On the calculation of the spectrum of large Hückel matrices, representing carbon nanotubes, using fast Hadamard and symplectic transforms

Abstract

The Hückel theory is reviewed and improved. The usefulness of several Hadamard fast transforms when preconditioning binary Hückel matrices is compared and analysed. The spectrum of large benchmark (circulant) matrices is obtained by combining the Sylvester–Hadamard transform, the Singular Value Decomposition (SVD) and the theory of Hamiltonian symplectic matrices. The developed methodology is used to calculate the spectrum of Hückel matrices representing nanotubes of 16 000 atoms.

Keywords:

• Hückel
• Diagonalization
• Eigenproblem
• Hadamard
• Symplectic
• Nanotubes

Acknowledgements

This project was financially supported by the CICYT, Spain, through grant CTQ2005-09105-C04-03/PPQ. Special thanks are due to Dr. I. Rodriguez Ramos and Dr. A. Guerrero Ruiz for their helpful advice. Also, special thanks are due to the designers of the Google search engine.