Relative Energies of the Lowest Levels of the $f^{q}p{s}^2$, $f^{q}d{s}^2$, and $f^{q+1\mathrm{}}{s}^2$ Electron Configurations of the Lanthanide and Actinide Neutral Atoms

Linearization of the differences between the lowest levels of the $f^{q}p{s}^2$, $f^{q}d{s}^2$, and $f^{q+1\mathrm{}}{s}^2$ electron configurations as a function of $q$ is demonstrated for the lanthanide and actinide series. A linear extrapolation of these differences estimates the energy of the lowest level of the $4f^{14}6p6s^2$ electron configuration of Lu to be 3.5 × ${10}^3$ ${\mathrm{cm}}^{-1\mathrm{}}$ higher than the measured value. This deviation from linearity is attributed to expected discontinuities at the $q=0\mathrm{} \mathrm{and} 14$ ends of the $f^{q}d{s}^2$ series. In the actinide series the corresponding linear extrapolation predicts the lowest level of the $5f^{14}7p7s^2$ electron configuration of Lr to be (2.3 ± 3) × ${10}^3$ ${\mathrm{cm}}^{-1\mathrm{}}$ above the expected $5f^{14}6d7s^2$ ground state, after correction for a corresponding 3.3 × ${10}^3$ ${\mathrm{cm}}^{-1\mathrm{}}$ deviation expected at the end of the actinide series.