Comparison study of crystal and electronic structures for chalcopyrite $(CuFeS_2)$ and pyrite $(FeS_2)$

Chalcopyrite $(CuFeS_2)$ and pyrite $(FeS_2)$ are commonly associated with each other, and they both belong to semiconductor minerals. The difference in crystal and electronic structures is an important factor for their flotation separation. Using the density functional method (DFT) combined with Hubbard U correction, their crystal and electronic properties are comparatively studied. The calculated results suggest that the use of antiferromagnetic calculations and Hubbard U correction are very important to the accuracy of the chalcopyrite results. Antiferromagnetic calculations combined with a U value of 2.0 eV on chalcopyrite show a band gap of 0.53 eV, which is very consistent with the experimental results of ~0.5 eV. The density of states (DOS) and Mulliken bond population results indicate that stronger hybridization between Fe 3d and S 3p states in chalcopyrite than in pyrite leads to a stronger covalency of Fe-S bonds in chalcopyrite, causing a reduction in the spin magnetic moment (3.5 μB) from the ideal value. In addition, the greater covalency of bonds in chalcopyrite results in greater hydrophobicity of chalcopyrite than pyrite. The DOS results suggest that S has similar electronic properties in pyrite and chalcopyrite. The oxidation states of Fe and Cu ions in chalcopyrite are discussed based on the coordination field theory according to the calculation results, which confirms an oxidation state of $Fe^{3+}Cu^{1+}S_2$