Geometry of nanostructures and eigenvectors of matrices

Abstract

The visualization of graphs describing molecular structures or other atomic arrangements is necessary in theoretical studying or examining nanostructures of several atoms. In the present paper, we review first the previous results obtained by drawing graphs with the help of various matrices as the adjacency matrix, the Laplacian matrix and the Colin de Verdiére matrix. We explain why they are applicable on if the atoms are on spherical surfaces. We have found recently a matrix boldW which could generate the Descartes coordinates for fullerenes, nanotubes and nanotori and also for nanotube junctions and coils as well. The construction of this matrix however is rather complicated in most of the cases. It needs energy minimization. Here will be shown that the spherical structures cut out from simple cubic, bcc, fcc and diamond lattices can be generated properly with the help of the matrix boldW.