Optical spectra of trivalent lanthanides in LiYF₄ crystal

Systematic calculations of multiplet energy levels of all trivalent lanthanides in LiYF₄ (YLF) crystal were performed using two completely different approaches: diagonalization of the commonly used semi-empirical Hamiltonian and a fully relativistic discrete-variational multi-electron (DV-ME) method which is based on a first-principles configuration-interaction (CI) calculation program using molecular spinors obtained by the discrete-variational Dirac-Slater (DV-DS) calculations. The energy level diagrams within 4fⁿ electron configurations were obtained by the former method, while those including both 4fⁿ and 4f^n-15d¹ configurations were obtained by the latter. Using the explicit many-electron wave functions, the absorption spectra of Pr³⁺, Ho³⁺, and Tm³⁺ in YLF were calculated and compared with the experimental data.