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 ${\mathrm{F}}^{\ensuremath{-}}$ 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 ${\mathrm{F}}^{\ensuremath{-}}$ ions and six positive ions adjacent to the ${\mathrm{F}}^{\ensuremath{-}}$ ions. This lattice energy is combined with the calculated energy for the ${\mathrm{F}}_{2}^{\ensuremath{-}}$ molecule to obtain the total energy as a function of the distance between the participating ${\mathrm{F}}^{\ensuremath{-}}$ ions for both the symmetric (${\ensuremath{\Sigma}}_{g}$) and antisymmetric (${\ensuremath{\Sigma}}_{u}$) states of the hole on the ${V}_{k}$ center. Only the energy curve for the ground (${\ensuremath{\Sigma}}_{u}$) state exhibits a minimum in the expected region of ${\mathrm{F}}^{\ensuremath{-}}$ -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.