István László

The geometric structure of deformed nanotubes and the topological coordinates

After summarizing the harmonic approach to topological coordinates and the null space embedding of graphs, three-coordinated tiling of the plane by hexagons, pentagons, and heptagons are presented and used for the construction of tubular, toroidal, and helical carbon structures. Physically realistic 3D geometries are formed from the corresponding adjacency matrices, and the final structure was obtained with the help of Brenner-potential based molecular mechanics methods.

A study of the UV spectrum of the truncated icosahedral C60 molecule

Abstract The PPP-CI molecular orbital theory for three-dimensional systems was applied to the study of the UV spectrum of the truncated icosahedral C 60 mole

Molecular dynamics study of the C60 molecule

Tight-binding molecular dynamics calculations were performed for 60 carbon atoms. Under helium atmosphere, cage like structures were obtained independent of the initial arrangement of the carbon atoms, but in the case of bulk simulation the final structure was determined by the density of the carbon atoms. After a simulation time of 30.8 ps in helium atmosphere of temperature 4000 K, a C60 cage structure of 11 pentagons, 19 hexagons, one tetragon and one heptagon was obtained.

Atomic structure and electronic density of states around the fermi level in amorphous carbon models

Abstract There are topologically determined energy levels concentrated around the Fermi level. Graph theory is used to estimate the density of states near the Fermi level (EF) of amorphous carbon (a-C) structure. Within the ab initio Hartree-Fock calculations these states have lower energies than EF, but they remain the highest occupied states in the electronic density of states.

A Possible Topological Arrangement of Carbon Atoms at Nanotube Junctions

Abstract Based on the intersection of cylinders, an algorithm is presented for constructing junctions between single‐wall nanotubes of any chirality and diameter.

Graph Drawing with Eigenvectors

The visualization of graphs describing molecular structures or other atomic arrangements is necessary in theoretical studying or examining nano structures of several atoms. In the present paper we review previous results obtained by drawing graphs with the help various matrices as the adjacency matrix, the Laplacian matrix and the Colin de Verdiere matrix. In examples we show their possibilities and limits of applicability. We suggest a new matrix that reproduces well the same structures and those ones which were not drawn by the previous matrices.

Topologically Determined Electronic Energy Levels in Fullerenes

Abstract Molecular and solid CuxC 60 and AgxC 60 (x < 5) structures are suggested in order to produce topologically determined electronic energy levels in fullerenes.

Topological and energetic conditions for lithographic production of carbon nanotubes from graphene

Density Functional Based Tight-Binding (DFTB) molecular dynamics (MD) simulations were performed for producing carbon nanotubes from graphene nanoribbons. The constant temperature simulations were controlled with the help of Nose-Hoover thermostat. In our systematic study we obtained critical curvature energies and determined topological conditions for nanotube production from two parallel graphene nanoribbons. We obtained linear relationship between the curvature energy and the square of the curvature.

Local Combinatorial Characterization of Fullerenes

We present a general method which enables a possible classification of fullerenes by means of local topological invariants. In this study fullerenes are considered as bifaced simple (trivalent) polyhedra. The method proposed is based on the combinatorial analysis of the first neighbor environments (coronas) of vertices and/or edges of bifaced simple polyhedra. For this purpose, we used the so-called line-corona detectors (LC detectors) which are simple connected acyclic graphs (trees) having only 1- and 3-valent vertices. It is demonstrated that by performing certain matching operations with appropriately defined LC detectors, a finite set of local, algebraically independent topological invariants can be obtained by which various fullerene structures can be partitioned into disjoint classes of equivalence. We found also linear interdependencies between similar parameters previously defined in the scientific literature. Discriminating performance of computed topological descriptors have been tested on the set of C40 fullerene isomers.

The Electronic Structure of Nanotubes and the Topological Arrangements of Carbon Atoms

After summarizing the topological coordinate methods for fullerenes, tori and nanotubes, an extension is presented for two dimensional periodic carbon sheets. This was applied for four Haeckelite structures. Contrary to the expectation, the leapfrog transformed Haeckelite structures did not revealed intrinsic metallic behavior. The corresponding nanotubes were found semiconductors independent of tube orientations.