The two iso-electronic molecules NpO4- and UO42- have been investigated by means of different ab initio methods: Hartree-Fock, Moller-Plesset perturbation theory at the second order, complete active space perturbation theory at the second order (CASPT2), coupled pair functional, coupled cluster single double with perturbative contributions from triple excitations, and density functional theory with hybrid functionals. Relativistic effective core potentials have been used in all calculations. NpO4- is a square planar molecule, whereas UO42-has a tetrahedral structure. The 5f orbitals, and, in particular, their lower energy in the neptunium compound that make them more available to form covalent bonds, play a crucial role in explaining the different structures of the two compounds.