  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.
