Theoretical electron density distributions for Fe- and Cu-sulfide earth materials: A connection between bond length, bond critical point properties, local energy densities, and bonded interactions

Bond critical point and local energy density properties together with net atomic charges were calculated for theoretical electron density distributions, ρ(r), generated for a variety of Fe and Cu metal-sulfide materials with high- and low-spin Fe atoms in octahedral coordination and high-spin Fe atoms in tetrahedral coordination. The electron density, ρ(r_c), the Laplacian, ∇²ρ(r_c), the local kinetic energy, G(r_c), and the oxidation state of Fe increase as the local potential energy density, V(r_c), the Fe-S bond lengths, and the coordination numbers of the Fe atoms decrease. The properties of the bonded interactions for the octahedrally coordinated low-spin Fe atoms for pyrite and marcasite are distinct from those for high-spin Fe atoms for troilite, smythite, and greigite. The Fe-S bond lengths are shorter and the values of ρ(r_c) and ∇²ρ(r_c) are larger for pyrite and marcasite, indicating that the accumulation and local concentration of ρ(r) in the internuclear region are greater than those involving the longer, high-spin Fe-S bonded interactions. The net atomic charges and the bonded radii calculated for the Fe and S atoms in pyrite and marcasite are also smaller than those for sulfides with high-spin octahedrally coordinated Fe atoms. Collectively, the Fe-S interactions are indicated to be intermediate in character with the low-spin Fe-S interactions having greater shared character than the high-spin interactions. The bond lengths observed for chalcopyrite together with the calculated bond critical point properties are consistent with the formula Cu⁺Fe³⁺S₂. The bond length is shorter and the ρ(r_c) value is larger for the FeS₄ tetrahedron displayed by metastable greigite than those displayed by chalcopyrite and cubanite, consistent with a proposal that the Fe atom in greigite is tetravalent. S-S bond paths exist between each of the surface S atoms of adjacent slabs of FeS₆ octahedra comprising the layer sulfide smythite, suggesting that the neutral Fe₃S₄ slabs are linked together and stabilized by the pathways of electron density comprising S-S bonded interactions. Such interactions not only exist between the S atoms for adjacent S₈ rings in native sulfur, but their bond critical point properties are similar to those displayed by the metal sulfides.