Experimental electron-density-distribution study of potassium iron disulfide, a low-dimensional material

The experimental electron-density distribution of potassium iron disulfide, ${\mathrm{KFeS}}_2$, has been determined from high-resolution single-crystal x-ray intensity measurements collected with Ag Kα radiation to a resolution of (sinθ)/λ=1.30 A${̊}^{\mathrm{-}1}$. The structure of ${\mathrm{KFeS}}_2$ consists of parallel chains of edge-sharing ${\mathrm{FeS}}_4$ tetrahedra extending along the c-axis. In addition to the conventional structural parameters, multipole deformation functions and third- and fourth-cumulant anharmonic thermal parameters were included in some least-squares refinements. In all cases, inclusion of anharmonic thermal vibration parameters yielded significantly better fits to the x-ray data. From the experimental multipole population parameters of the iron atom, apparent d-orbital occupancies and the number of unpaired 3$d_{\uparrow }$ electrons have been estimated within the crystal-field approximation and the assumption that a minimal basis set of atomic d orbitals is adequate for the d electrons. The values obtained for the number of 3$d_{\uparrow }$ electrons from various refinements of the x-ray data agree well with values deduced from previous magnetic-susceptibility measurements and from theoretical calculations. The crystal-field splitting of the iron d orbitals and the ensuing asphericity is clearly evident in the experimental electron-density maps. The electric field gradient at the iron nucleus, calculated from the x-ray multipole parameters due to the slightly distorted ($D_{2d}$) tetrahedral crystal field, predicts a quadrupole splitting of Δ$E_{\mathrm{QS}=3.3(10\mathrm{}}$) mm/sec, somewhat larger than observed in Mössbauer experiments (Δ$E_{\mathrm{QS}=0.53\mathrm{}}$ mm/sec). The major contribution to the electric field gradient comes from the valence-electron distribution, which is consistent with the observed asphericity of electron density around iron.