The approximate calculation of electronic band structure

Ab Initio Studies of Bimetallic-Doped {0001} Hematite Surface for Enhanced Photoelectrochemical Water Splitting

First-principles calculations based on density functional theory (DFT) were carried out to study the energetic stability and electronic properties of a bimetallic-doped α-Fe2O3 photoanode surface with (Zn, Ti) and (Zn, Zr) pairs for enhanced PEC water splitting. The doped systems showed negative formation energies under both O-rich and Fe-rich conditions which make them thermodynamically stable and possible to be synthesised. It is found that in a bimetallic (Zn, Ti)-doped system, at a doping concentration of 4.20% of Ti, the bandgap decreases from 2.1 eV to 1.80 eV without the formation of impurity states in the bandgap. This is favourable for increased photon absorption and efficient movement of charges from the valance band maximum (VBM) to the conduction band minimum (CBM). In addition, the CBM becomes wavy and delocalised, suggesting a decrease in the charge carrier mass, enabling electron–holes to successfully diffuse to the surface, where they are needed for water oxidation. Interestingly, with single doping of Zr at the third layer (L3) of Fe atoms of the {0001} α-Fe2O3 surface, impurity levels do not appear in the bandgap, at both concentrations of 2.10% and 4.20%. Furthermore, at 2.10% doping concentration of α-Fe2O3 with Zr, CBM becomes delocalised, suggesting improved carrier mobility, while the bandgap is altered from 2.1 eV to 1.73 eV, allowing more light absorption in the visible region. Moreover, the photocatalytic activities of Zr-doped hematite could be improved further by codoping it with Zn because Zr is capable of increasing the conductivity of hematite by the substitution of Fe3+ with Zr4+, while Zn can foster the surface reaction and reduce quick recombination of the electron–hole pairs.

The Muffin-Tin-Orbital Point of View

We review the interpretation of multiple-scattering theory in terms of muffin-tin orbitals. The use of slightly overlapping muffin-tin wells is justified rigorously. It is shown that the structure constants may be screened for a useful range of positive and negative energies, and that the screening may be chosen to yield desirable properties of the KKR matrix. Energy linearization and the linear muffin-tin-orbital method are discussed.