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

Using a semiphenomenological method, the energy and wave functions of a self-trapped hole (Vₖ center) in LiF are obtained as a function of the separation between the two 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 F^- ions and six positive ions adjacent to the F^- ions. This lattice energy is combined with the calculated energy for the F₂^- molecule to obtain the total energy as a function of the distance between the participating F^- ions for both the symmetric (Σg) and antisymmetric (Σᵤ) states of the hole on the Vₖ center. Only the energy curve for the ground (Σᵤ) state exhibits a minimum in the expected region of 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.