Dynamical charge overlap, electron-lattice coupling strength, and lattice dynamics of ionic crystals

Experimentally determined electron-phonon coupling in alkaline-earth halides is compared to that calculated using a classical extended-charge shell model in which the electronic charges of neighboring ions overlap each other. The electron-phonon interaction in Sr${\mathrm{F}}_2$:${\mathrm{Sm}}^{2+}$, Ca${\mathrm{F}}_2$:${\mathrm{Sm}}^{2+}$, Sr${\mathrm{F}}_2$:${\mathrm{Eu}}^{2+}$, and Ca${\mathrm{F}}_2$:${\mathrm{Eu}}^{2+}$ is calculated in detail with only one disposable model parameter which determines the extent of the charge distributions. The results lead to very good agreement with experimentally determined vibronic sidebands, with the coupling strengths determined from static stress measurements, and are also consistent with a Jahn-Teller interaction present in the case of ${\mathrm{Eu}}^{2+}$ but to a lesser extent in ${\mathrm{Sm}}^{2+}$. In comparison, a coupling model involving nonoverlapping charge distributions yields very poor agreement. The extent of the charge distribution as determined from the model parameter leads, however, to an unphysical "effective" charge of the ions. A possible source of this result is the neglect of quantum-mechanical overlap and exchange effects.