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Geometry of nanostructures and eigenvectors of matrices
Author(s) -
László István
Publication year - 2013
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201300091
Subject(s) - eigenvalues and eigenvectors , matrix (chemical analysis) , adjacency matrix , simple (philosophy) , fullerene , nanotube , laplacian matrix , nanostructure , energy minimization , tetrahedron , geometry , theoretical physics , physics , materials science , nanotechnology , mathematics , quantum mechanics , carbon nanotube , philosophy , epistemology , composite material
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 W 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 W .