Calculations of Complete 4fⁿ and 4f^n-1 5d¹ Energy Level Schemes of Free Trivalent Rare-Earth Ions

Abstract

Calculations of complete energy level schemes for 4 f n and 4 f n -1 5 d 1 electronic configurations of free trivalent rare-earth ions have been performed. Semi-empirical Hamiltonian was used for the calculation of 4 f n configuration while a fully relativistic first-principles many-electron method was used for the calculation including 4 f n -1 5 d 1 configuration. As a result, Dieke's diagram is extended to about 200000 cm -1 in the case of 4 f n electronic configurations and about 370000 cm -1 in the case of 4 f n -1 5 d 1 electronic configurations. Calculated energy levels are plotted as a function of the atomic number.