Theoretical study of electronic and geometric structures of a series of lanthanide trihalides LnX₃ (Ln = La-Lu; X = Cl, F)

Ab initio molecular orbital calculations are performed for a series of lanthanide trihalides LnX₃ (Ln = La to Lu; X = Cl, F), with the relativistic effective core potentials of Cundari and Stevens, to characterize the tendency in their electronic and geometric structures. In all the complexes (LnX₃), the planar structure (D(3h) symmetry) is calculated to be stable through normal mode analyses at the complete active space self-consistent field (CASSCF) levels. In the LnX₃, the number of 4f-electrons increases with increasing the atomic number, and 1.2-1.6 (2.1-2.2) electrons are transferred from Ln to Cl (F); the Ln-X bonds are dominated by charge- transfer but have a significant amount of covalent character that involves the 5d-orbital on Ln. It is also found that, along the lanthanide trihalide series, the first seven f-electrons occupy 4f-orbitals one by one from the lowest one up, while the second seven occupy 4f-orbitals from the highest one down, at the Hartree-Fock level. This occupation mechanism is explained in terms of the self-repulsion interactions between two electrons occupying the same spatial 4f-orbital. The Ln-X bond lengths, net charges, and vibrational frequencies show monotonic variation along the lanthanide series, which corresponds to the lanthanide contraction. State-averaged CASSCF calculations are also carried out for LnCl₃, in a combination with spin-orbit calculations using the atomic spin-orbit coupling constant for the f- electrons, to investigate the energy splitting of the nearly-degenerate low- lying states in the scheme of L-S coupling.