FACTORIZATION OF THE HUCKEL HAMILTONIAN MATRIX FOR HIGHLY SYMMETRICALMOLECULES

A simple approach to the group-theoretical factorizing of the Hamilton ian matrix of highly symmetrical molecules is presented. This approach , which is based on the Lanczos method, requires only a symmetry-adapt ed linear combination (SALC) for each category of irreducible represen tation (IR) of the molecular point-group, while it reduces the size of the problem by more than one order of magnitude. We demonstrate the t reatment by applying it to the study of electronic structures of the G oldberg type-II fullerenes, C-80, C-180, C-320, C-500 and C-980 within the Huckel tight-binding framework. The results, in terms of the fact or characteristic polynomial (or the subspectrum) for each category of irreducible representation, are presented for these giant molecules.