(1) Institute of Chemistry, Academia Sinica, Taipei, Taiwan 11529, Republic of China;(2) Institute of Mathematics, Academia Sinica, Taipei, Taiwan, Republic of China
Abstract:
A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Net sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.