Using density functional theory, we have theoretically studied various kinds of complexes of cyclopentadienyl and dicyclopentadienyl ligands with zinc and cadmium atoms of oxidation state +1. We first find that a sandwich complex Cp*-Zn-Zn-Cp* that was recently identified by Resta et al, (Science 2004, 305, 1136) has a large overall binding energy (=-3.19 eV), where Cp* denotes the pentamethyl cyclopentadienyl group. In addition, Cp-Zn-Zn-Cp is found to have a binding energy even larger by 0.93 eV, where Cp is a cyclopentadienyl ligand without methyl groups attached. Electronic structure analysis shows accumulation of electron density between Zn atoms, confirming the existence of Zn-Zn bond that is as strong as typical transition metal-halide bonds. In addition, our calculation suggests the possible existence of similar complexes Cp*-Zn-Cd-Cp* and Cp-Zn-Cd-Cp with a Zn-Cd bond not known thus far. Furthermore, study on the dimetallic complexes of dicyclopentadienyl ligands also predicts results which hold potential application to organometallic chemistry and organic synthesis: (a) Complexes involving a stiff ligand Dp can presumably exist in the form of dimerized sandwich complexes Dp-2M(1)-2M(2)-Dp (M-1, M-2 = Zn, Cd) with two metalmetal bonds. Their overall binding energies amount to -1.84 to -3.48 eV depending upon the kinds of metallic atoms, the strongest binding corresponding to dizinc complex. (b) Complexes involving more flexible ligand Ep can also form similar sandwich complexes Ep-2M(1) -2M(2)-Ep, but with much larger overall binding energies (=-4.97 to -7.09 eV). In addition, they can also exist in the form of nonsandwich complexes M-1-Ep-M-2 involving only one ligand. Unlike most of dimetallic complexes of other transition metals, syn conformations are found to be exceptionally stable due to the formation of M-1-M-2 bonds. Careful electronic structure analysis gives deep insight into the nature of observed phenomena.