ENDOR Hyperfine Constants and Lattice Distortion ofVK-Type Centers

The magnetic hyperfine dipole-dipole interaction between $V_K$-type centers (negatively charged diatomic halide molecule-ions) and the neighboring lattice nuclei has been calculated for the $V_K$ center in LiF and NaF and the $V_{\mathrm{KA}}$ (Li) center in NaF using the $\mathrm{F}_2^{}{}_{}{}^{-}$ wave function of Wahl. The calculated hyperfine constants are sensitive to the relative positions of the $\mathrm{F}_2^{}{}_{}{}^{-}$ molecule-ion and the neighboring nuclei. When the calculated hyperfine constants were compared with those measured in electron-nuclear double-resonance (ENDOR) experiments, the displacements of the nuclei surrounding the $V_K$-type centers were determined. In the vicinity of the center, the lattice contracts parallel to the axis of the molecule-ion and dilates perpendicular to this axis. The contact hyperfine interaction has been estimated and compared with the values measured in ENDOR experiments. The sign and order of magnitude of the contact hyperfine constants can be explained by assuming that the closed-shell orbitals of the molecule-ion are exchange-polarized.