The density functional approach has been used to compare the geometry and the frontier orbitals of the [(COT)Zr](2+), [CpZr](3+), [Cp2Zr](2+) and [calix[4]-(O)(4)Zr] fragments. The investigation on the [(COT)Zr](2+) and [Cp2Zr](2+)complexes shows that, in spite of the same number of low-lying empty orbitals available for bonding with additional ligands, the symmetries and the spatial extensions of these orbitals are different, and this has important consequences on their chemical behavior.