Charge densities in CoS₂ and NiS₂ (pyrite structure)

Abstract

The electron-density distributions in the pyrite-type structures of CoS2 and NiS2 have been determined from high-resolution single-crystal diffraction data [Ag Ka radiation; resolution and temperature (sin0/A)max = 1"49 /~-I at 295 K for COS2, 1.63 ~-1 at 135 K for NiS2]. The charge densities were refined using a multipolar deformation model [R(IFI) = 0.0119 and 0.0136, respectively]. The X-ray diffraction data of FeS2 [Stevens, DeLucia & Coppens (1980). lnorg. Chem. 19, 813-820; Ag Ka radiation, (sin0/a)m.x = 1.46 A-i, room temperature] were refined using the same deformation model and program in order to facilitate comparison of the results [R(IFI) = 0.0176]. The main features of the resulting deformation maps agree well for all three structures. They consist of important maxima in the immediate vicinity of the metal atoms pointing towards the faces of the coordination octahedron. The heavier the metal atom, the smaller is the distance of the maxima from the atomic centre. These features are interpreted by a preferential occupation of the metal d orbitals which correspond to the cubic t2e orbitals. An analysis of the d-orbital populations indicates that the symmetry of the electron distribution around the metal atom is in all cases very close to cubic, the site symmetry being 3; the t2g orbitals appear to be fully occupied by six electrons while the occupation of the eg orbitals increases in the series Fe, Co, Ni and indicates covalent overlap with the S ligands.

First-principles study of sulfur isotope fractionation in pyrite-type disulfides

“…For pyrite, cattierite, vaesite, and hauerite, our calculations by GGA underestimate the experimental lattice parameters by 0.2, 0.4, 1.1, and 0.7%; but the LDA underestimates the experimental lattice parameters by 2.4, 3.4, 3.7, and 2.5%. This indicates that our results based on GGA are in good agreement with experimental values (Brostigen and Kjekshus 1969;Andresen et al 1967;Nowack et al 1991;Hastings et al 1959). It is also found that the calculated interatomic distances by GGA are consistent with the available experiments much better.…”

“…As shown in Figure 2, disparity exists between the previous calculation, and our calculations are in between the previous results. The apparent discrepancy for 10 3 lnβ 34-32 between our results and the data of Blanchard et al Brostigen and Kjekshus (1969); b Andresen et al (1967); c Nowack et al (1991); d Hastings et al (1959). Blanchard et al (2009) the theoretical frequencies were multiplied by a scaling factor for determining the β-factors but not in the present study.…”

Anharmonic MotionvsChemical Bonding: on the Interpretation of Electron Densities Determined by X-ray Diffraction

“…Qualitatively reasonable values of such occupancies have been published, e.g. for pyrite-type structures (Stevens & Coppens, 1979;Stevens, DeLucia & Coppens, 1980;Nowack, Schwarzenbach & Hahn, 1991). However, anharmonic motions of the metal atom may result in similar features since they are expected to have larger amplitudes in directions towards secondnearest neighbors and smaller amplitudes towards nearest neighbors.…”

Accurate Charge-Density Studies as an Extension of Bayesian Crystal Structure Determination

“…The main sources of model bias in multipolar density studies are: the choice of exponents appearing in the radial parts of the deformation functions, still`more of an art than a science' (Flensburg et al, 1995); the insuf®cient radial¯exibility in modelling valence-charge density in metals, minerals (Nowack et al, 1991;Brown et al, 1993) and coordination complexes (Iversen, Larsen, Figgis & Reynolds, 1997);² and the limited order of the spherical harmonics used, which do not usually extend past the hexadecapolar level l 4. The latter limitation is not always imposed by the quality of the data, and can be due to the need to preserve an adequately high observations/parameters ratio.…”