Supporting Information
Enhanced Photoelectrochemical Activity for Cu, Ti Doped Hematite:
the First Principles Calculations
X. Y. Meng1, 2, G. W. Qin1*, S. Li1, X. H. Wen2, Y. P. Ren1, W. L. Pei1, L. Zuo1
1Key
Laboratory for Anisotropy and Texture of Materials (MOE), 2College of Sciences, Northeastern University,
Shenyang 110004, PR China
*Corresponding author, Email: qingw@smm.neu.edu.cn (Gaowu QIN)
The details of computational method
The present calculations make use of an expansion of the electronic wave functions in plane waves
with a kinetic-energy cutoff of 600 eV. The total energy is minimized with respect to the volume, the
unit shape and the Wyckoff positions of all atoms. Brillouin-zone integrations were performed using
Monkhorst-Pack k-point meshes
1s
and tests were carried out by using different k-point meshes to
ensure absolute convergence of the total energy with respect to the structural degrees of freedom to a
precision of better than 2 meV/atom. As is shown in Figure 1, a rhombohedral primitive cell of
hematite is used in our calculation. It is clear that the basic structure unit of octahedra built by oxygen
atoms and centered by iron atoms are slightly rotated against each other. We note that there are two
types of pairs of Fe atoms, which are characterized by a short Fe-Fe distance and by a larger distance
along the hexagonal [001] axis. The Hubbard U-parameter is treated as an adjustable parameter. This
method can deal with delocalized and localized electrons simultaneously, and it is particularly
advantageous in the case of α-Fe2O3 because the localized d electrons hybridize significantly with other
orbitals. To adjust U value, characteristic properties, such as parameters of the equilibrium cell,
magnetic moments, band gap, and composition of band were checked by experimental values. The
present value of 6 eV for U parameter yields an energy gap of the experimental size: the energy gap is
2.06 eV, the spin moment is 4.39 μB, and the equilibrium volume is 101.04 Å3.
Searching the ground state of hematite
For a discussion we first draw our attention to find the ground state of hematite. The zero energies
belonging to different magnetic order solutions are calculated according to the orientation of the local
spin density around the Fe atoms. The global zero energy minimum schemes yield a stable
antiferromagnetic + – – + (along the hexagonal [001] axis) ground state, which means that Fe atoms
with the short distance have opposite magnetic moment, while that with the larger distance have equal
magnetic moments (Figure 1). The current results are also consistent with GGA
2s
and hybrid DFT
3s
investigations . The calculated ground state parameters for the different magnetic states are compared
with experimental values in the Table 1S.
The calculation of formation energies for Cu, Ti doped hematite
Finally, we calculated the formation energy of charged states according to the formula to investigate
whether doped α-Fe2O3 is a stable compound 4s:
bulk
E f [Cu(Ti) Fe ]  Etot [Cu(Ti) Fe ]  Etot [ Fe2O3 , bulk]  2Cu
(Ti )  2 Fe  ()2[ EF  Ev  V ]
Etot[Cu(Ti)Fe] is the total energy derived from a doped supercell, and Etot[Fe2O3, bulk] is the total
energy for the equivalent supercell containing only α-Fe2O3. Two impurity (host) atoms are added to
(removed from) the supercell, and μ are the chemical potentials of the corresponding atoms. It should
be noted that the chemical potentials are free energies, temperature and pressure dependent. In the
present calculation, we put a bound on it, that is, the chemical potential is subject to an upper bound μ
= μbulk because the chemical potential of these species cannot be higher than the energy of bulk
materials in a thermodynamic equilibrium state. This method is very useful in interpreting the results.
EF is the Fermi level referenced the valence-band maximum. Ev is the top of the valence band for the
defect-free supercell, and a correction ΔV is introduced to align the Ev between the defect and
defect-free supercell. The charge states are –2 and +2 for Cu and Ti doped hematite, respectively. The
calculated negative formation energies Ef (as shown in Table 1) indicate that the both doped supercells
are thermochemical stable.
References
1s
H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976).
2s
G. Rollmann, A. Rohrbach, P. Entel, and J. Hafner, Phys. Rev. B 69, 165107 (2004).
3s
N. C. Wilson and S. P. Russo, Phys. Rev. B 79, 094113 (2009).
4s
C. G. V. Walle and J. Neugebauer, Appl. Phys. Rev. 95, 3852 (2004).
5s
M. Catti, G. Valerio, and R. Dovesi, Phys. Rev. B 51, 7441 (1994).
6s
E. Kren, P. Szabo, and G. Konczos, Phys. Lett. 19, 103 (1965).
TABLE 1S. The ground state parameters for the different magnetic states. Volume V0 are in Å3 / atom,
magnetic moments are in μB / Fe atom, total energy are in meV / atom.
Magnetic order
V0
Moment
c/a
Etot
AF + – – +
10.10
4.39
2.78
0
AF + + – –
10.23
4.47
2.68
93
AF + – + –
10.21
4.31
2.76
87
FM + + + +
8.91
3.17
2.80
202
NM
8.86
–
2.82
343
2.73
–
Expt.
a
from Ref.[5s]
b
from Ref.[6s]
10.06
a
4.90
b
FIG. 1S. The LDA + U calculated PDOS for the doped α-Fe2O3 compared with pure α-Fe2O3 (spin-up).
The Fermi level is set to zero respectively in the detail drawing, and only the partial DOS near the
Fermi level are considered.