Variation trends across the AnO(2) series of An5f-electron covalent bonding and An5f-->O3s, O2p-->An5f charge transfer energies, are studied using DV-X alpha relativistic spin-polarised computation of electronic structures applied to 11 'AnO(8)' clusters, from ThO8 to FmO8. It is found that the binding energies of 5f orbitals, therefore the An5f-O2p hybridisation, are increasing though the 5f orbitals are localising across the An series. In our calculations, the 3s and 3p ionic-like orbitals of O2- ions are included for the first time as LCAO-MO bases. Then, the conduction band is a mixing of O3s and An6d and its lower edge corresponds to an O3s-dominated state. Moreover, the calculated charge transfer (CT) energies of An5f-->O3s and O2p-->An5f transitions show the so-called tetrad effect when CT energies, respectively increasing and decreasing across the AnO(2) series. It is pointed out that the tetrad effect here comes mainly from the special spin-polarised pattern of 5f levels and the increasing general trend of 5f binding energies.