Energy differences between4fn+15d06s2and4fn5d16s2electron configurations for the lanthanide atoms

Abstract

We study the energy difference $\ensuremath{\Delta}E(n)$ between the ${4f}^{n+1}{5d}^{0}{6s}^{2}$ and ${4f}^{n}{5d}^{1}{6s}^{2}$ configurations of the entire neutral lanthanide series, where n runs from 0 (La) through 13 (Yb). The $\ensuremath{\Delta}E(n)$ values obtained by numerical multiconfigurational Dirac-Fock (MC-DF) calculations are lower than experiment, while those given by nonrelativistic self-consistent-field (NR-SCF) calculations are larger than experiment. The difference between the MC-DF and NR-SCF $\ensuremath{\Delta}E(n)$ values is about $3--5\mathrm{eV}.$ If we add the correlation energy corrections obtained by nonrelativistic second-order perturbation calculations to $\ensuremath{\Delta}E(n)$ given by MC-DF calculations, the resulting values of $\ensuremath{\Delta}E(n)$ for the neutral lanthanides agree with experiment to within 1.0 eV, except for La and Yb.