Wave Functions for theFCenter in Sodium Azide

Abstract

Wave functions have been calculated for the $F$ center in sodium azide (Na${\mathrm{N}}_{3}$) in both the high-temperature (rhombohedral) and low-temperature (monoclinic) phases, by the point-ion method. The point symmetry at the anion site is ${D}_{3d}$ in the rhombohedral phase and ${C}_{2h}$ in the monoclinic phase. A predicted ${A}_{1}^{+}\ensuremath{\rightarrow}{E}^{\ensuremath{-}}$ optical transition at 2.06 eV in ${D}_{3d}$ symmetry corresponds to two transitions, ${A}^{+}\ensuremath{\rightarrow}{A}^{\ensuremath{-}}$ at 1.82 eV and ${A}^{+}\ensuremath{\rightarrow}{B}^{\ensuremath{-}}$ at 1.96 eV, in ${C}_{2h}$ symmetry. The latter transitions are too close to resolve, and correlate well with the observed $F$ band at 1.70 eV. An ${A}_{1}^{+}\ensuremath{\rightarrow}{A}_{2}^{\ensuremath{-}}$ infrared transition at 0.82 eV in ${D}_{3d}$ symmetry, which corresponds to an ${A}^{+}\ensuremath{\rightarrow}{B}^{\ensuremath{-}}$ transition at 0.94 eV in ${C}_{2h}$ symmetry, is polarized parallel to the hexagonal $c$ axis, and could not be observed with the crystal orientations used in prior measurements. The calculated isotropic hyperfine interactions are larger by a factor of three than those inferred from ESR spectra, a common defect of point-ion calculations. However, it is shown that, as a consequence of wave-function anisotropy, the hyperfine constants remain nearly equal in spite of monoclinic distortion, thus explaining the resolved 19-line hyperfine pattern even in the monoclinic phase.