A previous self-consistent field molecular orbital method, able to describe systems having a large number of unpaired electrons, n, is reviewed and improved. This method is applied to the study of paramagnetism in large (1,000 -16,000 atoms) zigzag carbon nanotubes, represented by their n values. The computational scheme is based on the Hü ckel neglect differential overlap approach. It is shown that dependence of n on the semiempirical parameters is very small, and so they can be removed from the calculation. Enhancement of the paramagnetism (increase of n), by use of a strong external magnetic field, is also studied. Finally, the dependence of the Fermi one-electron potential energies and the spin atomic densities on both the parameters and the shape of the nanotubes is analyzed.The results have been multiplied by 10 3 , for compactness. The rows run over cycles and the columns run over atoms in a cycle.
In this work we have calculated the atomic spin densities and energy band gaps of three kinds of large carbon unlocalized high-spin aromatic systems, consisting of 1000 to 10,000 atoms. The selected systems, nanotubes, graphenes, and polyaryls, have obvious theoretical and technical interest. The results obtained for nanotubes and graphenes confirm and expand the ones published by other authors. The results for polyaryls are totally new.
To cite this article: J. R. Alvarez Collado (2006) On the calculation of the spectrum of large Hückel matrices, representing carbon nanotubes, using fast Hadamard and symplectic transforms, Molecular Physics,The Hu¨ckel theory is reviewed and improved. The usefulness of several Hadamard fast transforms when preconditioning binary Hu¨ckel matrices is compared and analysed. The spectrum of large benchmark (circulant) matrices is obtained by combining the SylvesterHadamard transform, the Singular Value Decomposition (SVD) and the theory of Hamiltonian symplectic matrices. The developed methodology is used to calculate the spectrum of Hu¨ckel matrices representing nanotubes of 16 000 atoms.
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