Effective-Hamiltonian parameters for \emph{ab initio} energy-level calculations of SrCl${}_2$:Yb${}^{2+}$ and CsCaBr${}_3$:Yb${}^{2+}$

Calculated energy levels from recent \emph{ab initio} studies of the electronic structure of SrCl${}_2$:Yb${}^{2+}$ and CsCaBr${}_3$:Yb${}^{2+}$ are fitted with a semi-empirical “crystal-field” Hamiltonian, which acts within the model space $4f^{14}+4f^{13}5d+4f^{13}6s$. Parameters are obtained for the minima of the potential-energy curves for each energy level and also for a range of anion-cation separations. The parameters are compared with published results parameters fitted to experimental data and to atomic calculations. The states with significant $4f^{13}6s$ character give a good approximation of the impurity-trapped exciton states that appear in the \emph{ab initio} calculations.