The Theory of Complex Spectra II

Formulas for the relations between the energies of multiplets arising from the same electron configuration for all two-electron configurations up to ff and several cases of three-electron configurations are worked out following Slater's method; Slater's table of a's and b's being extended to cover f electrons. A systematic comparison of the known data with this first order perturbation theory shows poor agreement in many cases and good agreement in many. The theory predicts the observed alternation in the relative positions of singlet and triplet through S, P, D, F, etc. in the pp, pd, and pf triads, and the dd and df pentads. In general the p electron configurations fit very poorly; a uniform trend with atomic number is observed for p³ and good fits are obtained for $4p3d$ in TiIII, VIV, and Cr V. For d electrons the theory fits very well in the first long period of the periodic table, and fairly well in the second. The ¹S of d² and the ²D of d²s are predicted much higher than the levels assigned to those multiplets when such an assignment is made. d³ fits well except for ²P. An energy level table of La II is given as recently analysed by Meggers and Russell. Here we have complete $5d4f$ and 4f² configurations which fit the theory very well, these calculations having assisted in the assignment of some of the singlets and resulted in a rearrangement of singlet lines.