Relativistic density-functional all-electron calculations of interconfigurational energies of lanthanide atoms

The interconfigurational energies (ICEs) of the lanthanide atoms, including the s ionization energies, the f ionization energy, and the fd transition energy, are studied based on the fully relativistic density-functional theory (RDFT). The exchange-correlation energy functional by the local-spin-density approximation (RLSD), the generalized gradient approximation (RGGA), and the approximation within the framework of the Krieger-Li-Iafrate treatment of the optimized effective potential (ROEP) incorporated by an explicit self-interaction correction term are used to perform the calculation. In addition, results obtained from the simple perturbation with the mass-velocity correction and the Darwin shift are also presented for comparisons. It is found that the ROEP, with the proper description of the long-range behavior of the outermost electron, yields the most best computations for the two s ionizations. For the f ionization potential and the fd transition energy, the RGGA surpasses the RLSD and the ROEP, reflecting the importance of the gradient expansion in dealing with the more localized f or d electron densities. The excellent satisfaction of the Koopmans' theorem for the two s binding energies is demonstrated within the ROEP framework. As predicted in previous work [C. Y. Ren, H. T. Jeng, and C. S. Hsue, Phys. Rev. B 66, 125105 (2002)], the perturbative ICEs for the first s ionization are almost the same with those by the fully RDFT through the whole lanthanide atoms, with a deviation smaller than 0.1 eV. However, the similarity of calculations by means of the fully RDFT and the standard perturbation method is destroyed in the cases of the f ionization and the fd transition energy.