Based on the Hubbard-Hirsch model, we studied the dynamical susceptibi
lity and spin excitation of an itinerant-electron system within the ra
ndom-phase approximation by using a Green's-function technique. It is
shown that the two-center matrix elements in the Hubbard-Hirsch model
not only change the dynamic property of the susceptibility, but also w
iden the gap between two spin subbands, which suppresses the electron-
hole single excitations. In contrast, the region of collective excitat
ions of the spin becomes larger.