镧系三氟化物的SCF-X_α-SW研究

SCF-X_α-SW Calculations on Lanthanide Trifluorides

对10个镧系元素(Ln)三氟化物进行了非相对论和相对论SCF-X_a-SW计算,通过能级、分子轨道、结合能及布居数对比,讨论化学键本质:共价键中4f轨道的作用及相对论效应。结果表明,在LnF_3中Ln原子轨道参与成键的次序是:轻稀土d>f>p>s,而重稀土则有f>d>p>s。相对论效应使Ln4f能级上移,扩大了与F2p能级的距离,减弱成键。原子序数增大,Ln4f能级下移,与F2p能级距离缩小,使重稀土氟化物中成键增强。结合能计算值与实验值定性趋势一致。重稀土氟化物电离能的计算表明,相对论方案是获得定量符合所应该采用的。

SCF-X_a-SW calculations are carrled out on ten species of LnF_3 with Ln being Nd, Sin, Eu, Gd, Tb, Dy, Ho, Er, Tm and Yb. Both of the nonrelativistic and relativistic schemes have been tried. Energy sequences, contour maps, binding energies, atomic populations and ionization potentials are given in order to explore the chemical bonding in essence with emphasis focusing in the behavior of f-orbitals as well as the role of relativistic effect. The basic aspects of Dirac theory and X_a method are outlined at first. The shift of energy sequence due to relativistic effect in comparison with that of non-relativistic case is attributable in a qualitative sense, to 'direct' and 'indirect' factors. The former pushes inner levels down which is originated from the mass-velocity and Darwin operators in Dirac wave equation (2). The latter being in relation to the selfconsistent procedure, it produces an additionally shielded potonpotential around the Ln nucleus, driving the outlying 4f levels up. The general feature of energy sequence is Ln4f>Fn>Ln—F>Ln5p—F2s>…shown in Fig. 1, where Ln4f represents the molecular orbital set involving dominantly 4f component that being partialiy occupied; Fn and Ln—F are dominant in fluorine atomic 2p component, a set of bonding species; Ln5p, F2s etc have analogous meaning.The distance between Ln4f and F2p levels plays an important role for binding. Regardless of the relativistic effect, Ln4f levels descend monotonously with respect to the atomic number of Ln, so a smaller distance between Ln4f and F2p levels would be resulted in heavier LnF_3, leading stronger bonding from NdF_3 to YbF_3. Calculated binding energies are in accord with this trend, having higher values for heavier species in general which are also consistent with experimentsf(see Fig. 6 and 7).Contour maps of molecular orbitals drawing in the molecular plane and that perpendicular to the molecular plane are given in Fig. 4. They exhibit pictures of orbital interaction for eleven valence species. 3A_1' and 3E' are strong bonding orbitals, the next four: 1E', 1A_2', 2A_2' and 4E' are weak ones, the remaining 4A_1', 5E', 2E', 2A_2' and 3A_2' are antibonding orbitals, atom sphere populations partitioned into s, p, d and f componnents for bonding orbitals vary a little bit from NdF_3 to YbF_3 with magnitude arranged in the order: d>f>p>s for lighter species but f>d>p>s for heavier ones.Calculations of ionization potentials of NdF_3 and TmF_3 reveal that the relativistic scheme is necessary for obtaining reliable results for heavy lanthanide compounds.