Charge centers in CaF$_2$: Ab initio calculation of elementary physical properties

Abstract

Charge centers in ionic crystals provide a channel for elementary interaction between electromagnetic radiation and the lattice. We calculate the electronic ground state energies which are needed to create a charge center -- namely a $F$- and a $H$-center. In well agreement with common understanding the $F$-center results in being accompanied by a small lattice distortion whereas the $H$-center is accompanied by a very large lattice deformation. Opposite to the common understanding the additional positive charge in the charge center results rather to be localized on a F$_4^{3-}$ complex than on a F$_2^-$-complex. From the ground states of the charge centers we derive binding energies, diffusion barriers and agglomeration energies for $M$-center formation. These microscopic quantities are of fundamental interest to understand the dynamic processes which are initiated if the crystals interact with extreme intense deep ultra violet radiation. We further derive the equilibrium concentrations of charge centers in grown crystals.