of ligand-field spectra and magnetic properties by first-principles calculations.

An ab initio multiconfigurational approach has been used to calculate the ligand-field spectrum and magnetic properties of the title cyano-bridged dinuclear molybdenum complex. The rather large magnetic coupling parameter J for a single cyano bridge, as derived experimentally for this complex by susceptibility measurements, is confirmed to a high degree of accuracy by our CASPT2 calculations. Its electronic structure is rationalized in terms of spin-spin coupling between the two constituent hexacyano-monomolybdate complexes. An in-depth analysis on the basis of Anderson's kinetic exchange theory provides a qualitative picture of the calculated CASSCF antiferromagnetic ground-state eigenvector in the Mo dimer. Dynamic electron correlations as incorporated into our first-principles calculations by means of the CASPT2 method are essential to obtain quantitative agreement between theory and experiment.

Oriented 2-cell embeddings of a graph and their symmetry classification: generating algorithms and case study of the möbius-kantor graph.

We discuss a method to derive all symmetry-distinct oriented 2-cell embeddings of a given graph and classify them based on their symmetry. As an example, we apply the algorithm to the highly symmetrical trivalent Möbius-Kantor graph. Considering the derived 2-cell embeddings as carbon networks leads to some interesting negative curvature carbon allotropes.

The electronic structure and spectrum of Mo(CN)8(3-).

State of the art CASSCF and CASPT2 calculations have been performed to elucidate the nature of the electronic transitions observed in the experimental spectrum of the octacyanomolybdate(V) cation. Assuming a triangular dodecahedral structure for this complex gives a convincing agreement between theory and experiment. All absorption bands are assigned to low-lying charge-transfer transitions involving excitations from ligand orbitals to 4dx2-y2. The calculated molecular orbitals reveal weak pi interactions between the metal and ligand orbitals, compared to much stronger sigma interactions. This calculated electronic structure substantiates the previous hypothesis concerning the giant spin ground states of magnetic clusters and networks containing Mo(CN)8(3-) as a constituent part.

Symmetry-induced formation of antivortices in mesoscopic superconductors.

Recent progress in nanotechnology has stimulated interest in mesoscopic superconductors as components for quantum computing and cryoelectronics. The critical parameters for superconductivity (current and field) of a mesoscopic sample are determined by the pattern of vortices in it, which in turn is controlled by the symmetry imposed by the shape of the sample (see ref. 1 and references therein). Hitherto it has been unclear what happens when the number of vortices is not consistent with the natural symmetry. Here we show that additional vortex-antivortex pairs nucleate spontaneously so as to preserve the symmetry of the sample. For example, in a square with three vortices, the spontaneously generated pair, along with the original three vortices, distribute themselves so that the four vortices sit in the four corners, with the antivortex in the centre. The measured superconducting phase boundary (of superconducting transition temperature Tc versus magnetic field strength) is in very good agreement with the calculations, giving direct experimental evidence for these symmetry-induced vortex-antivortex pairs. Vortex entry into the sample is also changed: vortices enter a square in fours, with antivortices generated to preserve the imposed vorticity. The symmetry-induced nucleation of antivortices is not restricted to superconductors, but should also apply to symmetrically confined superfluids and Bose-Einstein condensates.

Vortex entry and nucleation of antivortices in a mesoscopic superconducting triangle.

The nucleation of superconductivity in mesoscopic equilateral triangles is investigated by using the linearized Ginzburg-Landau equation (LGLE). The trigonal symmetry of the sample has a profound effect on the superconducting state in the presence of a magnetic field H leading, in particular, to the formation of antivortices in symmetry-consistent states. For the same given irreducible representation, vortices enter always by three via the middle of the edges, approach the center, and then are dispatched towards the corners of the triangle. The measured superconducting phase boundary T(c)(H) is in good agreement with the T(c)(H) line found from the LGLE.

Assignment of the electronic spectra of [Mo(CN)(8)](4)(-) and [W(CN)(8)](4)(-) by Ab initio calculations.

CASPT2 calculations are performed on the dodecahedral and square antiprismatic isomers of the [Mo(CN)(8)](4)(-) and [W(CN)(8)](4)(-) complexes. The high-energy experimental bands above 40000 cm(-)(1) are assigned to MLCT transitions. The experimental observed trend of the extinction coefficients for the molybdenum and tungsten complex is reproduced by our CASSCF oscillator strengths. All bands below 40000 cm(-)(1) can be ascribed to ligand-field transitions, although small contributions from forbidden MLCT transitions cannot be excluded. In order to account for all experimental bands in the electronic spectrum of these octacyanocomplexes, a dynamic equilibrium in solution between the two isomeric forms must be hypothesized. Spin-orbit coupling effects are found to be more important for the square antiprismatic isomers; in particular, large singlet-triplet mixings are calculated for this isomer of [W(CN)(8)](4)(-). Ligand-field and Racah parameters as well as spin-orbit coupling constants are determined on the basis of the calculated transition energies. The obtained values for these parameters support the recently proposed model for exchange interactions in magnetic clusters and networks containing pentavalent octocyanometalates of molybdenum and tungsten.