Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Photoabsorption in sodium clusters on the basis of time-dependent density-functional theory sodium clusters

The photoabsorption spectra of a continuous series of Nan clusters (n⩽14, n=20, n=40) have been calculated using a time-dependent density-functional scheme. Accordingly, we present these spectra and show that they are in very good agreement with other theoretically and experimentally obtained photoabsorption spectra. Furthermore, we discuss the influence of the cluster structure on the photoabsorption spectrum for some selected clusters and present for several cluster sizes photoabsorption spectra of different geometrical isomers. The spectra of clusters with five or more atoms are dominated by a few large peaks which can be interpreted as collective plasmon excitations.Peer reviewe

Tubular structures from the LnS-TaS2(Ln=La,Ce,Nd,Ho,Er) and LaSe-TaSe2_{2} misfit layered compounds

Nanotubular structures from a new family of misfit compounds LnS–TaS2 with (Ln = La, Ce, Nd, Ho, Er) and LaSe–TaSe2 (some of them not known hitherto) are reported. Stress relaxation originating from the lattice mismatch between the alternating LnS(Se) and TaS2(Se) layers, combined with seaming of the dangling bonds in the rim, leads to the formation of a variety of nanotubular structures. Their structures are studied via scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), scanning transmission electron microscopy (STEM) and selected area electron diffraction (SAED). Tubules exhibiting a single folding vector for the LnS(Se) as well as TaS2(Se) layers were often found. The small values of the c-axis periodicities are indicative of a strong interaction between the two constituent layers which was also supported by Raman spectroscopy and theoretical calculations

Single-wall-carbon-nanotube/single-carbon-chain molecular junctions

Stable junctions between a single carbon chain and two single-wall carbon nanotubes were produced via coalescence of functionalized fullerenes filled into a single-wall carbon nanotube and directly imaged by in situ transmission electron microscopy. First principles quantum chemical calculations support the observed stability of such molecular junctions. They also show that short carbon chains bound to other carbon structures are cumulenes and stable semiconductors due to Peierls-like distortion. Junctions like this can be regarded as archetypical building blocks for all-carbon molecular electronics. © 2010 The American Physical Society