On the Diagonalization of Hermitian Matrices, and Its Use to Calculate the Hückel Electronic Structure of Large Carbon Nanotubes

Abstract

In this paper, a method for calculating all the Hückel molecular orbitals (MO) of large (16.000 atoms) carbon zigzag nanotubes is presented. These MO have been obtained by combining the singular value decomposition (SVD), the Sylvester-Hadamard transform, and the theory of Hamiltonian-Symplectic matrices. Numerical diagonalization of hermitian matrices is reviewed and improved. A new, more advantageous, (tri-diagonal) algorithm is proposed and analyzed. The reactivity of the atoms is described by calculating their free valence indices.