Jahn-Teller Instability of Icosahedral [W@Au12](.).

The anionic state of the icosahedral W@Au12 cluster offers a rare example of a Jahn-Teller (JT) instability in an icosahedral fourfold degenerate Γ8 spinor level. The JT energy splittings of the ground Γ8 and excited sixfold degenerate Γ9 splittings in the vicinity of the degeneracy point are calculated with relativistic density functional theory. The results are very well explained by a first-order coupling model, based on the orbital instability of the spherical d-shell of the cluster.

The boron conundrum: which principles underlie the formation of large hollow boron cages?

Extensive optimisation calculations are performed for the B(80) isomers in order to find out which principles underlie the formation of large hollow boron cages. Our analysis shows that the most stable isomers contain triangular B(10) or rhombohedral B(16) building blocks. The lowest-energy isomer has C(3v) symmetry and is characterised by a belt of three interconnected B(16) units and two separate B(10) units.

Encapsulation of small base molecules and tetrahedral/cubane-like clusters of group V atoms in the boron buckyball: a density functional theory study.

A density functional theory study of small base molecules and tetrahedral and cubane-like group V clusters encapsulated in B(80) shows that the boron buckyball is a hard acid and prefers hard bases like NH(3) or N(2)H(4) to form stable off-centered complexes. In contrast, tetrahedral and cubane-like clusters of this family are metastable in the cage. The most favorable clusters are the mixed tetrahedral and cubane clusters formed by nitrogen and phosphorus atoms such as P(2)N(2)@B(80), P(3)N@B(80), and P(4)N(4)@B(80).

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.

Radial rescaling approach for the eigenvalue problem of a particle in an arbitrarily shaped box.

In the present work we introduce a methodology for solving a quantum billiard with Dirichlet boundary conditions. The procedure starts from the exactly known solutions for the particle in a circular disk, which are subsequently radially rescaled in such a way that they obey the new boundary conditions. In this way one constructs a complete basis set which can be used to obtain the eigenstates and eigenenergies of the corresponding quantum billiard to a high level of precision.

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.

Addition patterns in carbon allotropes: independence numbers and d-codes in the Klein and related graphs.

The problem of predicting stoichiometries and patterns of chemical addition to a carbon framework, subject solely to the restriction that each addend excludes neighboring sites up to some distance d, is equivalent to determination of d-codes of a graph, and for d = 2 to determination of maximum independent sets. Sizes, symmetries, and numbers of d-codes are found for the all-heptagon Klein graph (prototype for "plumber's nightmare" carbon) and for three related graphs. The independence number of the Klein graph is 23, which increases to 24 for a related, but sterically relaxed, all-heptagon network with the same number of vertices and modified adjacencies.