Naslov
Nanostructures and Eigenvectors of Matrices

Autori
László, István ; Graovac, Ante ; Pisanski, Tomaž

Vrsta, podvrsta i kategorija rada
Poglavlja u knjigama, znanstveni

Knjiga
Topological Modelling of Nanostructures and Extended Systems

Urednik/ci
Ashrafi, Ali Reza ; Cataldo, Franco ; Iranmanesh, Ali ; Ori , Ottorino

Izdavač
Springer

Grad
Dordrecht

Godina
2013

Raspon stranica
287-302

ISBN
978-94-007-6413-2

Ključne riječi
Nanostuctures, eigenvectors, W matrices

Sažetak
Very often the basic information about a nanostructure is a topological one. Based on this topological information, we have to determine the Descartes coordinates of the atoms. For fullerenes, nanotubes, and nanotori, the topological coordinate method supplies the necessary information. With the help of the bi-lobal eigenvectors of the Laplacian matrix, the position of the atoms can be generated easily. This method fails, however, for nanotube junctions and coils and other nanostructures. We have found recently a matrix W which could generate the Descartes coordinates not only of fullerenes, nanotubes, and nanotori but also of nanotube junctions and coils. Solving namely the eigenvalue problem of this matrix W, its eigenvectors with zero eigenvalue give the Descartes coordinates. There are nanostructures, however, whose W matrices have more eigenvectors with zero eigenvalues than it is needed for determining the positions of the atoms in 3D space. In such cases the geometry of nanostructure can be obtained with the help of a projection from a higher-dimensional space in a similar way as the quasicrystals are obtained. In this chapter, we study the structure and geometrical properties of some selected graphs which bring us to higher-dimensional spaces. A simple harmonic potential is suggested for constructing the matrix W.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika, Kemija

POVEZANOST RADA