Theory of the Optical and Magnetic Properties of the Self-Trapped Hole in Lithium Fluoride

Abstract

Using a semiphenomenological method, the energy and wave functions of a self-trapped hole ($V_k$ center) in LiF are obtained as a function of the separation between the two ${\mathrm{F}}^{-}$ ions at which the hole is assumed trapped. The lattice distortion energy due to the changes in Madelung, repulsive, and polarization energies is calculated as a function of the totally symmetric displacement of the two participating ${\mathrm{F}}^{-}$ ions and six positive ions adjacent to the ${\mathrm{F}}^{-}$ ions. This lattice energy is combined with the calculated energy for the ${\mathrm{F}}_2^{-}$ molecule to obtain the total energy as a function of the distance between the participating ${\mathrm{F}}^{-}$ ions for both the symmetric (${\Sigma }_g$) and antisymmetric (${\Sigma }_u$) states of the hole on the $V_k$ center. Only the energy curve for the ground (${\Sigma }_u$) state exhibits a minimum in the expected region of ${\mathrm{F}}^{-}$ -ion separation. From the resulting configurational coordinate curves, the optical absorption energy and width are computed and found to be in order-of-magnitude agreement with experiment. Computed values of the experimentally known isotropic and anisotropic hyperfine constants are used to assess the validity of our molecular wave functions, which were obtained in a one-electron approximation.