The electronic structures and magnetic anisotropies for compounds [An(COT)(2)] (An = U-III/U-IV, Np-III/Np-IV and Pu-III/Pu-IV, COT = cyclooctatetraene) are characterized using scalar relativistic density functional theory calculations and second-order perturbation theory based on a complete active space self-consistent field reference including spin-orbit coupling. The degree of participation of 5f orbitals in actinide-ligand bonding and the associated metal-ligand covalency is found to trend as U > Np >= Pu for both the tetra-positive and tripositive An complexes. A spin-Hamiltonian analysis indicates only weak single-molecule magnet (SMM) characteristics for [U(COT)(2)](-) and [Np(COT)(2)] complexes and no significant SMM behavior for the other complexes. The weak SMM behavior in [U(COT)(2)](-) and [Np(COT)(2)] is attributed to a subtle interplay between local symmetry and ligand-field splitting. Such a result suggests that magnetic anisotropy in Sf(3) ions can be modulated in general by electrostatic ligand field design. In particular, sigma-donor ligands oriented 180 degrees relative to one another will have a maximal influence on the 5f-orbital ligand field splitting, while pi donors like cyclopentadiene and COT generate ligand field influences that have more acute angles associated with corresponding atoms on the individual ligands. These observations rationalize the differences in SMM characteristics for [U(Bc(Me) )(3)] (Bp(Me-) = dihydrobis(methylimidazolyl)borate) and [U(Bp(Me))(3)] (Bp(Me-) = dihydrobis(methylpyrazolyl)borate) and indicate strategies to design new actinide-based SMMs with high magnetic relaxation barriers.