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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Hybrid Functional Study of the Electro-Oxidation of Water on Pristine and Defective Hematite (0001) Richard Baochang Wang, and Anders Hellman J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06580 • Publication Date (Web): 14 Jan 2019 Downloaded from http://pubs.acs.org on January 19, 2019

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The Journal of Physical Chemistry

Hybrid Functional Study Of The Electro-oxidation Of Water On Pristine And Defective Hematite (0001) Richard Baochang Wang∗ and Anders Hellman∗ Department of Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden E-mail: [email protected]; [email protected]

Abstract In this study, water oxidation on both pristine and hematite containing oxygen vacancies was investigated using hybrid functional methods. The onset potentials for R-Fe-Fe-(OH)3 and R-Fe-Fe-O3 surface terminations were determined. It is found that oxygen vacancy stabilizes O adsorption on both terminations. The electronic structure was studied in order to explain the obtained reaction energy landscape. The density of states (DOS), projected density of states (PDOS) and the projected Crystal Orbital Hamilton Population (pCOHP) of bond between O and surface Fe atom of both terminations were plotted in order to explain the stabilization caused by oxygen vacancy. The pCOHP plot clearly illustrate a change in bond strength and provides a direct explanation for the stabilization. The results show that the presence of subsurface oxygen vacancies increase the overpotential for electro-oxidation of water and that the lowest overpotential is found on oxygen-terminated hematite.

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Introduction Photoelectrochemical (PEC) water splitting, first reported by Fujishima and Honda in 1972, 1 has received considerable attention as a promising route for harvesting and transforming solar energy into chemical energy. In simple terms, a PEC device should be able to (i) harvest sunlight and create an electron-hole pair, (ii) separation of the electron-hole pair (holes should go to the surface of the anode and electrons to the cathode side), (iii) facilitate the oxidation of water at the anode side using the holes at the valance band and the reduction of protons at the cathode side using the electrons at the conduction band. Iron oxides are abundant in the crust of Earth and can be found in the composition of many minerals, such as, hematite (α-Fe2 O3 ), maghemite (γ-Fe2 O3 ) and magnetite (Fe3 O4 ). 2 Of all iron oxides, hematite is the most stable and abundant iron oxide in nature, and is used in many important environmental and industrial technologies, such as waste-water treatment 3–5 , gas sensors, 6–10 and photoelectrocatalysis. 1,11–15 Owing to the importance of hematite there exist several of dedicated reviews in the literature, for instance. 16,17 Hematite (α-Fe2 O3 ) is a promising material candidate for PEC water splitting thanks to its low materials cost, high stability under operational conditions and a suitable band gap (1.9 - 2.2 eV) able to absorb a broad range of the visible light spectrum. 11–14 However, significant challenges still remain associated with its application to PEC electrodes, including low absorption cross sections in the visible and, especially, midvisible region, 18 substantial electron-hole recombination losses on timescales ranging from picoseconds to milliseconds 19–21 and a high overpotential requirement for oxygen evolution. 22,23 Many efforts have been made to address these challenges, including nanostructuring, 24–28 doping, 29–31 coating with co-catalysts, 22,32 and light trapping. 33 However, more understanding is still needed in order to commercialize it, which includes its optical transitions, 34–36 carrier dynamics 19,37–39 and the catalytic reaction mechanism on its surface. 40–42 Water oxidation reaction takes place at the surface of α-Fe2 O3 photoanodes, where hole accumulation at the surface state and later used in the oxidation reaction. 43–46 Simultaneously, the surface 2


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state works as the recombination center, which is the main limiting factor to PEC performance. 47–49 Therefore, effectively passivating the surface state would decrease the surface charge recombination and increase charge transfer, leading to improved PEC efficiency. Another drawback is the high oxygen evolution reaction (OER) overpotential. Reducing the overpotential is beneficial to solar-to-hydrogen conversion. There exist several theoretical studies focusing on simulation of the reaction mechanism using DFT + U method, 50–60 where both pristine and defective hematite surfaces were studied. It was found that oxygen vacancy can reduce the overpotential on the oxygen terminated (0001) surface 52,54 as well as on (110) and (104) surfaces. 53 It should be noted that hematite is an oxide with strong electronic correlations, more specifically between its 3d electrons. As a consequence, standard DFT is not able to describe the electronic structure accurately, e.g., the band gap of hematite is underestimated with as much as 1.7 eV. 61–63 DFT + U improves the description of the band gap and magnetic moments of bulk, 60,61,64 and surface phase diagram calculated using DFT + U predicted that Fe-terminated surface will be stable over a wide range of oxygen chemical potential 60,61,65 with a small, stable region of ferryl termination. Another way to treat strongly correlated electrons is by including the corresponding Hartree-Fock exchange energy, 66 which removes self-interaction errors (SIE) and can, consequently, improve the calculation of band gaps and the description of localized d and f electrons with respect to local density approximation and generalized-gradient approximation. 67 Hybrid exchange-correlation functionals are usually constructed by a linear combination of the Hatree-Fock exact exchange functionals and any number of exchange and correlation functionals, which can partially remove the SIE. 68,69 Pozun and Henkelman 70 used a screened hybrid functional with 12% exact exchange, which resulted in a band gap in accordance with measurements. Zhou et al. 71 recently evaluated bulk properties of hematite with respect to different exchange-correlation functionals, and they concluded that hybrid functionals were in better agreement with experiment. It should, however, be noted that the use of a global hybrid functional is not a guarantee that the

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results will be more accurate, especially considering that the Fe coordination change when introducing defects and under the water-oxidation reaction. For instance, Wang et al. 60 studied the surface terminations of hematite with hybrid functional and they found that hybrid function results in similar structural information but different surface stability, work function, as well as electronic structure as compared to DFT and DFT + U . In this paper we have employed hybrid functionals to study the OER on hematite (0001) surface. Both pristine and defective surfaces are studied and two different terminations are considered here, i.e. O-termianted and OH-termianted surfaces. The reason for focusing on these two surfaces are that they have been suggested to be the most relevant terminations under aqueous conditions and also under the working conditions of light-induced water splitting. 50,72 To further deepen our understanding, the electronic density of states (DOS), projected DOS (PDOS) as well as projected Crystal Orbital Hamilton Population (pCOHP) 73 on bare and oxygen adsorbed surfaces are calculated and analyzed.

Computational methods The first-principles calculations were performed using density functional theory (DFT) as implemented in the VASP package. 74–76 The interaction between the valance electrons and the core follows the projector augmented wave (PAW) method. 77 PAW potentials with the valence states 1s for H, 2s and 2p for O and 3d and 4s for Fe have been employed. A plane wave basis with a kinetic energy cut-off of 600 eV was used. 78 To improve convergence, a Gaussian smearing broadening of the Fermi surface of 0.1 eV was employed. The exchange-correlation (XC) interaction was treated using a hybrid functional, the screened Heyd-Scuseria-Ernzerhof (HSE). 79,80 In the HSE functional the Coulomb kernel is decomposed into short- and long-range components with the XC energy having the following form, HF,SR PBE,SR PBE,LR HSE EXC = aEX (ω) + (1 − a)EX (ω) + EX (ω) + ECPBE .

4


(1)

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Here a is the mixing parameter and ω is an adjustable parameter governing the extent of short-range interactions. The superscript SR and LR refer to short- and long-range components of the XC energy. In the present study we choose HSE(12%) using a = 0.12 and ω = 0.2/Å, which gives a band gap around 2.0 eV. This is in accordance with the study of Pozun and Henkelman et al. 70 The Fe2 O3 (0001) surface was modeled by stoichiometric (-Fe-Fe-O3 -) sequences in a slab geometry with a (1x1) lateral periodicity. Henceforth the Fe-Fe-O3 sequences are represented by R. The R-Fe-Fe-O3 is cut from bulk hematite. In the R-Fe-Fe-3OH case, the three H atoms are added to the surface oxygen atoms in R-Fe-Fe-O3 . All the surface calculations have been carried out using symmetric slabs of with a vacuum region of 20 Å added between their periodic images. For the surface cells, a 2×2×1 k-point grid for hybrid functional were used, which resulted in almost the same results as that of k grid of 4×4×1 (the total energy difference within 3 meV). The antiferromagnetic ordering of the bulk was taken as the initial spin configuration for all of our calculations. The geometries of the lattice and atoms are optimized using hybrid functional. The atomic positions were fully optimized until the forces on the atoms are smaller than 0.01 eV/Å. The crystal orbital Hamilton population (COHP) provides a straightforward view onto oribital-pair interactions. By calculating COHP one can analyze and interpret bonding situations to identify stabilising (bonding) and destabilising (anti-bonding) interactions between pairs of neighbouring atoms in solid materials. In the present work, we adopted a variant of the familiar COHP approach that stems from a PW calculation and was dubbed “projected COHP” (pCOHP) using Lobster, 73,81 which can process PAW parameters and self-consistent results from VASP. The adsorption energy of ∗ O is calculated by,

∆E = E(∗ O) − E(∗ ) − E(H2 O) + E(H2 ),

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(2)


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where E(∗ O) is the energy of the surface slab with ∗ O and E(∗ ) is the total energy of the bare surface.

Results and discussion Reaction landscape The following reaction mechanism of water oxidation is adopted as suggested in the literature: 15,50–52,54,82–85

H2 O+∗ →

OH2

(3)

OH + H+ + e−

(4)

OH → ∗ O + H+ + e−

(5)

H2 O +∗ O → ∗ OOH + H+ + e−

(6)

∗

OH2 → ∗

∗

The lone

∗

∗

∗

OOH → O2 +∗ +H+ + e−

(7)

represents a surface with one vacant site (or active site) in the topmost

layer, while ∗ OH2 , ∗ OH, ∗ O, and ∗ OOH represent the surface with the corresponding species chemisorbed at the active site. Two different surface terminations have been studied, i.e. the OH-terminated surface (R-Fe-Fe-(OH)3 ) and O-terminated surface (R-Fe-Fe-O3 ), shown in Fig. 1 (a) and (b). The oxygen vacancy is created at the subsurface layer, which is similar to previous studies. 52,54

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The corresponding equations for calculating the free energies are:

∆G1 = 1/2E∗ OH2 − 1/2(E∗ + 2EH2 O ) + ∆ZPE1 − T ∆S1

(8)

∆G2 = 1/2(E∗ OH + EH2 ) − 1/2E∗ OH2 + ∆ZPE2 − T ∆S2

(9)

∆G3 = 1/2(E∗ O + EH2 ) − 1/2E∗ OH + ∆ZPE3 − T ∆S3

(10)

∆G4 = 1/2(E∗ OOH + EH2 ) − 1/2(E∗ + 2EH2 O ) + ∆ZPE4 − T ∆S4

(11)

∆G5 = 1/2(E∗ + EH2 + 2EO2 ) − 1/2E∗ OOH + ∆ZPE5 − T ∆S5 .

(12)

Here for example, E∗ OH2 is the total energy of the slab with H2 O adsorbed on both side of the slab. ∆ZPEi and T ∆Si stand for the zero point energy (ZPE) differences and entropic differences for each reaction step i. We have employed previously published entropy correction values for our calculation, see references 50,51 for details. Here the free energy difference is calculated by setting the total energy of O2 molecule such that the potential for water oxidation per electron transfer step equals the experimental value, 1.23 V. 85 The overpotential is calculated by substracting the final cumulative free energy per electron transfer from the largest free energy difference of an intermediate step:

eΦ = max{∆Gi } − 1/4Σi ∆Gi .

(13)

The reaction energy landscape and the overpotential of the OH-terminated surface is shown in Table 1 and Fig. 2 (a). As seen from the table, the overpotential of water oxidation on R-Fe-Fe-(OH)2 calculated using HSE (12%) is 0.99 V. The potential-limiting step given by HSE (12%) is reaction step 4, deprotonation of the second water and is different from previous PBE + U results, 54 which predicted that reaction step 3, deprotonation of ∗ OH, is the potential-limiting step (a comparison between HSE(12%) and DFT + U is included in Table S2 in SI). Introducing an oxygen vacancy in this termination, the reaction energy landscape is changed (shown in Fig. 2 (a)). The adsorption energies of OH and OOH

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adsorbates only change slightly, while O adsorbate is changed by 0.39 eV. In the following section, the O adsorption energy will be employed as an indicator, on which we will do a further analysis in terms of electronic structure.

(a)

(b)

Figure 1: (a) Water oxidation reaction on R-Fe-Fe-(OH)3 termination; (b) Water oxidation reaction on R-Fe-Fe-O3 termination. The red color ball indicates oxygen atom, white color ball is hydrogen atom, and brown ball is Fe atom. The black circle indicates the subsurface O atom removed to create defective surface structure.

On the O-terminated surface, the calculated reaction landscape and overpotentials are shown in Table 1 and Fig. 2 (b). The reaction free energy differences of OH and O adsorbates are very close to ideal values. The overpotential is due to reaction step 4, i.e., the deprotonation of ∗ OOH, which is in mark difference with PBE + U results that instead identify reaction step 3 as the potential-limiting step, 54 for more details see Table S2 in SI. Introducing oxygen vacancy at the subsurface layer results in increased free energy difference of reaction step 4 with an overpotential of 1.10 eV, i.e., the OOH adsorbate is strongly destabilized. It should be noted that also for this system the HSE (12%) results in a different

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Table 1: The calculated free energy difference of different reaction steps and the overpotential with HSE (12%). Surface termi- ∆G1 (eV) nations R-Fe-Fe1.47 (OH)3 R-Fe-Fe0.93 (OH)3 (O vacancy) R-Fe-Fe-O3 -0.54 R-Fe-Fe-O3 -0.20 (O vacancy)

∆G2 (eV)

∆G3 (eV)

∆G4 (eV)

-1.19

1.48

2.22

0.95

0.99

-0.58

1.00

2.44

1.13

1.29

1.62 1.27

1.49 1.37

1.68 2.33

0.67 0.15

0.45 1.10

Gibbs free energy (eV)

O2

5 R-Fe-Fe-(OH)3

4

*OOH

3

*O

2

Pristine Ov

*OH

1 0

∆G5 (eV) Overpotential (V)

6

6

Gibbs free energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ideal

H 2O

0

1

2

3

4

5

5

*OOH

4 3

*O

2

Pristine Ov

*OH

1 0

O2

R-Fe-Fe-O3

Ideal

H 2O

0

1

2

3

4

5

Reaction step

Reaction step

(a)

(b)

Figure 2: (a) Calculated reaction energy landscapes of OER on OH-termination; (b) Calculated reaction landscapes of OER on O-termination.

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potential-limiting step, namely reaction step 4, as compared to PBE + U results, namely reaction step 2, for more details see Table S2 in SI. The fact that HSE systematically identifies the formation of OOH (reaction step 4) as the potential-limiting step indicates that hematite behaves as a weak binding catalyst, independent of surface termination or the existence of vacancies. As a consequence, any modifications to hematite, e.g. doping, that result in stabilization of OOH will improve the overpotential of the oxygen evolution reaction on hematite. However, it should be noted that this result is dependent on the actual XC functional.

The O adsorption energy as a reaction indicator Table 2 shows the calculated O adsorption energy using Eq. (2). The O adsorption energy on OH-termination is 1.69 eV. When oxygen vacancy is presented at the surface, the O adsorption energy becomes 1.30 eV. Oxygen vacancy stabilizes O adsorption on R-Fe-FeTable 2: The calculated ∗ O adsorption energy (in eV) using HSE (12%). Surface terminations HSE (12%) R-Fe-Fe-(OH)3 1.69 R-Fe-Fe-(OH)3 (O vacancy) 1.30 R-Fe-Fe-O3 2.50 R-Fe-Fe-O3 (O vacancy) 2.37

(OH)3 by 0.39 eV. However, on the R-Fe-Fe-O3 termination, the O adsorption energy is 2.50 eV. On the defective surface, the O adsorption energy changes to 2.37 eV, i.e., O adsorption is stabilized by 0.13 eV on the defective R-Fe-Fe-O3 surface. It is clear that the use of HSE when introducing oxygen vacancies results in a trend, i.e. O adsorption energy is stabilized, however, that the strength is dependent of the surface termination. In order to explain the stabilization of O adsorption on both surfaces by the oxygen vacancy, the DOS, PDOS as well as pCOHP are plotted for further analysis in the following section.

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Electronic structure analysis Electronic structure of R-Fe-Fe-(OH)3 termination The density of states (DOS) of bare surface and surface with O adsorbates are plotted for the pristine surfaces and defective surfaces as shown in Fig. 3. HSE (12%) results in a localized 6

total Fe1 eg Fe1 t2g O 2p Fe2 eg Fe2 t2g

3

DOS(arb. unit)

DOS(arb. unit)

6

0 -3 -6


3 0 -3 -6

-3

-2

-1

0 1 Energy (eV)

2

3

-3

-2

-1

(a)

0 1 Energy (eV)

2

3

2

3

(b)

Fe1 t2g O 2p

total Fe1 eg

Fe1 t2g O 2p

total Fe1 eg

Fe2 eg Fe2 t2g

Fe2 eg Fe2 t2g

4 DOS (arb. unit)

4 DOS (arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 -4 Fe3 eg

4

Fe3 t2g

Fe4 eg

Fe4 t2g

0 -4

0

0

-4

-4 -3

-2

-1

0

1

2

3

Fe3 eg

4

-3

-2

Fe3 t2g

-1

Fe4 eg

0

Fe4 t2g

1

Energy (eV)

Energy (eV)

(c)

(d)

Figure 3: (a) DOS and PDOS of pristine R-Fe-Fe-(OH)2 termination. (b) DOS and PDOS of surface with O adsorbate on this termination. (c) DOS and PDOS of defective R-Fe-Fe(OH)2 termination. (d) DOS and PDOS of defective R-Fe-Fe-(OH)2 -O termination. Here Fe1 and Fe2 refer to Fe atoms in the top most two Fe layers and Fe3 and Fe4 refer to Fe atoms in the top third and fourth Fe layers. Subsurface O vacancy is created in the O layer lying in between Fe2 atomic layer and Fe3 atomic layer.

states on top of the valence band. The localized states consists mainly of electrons localized on the two subsurface Fe atoms according the PDOS, see Fig. 3 (a). When O adsorbs on the surface, the active site is filled. Consequently, the localized states on top of valence band 11



is removed and now sit inside of valence band (Fig. 3 (b)). The calculated DOS and PDOS of defective R-Fe-Fe-(OH)2 are shown in Fig. 3(c). It is clear that HSE (12%) results in two localized states appearing on top of the valence band in the energy range of -1.5 eV to 0 eV, which mainly comes from the Fe1 t2g , Fe2 eg and Fe3 eg states of the top Fe atomic layers. When O adsorbate is present on the surface, the two excess electrons left by the empty active site are localized at the Fe atoms closeby as shown in PDOS plot (Fig. 3(d)). It is clear that there is a remarkable difference of the DOS of pristine and defective R-FeFe-(OH)2 termination. The main difference comes from the localized states on top of valence band. The excess electrons left by the subsurface oxygen vacancy is mainly localized at the nearby Fe atoms appearing as the surface states. It seems that O adsorption stabilizes the pristine surface due to the elimination of the gap states in Fig. 3 (a), which can explain the large adsorption energy in Table 2. On the other hand, in the defective surface, O adsorption induces combination of the two localized states into one band without changing the band gap. 1.5 1

(a)

0.5 0 -0.5

-pCOHP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-1 1.5 1

(b)

0.5 0 -0.5 -1 -1.5 -4

-3

-2

-1

0

1

2

3

4

Energy (eV)

Figure 4: pCOHP plot of O-Fe bond the R-Fe-Fe-(OH)2 -O terminations: (a) pristine surface, and (b) defective surface.

In order to explain why an oxygen vacancy stabilizes the O adsorption on the pristine and defective R-Fe-Fe-(OH)2 termination, the pCOHP of bond between O adsorbate and surface 12


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Fe atom was calculated and shown in Fig. 4. The negative value of -pCOHP indicates the bonding contribution to the Fe-O bond. There is a dramatic change of the pCOHP(both spin-up and spin-down) by introducing O vacancy. The pCOHP of spin-up channel is shifted downward from Fermi-level and the magnitude is increased in the energy range between -3 eV and -2 eV as compared to pristine surface, which indicates that the bonding part between Fe-O is increased, which results in a stronger Fe-O bond. Electronic structure of R-Fe-Fe-O3 termination 6


3

DOS(arb. unit)

DOS(arb. unit)

6

0 -3 -6


3 0 -3 -6

-3

-2

-1

0 1 Energy (eV)

2

3

-3

-2

-1

(a) Fe1 t2g O 2p

total Fe1 eg

0 1 Energy (eV)

2

3

2

3

(b) Fe2 eg Fe2 t2g

3 0 -3 -6

Fe1 t2g O 2p

total Fe1 eg

6 DOS (arb. unit)

6 DOS (arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fe2 eg Fe2 t2g

3 0 -3 -6

-3

-2

-1

0 1 Energy (eV)

2

3

-3

-2

(c)

-1

0 1 Energy (eV)

(d)

Figure 5: (a) DOS and PDOS of R-Fe-Fe-O2 termination. (b) DOS and PDOS of R-Fe-Fe-O3 termination. (c) DOS and PDOS of R-Fe-Fe-O2 termination with oxygen vacancy. (d) DOS and PDOS of R-Fe-Fe-O3 termination with oxygen vacancy.

The calculated DOS and PDOS on bare and O adsorbed R-Fe-Fe-O2 are shown in Fig. 5 (a) and (b). The DOS of pristine and O adsorbed surfaces are close to each other where 13



occupied states are located on top of the valence band, which mainly are composed of the hybridization of surface Fe 3d states and O 2p states(Fig. 5 (a)). Adsorption of an O atom on the surface shifts the localized states downward to the top of valence band. Moreover, the localized states becomes more narrow and sharper and the band gap is enlarged by 0.5 eV. This indicate that the strengthening of Fe-O bonds at the surface is a result of more degenerate states contributing to the overlapp between Fe 3d and O 2p states via O adsorption (Fig. 5 (b)). 1.5 1

(a)

0.5 0 -0.5

-pCOHP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-1 1.5 1

(b)

0.5 0 -0.5 -1 -1.5 -4

-3

-2

-1

0

1

2

3

4

Energy (eV)

Figure 6: pCOHP plot of the R-Fe-Fe-O3 terminations: (a) the pristine surface calculated and (b) defective surface.

The DOS and PDOS of defective R-Fe-Fe-O2 surface are shown in Fig. 5 (c). The two excess electrons left by removing O become delocalized on surface Fe atoms in the energy range of -0.8 eV to -0.2 eV. As a result the valence band edge is composed of localized Fe 3d states and the conduction band edge mainly consists of O 2p states. When O adsorbs on the surface, two localized states are introduced in band gap by the overlap between O 2p and Fe t2g states sitting on both side of the Fermi-level, forming bonding and anti-bonding states sitting in the energy range of -0.5 eV to 0 eV and 0 eV to 0.5 eV, respectively, as shown in Fig. 5 (d). The calculated pCOHP of Fe-O bond between O adsorbate and surface Fe atom for both pristine and defective R-Fe-Fe-O2 are shown in Fig. 6. Compared with the pristine surface, 14


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the bonding states in pCOHP on the defective surface is increased in the spin-down channel in the energy range of -2 eV to 0 eV. Similar as the analysis of pCOHP of Fe-O bond at OH terminated surface, the change of pCOHP indicates that the strengthen of the Fe-O bond can account for the stabilization of O adsorption shown in the energy landscape in Fig. 2.

Conclusions In summary, we have studied the water oxidation on pristine and defective hematite (0001) using HSE (12%). Two terminations were studied, i.e. the OH terminated and O terminated surface. The overpotential of water oxidation on the OH termination is 0.99 eV which is slightly larger than PBE + U result found in literature. 52,54 The predicted potential-limiting step changes as well, for example, deprotonation of the second water (reaction step 4) are identified by HSE (12%) while deprotonation of ∗ OH (reaction step 3) are found by PBE + U . 52,54 Introducing oxygen vacancy changes the reaction landscape, however, the potentiallimiting step remains the same but with a higher overpotential (1.29 eV), which is similar to the results from PBE + U . 54 While adsorption energies of OH and OOH are changed only slightly, O adsorbate is notably stabilized. On the O-terminated surface, HSE (12%) results in the lowest overpotential (0.45 eV for reaction step 4) on the pristine surface, while using PBE + U , 52,54 the overpotential of water oxidation is 0.86 eV owing to the deprotonation of ∗

OH. Introducing oxygen vacancy at the subsurface layer, the overpotential is increased to

1.10 eV (reaction step 4) with the OOH adsorbate strongly destabilized using HSE (12%), while the O adsorbate is strongly stablized by PBE + U 54 resulting in an overpotential of 0.60 eV. It is found that oxygen vacancy stabilizes O adsorption on OH termination by 0.39 eV. However, on the O termination, O adsorption is stabilized by only 0.13 eV. The DOS, PDOS and the pCOHP of bond between O adsorbate and surface Fe atom of both terminations were plotted in order to explain the stabilization of O adsorption by oxygen vacancy. Based

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on our analysis, it is clear that the difference of O adsorption energy changes induced by oxygen vacancy is due to different solutions of the localization of the two excess electrons in the systems indicated by the DOS and PDOS plot. The pCOHP plot clearly show a change in bond strength and gives a direct explanation of the stabilization of O adsorption by oxygen vacancy. A consequence of the stabilization caused by subsurface oxygen vacancies are that the overpotential for the electro-oxidation of water becomes higher, i.e, vacancies prohibit the surface reaction. As a last observation we see that the presence of vacancies results in a higher overpotential for the electro-oxidation of water, independent of surface termination. This means that, according to HSE(12%), to improve water splitting reaction on hematite the surface should be as pristine as possible.

Support Information Relaxed structure information, comparison of reaction landscapes with DFT + U results, as well as comparison of electronic structure of pristine and defective surfaces are listed in the Support Information.

Acknowledgement The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at C3SE. Support from the Swedish Research Council, Formas and the Chalmers Area of Advance Material Science and Energy is acknowledged.

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