The difference between the lowest energy level of the ƒ<sup><i>q</i></sup><i>d</i><sup>1</sup><i>s</i><sup>2</sup> electron configuration and the lowest energy level of the ƒ<sup><i>q</i>+1</sup><i>s</i><sup>2</sup> electron configuration for the metal vapors of nine members of the lanthanide series and four members of the actinide series are shown to be neatly and simply correlated by an adaptation of Jørgensen’s refined electron-spin-pairing energy theory. The theory is also used to extrapolate the corresponding energy differences for those lanthanide and actinide metal vapors for which this information was previously undetermined. The results will be helpful as a guide in making spectral assignments, and they are generally useful in correlating the thermodynamic properties of the chemical compounds of the lanthanide and actinide series. The theoretical basis of the treatment should also be applicable for correlating the relative energies of other electron configurations in these metal atoms and ions.
L. J. NUGENT and K. L. VANDER SLUIS, "Theoretical Treatment of the Energy Differences between ƒqd1s2 and ƒq+1s2 Electron Configurations for Lanthanide and Actinide Atomic Vapors," J. Opt. Soc. Am. 61, 1112-1115 (1971)