The Analytical Solutions for Finite Clusters of Cubic Lattices

Using the Huckel method, we obtain the analytical expressions for eigenvalues and eigenvectors of s.c., f.c.c. and b.c.c. clusters of rectangular parallelepiped shape, and of an arbitrary size. Our formula converage to those derived from the Bloch sum, in the limit of infinite extension. DOS and LDOS reveal that the major contribution of the states near Fermi level originates from the surface atoms, also symmetry of DOS curves disappears by the introduction of 2nd nearest neighbor interactions, in all the cubic lattices. An accumulation of the negative charges on surface of cluster is observed.