Role of Oxygen Vacancies on Oxygen Evolution Reaction Activity: Î²

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On the role of oxygen vacancies on Oxygen Evolution Reaction activity: #-Ga2O3 as a case study Taifeng Liu, Zhaochi Feng, Qiuye Li, Jianjun Yang, Can Li, and Michel Dupuis Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b03015 • Publication Date (Web): 27 Sep 2018 Downloaded from http://pubs.acs.org on September 28, 2018

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Chemistry of Materials

On the role of oxygen vacancies on Oxygen Evolution Reaction activity: β-Ga2O3 as a case study Taifeng Liu*a, Zhaochi Fengb, Qiuye Lia, Jianjun Yanga, Can Lib, Michel Dupuis*b,c (a) National & Local Joint Engineering Research Center for Applied Technology of Hybrid Nanomaterials, Collaborative Innovation Center of Nano Functional Materials and Applications of Henan Province, Henan University, Kaifeng, 475004, China. (b) State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian National Laboratory for Clean Energy, Zhongshan Road 457, Dalian 116023, P.R. China. (c) Department of Chemical and Biological Engineering, University at Buffalo, State University of New York, Buffalo, NY 14260, USA

ABSTRACT: Neutral oxygen vacancies (Ov’s) in semiconductor oxides give rise to excess electrons that have the potential to affect the binding of adsorbates to the surface through surface-to-adsorbate charge transfer, and, as a result, to alter the over-potential (OP) of reactions on oxygen-deficient materials compared to stoichiometric materials. We report a systematic computational investigation of the effects of Ov’s on the Oxygen Evolution Reaction (OER) over-potential for β-Ga2O3, a d10 semiconductor that has been shown to exhibit high activity for water splitting. We investigated eighteen β-Ga2O3 surfaces / slabs, with and without Ov’s and observed a clear dependence of OER activity on Ov’s. A general finding emerged, that the excess electrons associated with Ov’s are found to participate in charge transfer to OER intermediates, making their bonds to the surface more ionic and stronger, depending on the amount of charge transfer. The OER reaction step free energies are significantly affected and the ensuing over-potentials are altered. The amount of charge transfer varies with the types of intermediates (OH*, dangling O*, surfacebound peroxo O*, and dangling OOH*), their open valencies, and their electronegativity. The work function and the position of the gap states of the excess electrons in the band gap are found to be useful descriptors of whether and how much Ov-induced charge transfer may occur and affect the over-potential. However, it was also found that the chemical environment of the O atom where the vacancy was created, may have a negating effect on the general observation. Specifically some Ov structures underwent a strong relaxation to form Ga-Ga bonds, trapping the vacancy electrons, and preventing them to engage in charge transfer. Oxygen vacancies are common defects in photocatalyst materials so that our investigation can provide guiding principles for designing efficient photocatalysts.

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I. INTRODUCTION Solar-driven water splitting with semiconductor-based photo-catalysts is an ideal route to convert solar energy into chemical fuels. 1-3 Water splitting occurs via an oxidation reaction of water to evolve di-oxygen O2 (oxygen evolution reaction OER) and a reduction reaction of protons to evolve di-hydrogen H2 (hydrogen evolution reaction HER).4 OER takes place on surfaces of semiconductor particles that, in general, contain defects.5-7 Oxygen vacancies (Ov) are the most common defects in semiconductors.8,9 For charge neutrality, an Ov created by removal of a neutral oxygen atom from the solid leaves behind two excess electrons per Ov.10 These excess electrons are likely to affect the surface chemistry via partial transfer of the electrons onto adsorbates during a surface reaction. Indeed, a systematic study by Deskins et al.11 of the effect of excess electrons on the surface chemistry of adsorbates identified charge transfer as a key factor that alters adsorbate binding energies, based on the number of available excess electrons and on the adsorbate electronegativity compared to the surface electronegativity. Thus Ov’s have the potential to enhance the ionic character of the surface-species bonds and to increase binding energies and free energies of intermediates. In the case of OER, Ov’s would alter the reaction step free energies and the OER over-potential.11,12 Thus Ov’s may play a critical role on the OER performance of semiconductors in the context of Sabatier principles of ‘optimum bond strength’ for efficient catalytic reactions.13 A limited number of theoretical investigations of the role of Ov’s on OER have been reported so far. Nguyen et al.14 investigated water oxidation on hematite (0001) with Ov’s and observed that one Ov lowers the OER over-potential by ~0.3 V compared to the defect-free surface. Hellman et al. 15 studied the OER reaction on hydroxyl- and oxygen-terminated hematite (0001) surfaces and suggested that OER is most likely to occur on oxygen-terminated hematite when Ov’s are present. Tyminska et al. 12 reported a theoretical study of the effects of Ov’s on OER, specifically on the TiO2-terminated (001) surface of cubic BaTiO3. These authors found that Ov’s increase the OER over-potential, an observation at odd with experiments by Chen et al.16 In fact these authors suggested that controlling the degree of oxygen deficiency in materials was a potentially good strategy for reducing over-potentials. In another study, Zhang et al.17 investigated the OER reaction on hematite surfaces with DFT+U calculations and they found that the Ov concentration is a very effective parameter in reducing the over-potential. A recent investigation of water oxidation on WO3 included the effect of oxygen vacancies on the over-potential as well.18 Interestingly, the authors reported that Ov’s on the first sublayer does not affect the overpotential, but Ov’s in the second layer do. We note that most of these studies adopted the broadly accepted four-step proton-couple-electron-transfer (PCET) mechanism19 for OER, also termed ‘adsorbate evolution mechanism’ (AOM), that fundamentally is concerned with the redox activity of cationic sites. Recently a new type of mechanism termed ‘lattice oxygen mechanism’ (LOM) has gained some attention, whereby lattice oxygens appear to be active species in the redox mechanism.20-22 The present work deals with a mix of AOM and LOM-like mechanisms. Semiconductors with d10 electronic configuration exhibit superior photocatalytic activity, mainly because their conduction bands are formed by hybridized sp orbitals with large band dispersion that can result in photoexcited electrons with large mobility. Gallium oxide (Ga2O3) is an example of such d10 metal oxides, exhibiting high activity for water splitting and degradation of organic pollutants.23,24 Ga2O3 has five different crystalline structures, and among these the β-


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Ga2O3 phase is the most stable crystal phase and it has drawn most attention. The β-Ga2O3 phase also exhibits higher photocatalytic activity toward the decomposition of aromatic compounds than other phases24. It has been shown to exhibit high activity for water splitting, in particular for mixed α-β phases.25 We presented previously the details of the bulk and surface properties of β-Ga2O3, including the nature of the surface exposed atoms and the surface energies.26 In brief (see Figure 1), bulk β-Ga2O3 has two distinct types of Ga atoms and three distinct types of O atoms. Ga[I]’s are bound to four oxygen anions in distorted tetrahedra while Ga[II]’s are bound to six anions in highly distorted octahedra. O(I)’s are threefold coordinated and are shared by two octahedra and one tetrahedron. O(II)’s are also threefold coordinated and are shared by two tetrahedra and one octahedron. O(III)’s are fourfold coordinated and shared by three octahedra and one tetrahedron. There are five low-index surfaces27 labeled (100-A), (100-B), (001)-A, (001)-B, and (010). The type and the coordination of the exposed surface atoms are shown in Figure 1. The computed surface energies are 0.84 Jm-2 for (100-A), 0.47 Jm-2 for (100-B), 1.75 Jm-2 for (001-A), 1.18 Jm2 for (001-B) and 1.49 Jm-2 for (010) so that the (100-B) surface is the most stable one. This is the one for which we carried out the most detailed investigation of the role of oxygen vacancies on OER. The (001-A) surface has the largest surface energy and is highly unstable. We did not use it further in our OER investigations.

Figure 1. Structures of bulk β-Ga2O3 and of selected low-index stoichiometric surfaces.




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Figure 2. Typical model systems investigated in this paper and shown for the β-Ga2O3 (100B) surface, with the locations of the Ov’s and the structures of the OER intermediates OH*, O*, and OOH*. For O* the surface-bound peroxo species (O1*) (see close-up insert), and the dangling species (O2*) are depicted. The total and project density of states (DOS) of clean 100-B slab are also shown. The red, brown, and white spheres represent oxygen, gallium, and hydrogen atoms, whereas the yellow spheres represent the oxygen atoms of water.

The studies cited above are clear indications that Ov’s have an effect on OER. While Ov’s been shown to have impact on OER, the underlying reason of the Ov effect has not been systematically quantified along the line spelled out by Deskins et al. 11 and a systematic and clear relationship between Ov’s and OER activity has yet to emerge. In this paper, we report such a systematic study of the effect of Ov’s on OER, using β-Ga2O3 as model material. We considered the four most stable β-Ga2O3 surfaces, namely the 100-A, 100-B, 001-B and 010 surfaces. For Ov positions, we selected surface sites away from the Ga reaction site, subsurface sites close and far from the reaction site, and several other sites at increasing depth in the bulk, as illustrated in Figure 2 for the (100-B) surface. These variations in structure were selected to allow us to gauge the effect of charge transfer on the binding energies of OH*, O*, and OOH* intermediates in the widely used four proton-coupled electron transfer (PCET) mechanism of OER and on the overpotential.19 The paper is organized as following: in section II, we describe the computational details, and in section III, we present and discuss the results. Conclusions are provided in section IV. II. COMPUTATIONAL DETAILS We carried out spin-polarized density-functional theory (DFT) calculation using the Vienna Ab-Initio Simulation Package (VASP) code. 28,29 For structure determination we adopted the Perdew-Burke-Ernzerh (PBE) parametrization of the exchange and correlation potential in the generalized gradient approximation (GGA)30. The electronic wave function was expanded in plane waves up to an energy cutoff of 400 eV. The Ga, O and H atoms were treated with valence configurations of 4s23p1 for Ga (3 valence electrons for Ga atom), 2s22p4 for O (6 valence electrons for O atom), and 1s for H (1 valence electron for H atom). Self-consistent DFT energies were converged to 10−4 eV, and geometry optimization were deemed converged when the residual forces on the atoms were less than 0.01 eV/Å. The Γ-centered k-point mesh of the Brillouin zone sampling for the primitive cells and all slabs were set at 3 × 11 × 7 and 2 × 2× 1 based on the Monkhorst−Pack scheme.31 The four most stable β-Ga2O3 surfaces denoted 100-A, 100-B, 001-B and 010 were used in OER mechanisms. The details of these four surfaces are shown in Table S0 in the supporting information (SI). All electronic properties (beyond geometries) were calculated using the Heyd-Scuseria-Ernzerhof (HSE) hybrid density functional.32 Lastly, we note that all clean surfaces are symmetric and stoichiometric, so that there are no artificial slabinduced surface dipoles. The surfaces with oxygen vacancies are non-stoichiometric and have the potential to exhibit a surface-induced dipole. In these cases we have applied a dipole correction to eliminate the dipole effects. In this work we followed Nørskov’s four step PCET protocol19 with intermediates denoted *, OH*, O*, and OOH* throughout, and the OER over-potential determined by:



EOP (V) = max {∆Gn } / e − 1.23 [V] n =1,4

where ∆Gn in eV denotes the step free energy for step n (n = 1 to 4), with the zero of energy taken as the energy of the free surface site (denoted *) plus the energy of two water molecules, n is the step index (1 to 4), e is the electron charge. The rate-limiting step is the step among the four responsible for the value EOP. Step free energies were calculated from the DFT step energies by applying a contribution for changes in zero point energy (ZPE) and entropy (TS) for the steps. In this work, we considered two kinds of O* intermediates, one (denoted O1*) is an oxygen atom inserted into a surface Ga-O-Ga motif and forming a surface-bound peroxo (O22-) species Ga-OO-Ga,19,33 the other is a dangling oxygen atom (denoted O2*).34 Structures of surfaces and intermediates are depicted in Figure 2 for Ga2O3 (100-B). ZPE and TS corrections were taken from Valdes et al.19 and from Rossmeisl et al..34 The thesis of the present work is that charge transfer of the excess electrons arising from Ov’s make adsorbate bonding more ionic and the binding energies stronger. The ZPE of the adsorbate will also increase, an estimate of the ensuing increase being ~ 500 cm-1 or ~ 0.06 eV (corresponding to ~ doubling of the solid-adsorbate stretching frequency). The stronger the charge transfer, the stronger the bond, the larger the ZPE. However we did not calculate the vibrational frequencies for any of the adsorbates, and adopted the literature values for ZPE. We note that the peroxo O* structure has been used in several other studies, by Qu and Kroes33, by Zhou et al.35, and by Li et al.36,37, and it is the structure used by Valdes et al.19 As pointed out by these authors and as shown here, both O* structures (peroxo and dangling O*) may be found as intermediates of OER on various oxide surfaces, so that both ought to be computed and compared, and the lowest energy O* structure ought to be used to construct the OER reaction energy diagram. An important new aspect discussed below is the difference in the ability of these two types of O* intermediates to participate in charge transfer from the solid (using the excess charge created by Ov’s). The bonding valencies of the surface peroxo O* species are filled already, so that peroxo O* species are unlikely to be involved in charge transfer, while the open valencies of the dangling O* species are conducive to charge transfer, a situation that alters the OER step 2 energetics. We calculated the OER energy profiles on the clean 100-B surface and seven oxygendeficient surfaces. These clean and defected surfaces were constructed according to our earlier work.26 To investigate the effect of the position of the Ov’s on OER we assigned the Ov’s to successive layers of the 100-B slab and not directly adjacent to the OER active site, except in one case. The locations of the Ov’s can be seen for the (100-B) surface in Figure 2. The nomenclature reflects the layer on which the Ov resides: Ov1 on the 1st layer, Ov2 on the 2d layer, Ov3 on the 3d layer, and so on, all the way to the 6th layer for Ov6. We also chose a second position on the 2d layer for an Ov right below the surface active site, and it is denoted Ov2’. We believe the various Ov’s may exhibit different charge transfer ability, thermodynamics, and redox properties. 100-B-Ov1, 100-B-Ov3, 100-B-Ov4, and 100-B-Ov6 systems correspond to vacancies arising from type-III oxygen O(III) connected to four Ga atoms, one Ga(I) and three Ga(II)’s while 100-B-Ov2, 100-B-Ov2’, and 100-B-Ov5 systems arise from type-II oxygen atoms O(II) that are connected to three Ga atoms, one Ga(II) and two Ga(I)’s. It is interesting to note that the


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different chemical environments between O(I), O(II), and O(III) leads to strikingly different contributions to the valence band, even for a clean 100-B, with O(II) contributing much more to the top of the VB than O(I) and O(III). The projected density of state PDOS is shown in Figure 2, based on our hybrid functional HSE calculations. The same calculations yielded a β-Ga2O3 band gap of ~ 4.5 eV, in good accord with the ~ 4.2-4.7 eV experimental values.38 Neutral vacancies are common in catalysts prepared by calcination16. The excess electrons created by Ov’s in many oxides, such as WO339, Cu2O40, and TiO241, have been shown to have high mobility, as such they can find their way to surface adsorbates when thermodynamics are favorable. We also note that, while the structure of excess electrons in solid oxides is open to the self-interaction error of DFT that requires ad hoc treatments (hybrid functionals or Hubbard U interactions)42, the transfer of charge to the adsorbates fills partly open valencies and is not sensitive to self-interaction correction (SIC).11 We note that we do not model the electrolyte phase in the present work. This is a wellaccepted practice, seen in the many studies by Nørskov and collaborators, and many other groups that use the same protocol to model OER on many different systems, and that, at times, have led to useful volcano predictions. The concept of charge transfer from Ov’s to adsorbates and the volcano behavior arising from the role of Ov’s can be dramatic compared to stoichiometric situations and are likely to remain valid with larger supercell models, with or without electrolyte. We note that the work of Li and Selloni dealing with OER on pure and mixed Ni-Fe oxides37 where these authors included one layer of water molecules on the surface, is in essential agreement with Nørskov’s and other studies that did not include a model of the liquid phase43,44. Nonetheless the amount of charge transfer that the present calculations suggest, is quite large. However it is unlikely that a model of the electrolyte will significantly alter this finding. In fact the dielectric constant of Ga2O3 is ε ~ 10, a value45 much less than ε ~ 78 for liquid water, so that an electrolyte is likely to enhance localization of electron charges on the exposed adsorbates. Accordingly, we believe that the concept of charge transfer to explain adsorbates’ bond strengthening will remain valid. III. RESULTS AND DISCUSSION Beyond the structures displayed in Figure 2, the OER intermediates for all the oxygen-deficient surfaces are shown in Figure S1-S4 in the supporting information. For all the model systems, step energies and over-potentials are presented in Table1.



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Table 1. OER reaction step free energies (in eV) and over-potential (in V) on Ga2O3 surfaces. In the step energy columns 3 and 4, a in the a/b entry is the step energy to/from surfacebound peroxo species O* while b is the step energy to/from the dangling O* species. The bold font entries correspond to the over-potential determining step. Step 1: * + H2O → OH* + ½ H2

Step 2: OH* → O* + ½ H2

Step 3: O* + H2O → OOH* + ½ H2

Step 4: OOH* →*+O2 + ½ H2

Surface

Step 1 from * to OH*

Step 2 from OH* to peroxo O*/ dangling O*

Step 3 from peroxo O*/ dangling O* to OOH*

Step 4 from OOH* to *

Over-potential through peroxo O*/ dangling O*

0.95/2.24 2.03/2.61

1.11/-0.18

0.36

1.27/1.27

1.08/0.50

0.35

0.80/1.38

1.12/-0.16

0.35

1.27/1.27

0.80/0.15 1.09/0.13

0.64 0.36

0.65/1.30 0.66/1.31

100-B

2.50

100-B-Ov1 100-B-Ov2

1.46 2.50

100-B-Ov2’ 100-B-Ov3

1.60 1.89

0.95/2.23 1.88/2.53 1.58/2.54

100-B-Ov4

1.74

1.71/2.53

1.11/0.28

0.37

0.51/1.30

100-B-Ov5

2.50

1.11/-0.18

0.36

1.27/1.27

100-B-Ov6

2.15

0.95/2.24 1.29/2.45

1.11/-0.05

0.37

0.92/1.22

100-A

1.86/2.46

1.21/0.61

0.08

0.63/1.23

100-A-Ov1

1.77 2.03

1.63/2.21

1.20/0.62

0.06

0.80/0.98

100-A-Ov2

1.34

2.38/2.61

1.24/1.00

-0.04

1.15/1.38

100-A-Ov3

1.77

1.86/2.42

1.21/0.65

0.08

0.63/1.19

001-B

0.72

2.81/2.69

0.47/0.59

0.92

1.58/1.46

001-B-Ov1

0.67 1.80

2.71/2.54

0.47/0.64

1.07

1.48/1.31

1.66

1.73/1.57 1.85/2.64

0.46/0.62 1.40/0.62

0.93 0.01

0.57/0.57 0.62/1.41

010-Ov1

1.55

1.77/2.63

0.02

0.54/1.40

010-Ov2

0.42

3.06/1.64

1.58/0.72 0.73/2.15

0.71

1.83/0.97

001-B-Ov2 010

1. OER on 100-B and its oxygen-deficient surfaces Overpotentials and rate-determining steps: The 100-B surface is one for which we assessed the effect of Ov’s at the seven positions described earlier. Recall that in the vacancy label Ovn, the n index is indicative of the Ga layer on which the Ov resides, the larger n, the deeper the vacancy.


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First we consider the OER pathways involving the non-dangling surface-bound peroxo O* intermediate (denoted O1*). The free-energy diagrams for the four steps of OER on 100-B (reference system, and over-potential), and 100-B-Ov4 are shown in Figure 3. 100-B-Ov6 exhibits the largest over-potential, and 100-B-Ov4 the smallest over-potential. The 100-B system is the non-defective surface serving as the reference system with an over-potential of ~ 1.27 V. The over-potential is ~ 0.80 V on 100-B-Ov1 (Ov on 1st layer), ~ 1.27 V on 100-B-Ov2, ~ 0.65 V on 100-B-Ov2’, ~ 0.66 V on 100-B-Ov3, ~ 0.51 V on 100-B-Ov4, ~ 1.27 V on 100-B-Ov5, and ~ 0.92 V on 100-B-Ov6. In presence of Ov’s the over-potential is never larger than in the nondefective system. The smallest over-potential (~ 0.51 V) is for 100-B-Ov4 (Ov on the 4th layer) with a decrease of ~ 0.76 V compared to the reference system.

Figure 3. Energy diagrams for the four steps of the OER at different applied potentials for systems 100-B, and 100-B-Ov4 (the 100-B system with the lowest overpotential) for the peroxo O* mechanisms. Except for 100-B-Ov2 and 100-B-Ov5 for which the over-potential is no smaller than for the clean surface, the other over-potentials have decreased. Recall that 100-B-Ov2, 100-B-Ov2’, and 100-B-Ov5 are O(II)-type vacancies, while all others are O(III)-type vacancies. The different coordination of O(II) compared to O(III) appears to lead to two trends of over-potential in the oxygen-deficient 100-B surfaces. We discuss this finding further below, but in brief we believe



that this observation finds its origin in strong lattice relaxation around O(II)-type vacancies that traps strongly the vacancy electrons into a Ga-Ga bond at the vacancy site. Overall, Ov’s not only affect the over-potential (as seen here), but they also change the OER rate-limiting step. All the rate-limiting steps for OER in the presence of Ov’s are the first (proton + electron) removal step, except for 100-B-Ov1 and 100-B-Ov2’ where the rate-determining steps are the second (proton + electron) removal step. We consider now OER mechanisms involving the dangling O* species (denoted O2* earlier). The other intermediates are as before, mainly dangling OH* and dangling OOH*. The first point to note is that the over-potentials for mechanisms involving dangling O*’s are in all cases larger than those for mechanisms with peroxo intermediates. At the same time, in all cases, the over-potentials arise from the second (proton + electron) removal. As before with the nondangling peroxo intermediate O1* species, the OER over-potentials on 100-B-Ov2 and 100-BOv5 remain unchanged compared to the clean surface. In all other cases the over-potentials have changed a little, by ~ -0.05 V up to only ~ 0.11 V compared to the value for the reference system 100-B. In summary, the following observations emerge from Table 1: (1) on clean surfaces the peroxo O1* mechanisms are more facile than the dangling O2* mechanisms so that the reaction will proceed via peroxo O1* intermediates; (2) Ov’s lower the over-potential in all cases when considering the peroxo O1* mechanism; (3) an Ov in the 4th layer yields the lowest overpotential; (4) Ov’s change the OER over-potential slightly when considering the dangling O2* mechanism. Later we discuss the stability of the various oxygen-deficient surfaces in some details. Stabilities are as follows: Ov2=Ov2’> Ov5> Ov1> Ov3> Ov4~Ov6 (The data are in section 6 of SI). Thus Ov’s prefer the 2d sub-layer. The 2d sub-layer has the second lower over-potential ~ 0.65 V. Ov’s in the 4th and 3d layer have the lowest and third lower over-potential ~ 0.51 V and ~ 0.66 V. But the Ov’s in these two sub-layers are less stable. These results highlight the possible dichotomy between stability and over-potential. The present results support the thesis that, when assessing the effect of Ov on the OER activity at semiconductor surfaces, we must consider that Ov’s leave behind excess electrons in the semiconductor materials and that these electrons can be involved in charge transfer to the adsorbate (transfer of a fraction of an electron from the surface substrate to the adsorbate), making the binding of the adsorbate species to the surface more ionic in character and therefore stronger.11 The amount of charge transfer is commensurate with the electronegativity of the adsorbate, suggesting that Ov’s are likely to have a differential effect on the adsorption of the OER intermediates (OH*, peroxo O*, dangling O* and OOH*). As a result, the Gibbs free energies of the OER steps, the catalytic reaction energy profile, and the catalytic activity, all get altered, an observation readily found here. Bader Charge Analysis: To quantify the partial charge transfer occurring in OER, we used the Bader charge analysis46 to characterize the amount of charge transfer from the surfaces to the intermediates. The Bader charges (BCs) for surface Ga atoms and for the O and H atoms of the intermediate species OH*, peroxo O1*, dangling O2*, and OOH* for the clean 100-B surface and for all the oxygen-deficient surfaces are summarized in Table S1 of the Supporting Information. We also show the Bader charges and spin charges for OH* and dangling O2* on 100-


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B, and 100-B-Ov6 in Figure 4 to visualize the charge transfer. Taking the 100-B-OH structure as an example, the BC’s of the surface Ga’s, and O and H atoms are ~ 1.30, 6.83, and 0.39 electrons respectively, which means that Ga and H carry a positive charge ~ +1.70 and ~ +0.61 on average respectively, while O atoms carry a negative charge ~ -0.83 on average. Changes in BCs reflect charge transfer. We expect the excess electrons arising from the Ov’s to interact strongly with the uncoordinated metal atoms.9

We now consider differences in BCs for the three Ga atoms adjacent to the position of the oxygen vacancy in the 100-B-Ov1 structure and the 100-B-Ov1-OH structure. Upon analysis of the BC’s, we noted that the localization of the excess electrons is not limited to a single Ga atom around the vacancy site and found that summing-up the BC’s over the several Ga’s reflects better the shift in charge distribution. Accordingly we use below a quantity ΣGa that arise from summing-up the BC’s over these three surface Ga atoms. The total BC summed over the three Ga

Figure 4.Bader charge (BC) and spin densities of OH* and dangling O2* on 100-B and 100-B-Ov6. The symbols δ(ΣGa), δ(OH*), and δ(O2*) are changes in BC’s as defined in the text and shown in Table 2. From left to right, top column: 100-B-Ov6-OH, 100-B-Ov6, and 100-B-Ov6O2; bottom colum: 100-B-OH, and 100-B-O2.



atoms is 4.96 and 4.07. Thus the change in BC’s δ(ΣGa) for these Ga atoms is large, δ(ΣGa) ~ 0.89. We then consider changes in BC’s for the O and H atoms of the OH*, peroxo O1*, dangling O2*, and OOH* structures between the clean surface and oxygen-deficient surfaces. Here we add up the BC’s on O and H of OH*. In 100-B-OH the OH* charge is ~ 7.22, and for 100-BOv1-OH it is ~ 7.55, which corresponds to an increase in charge δ(OH*) of ~ 0.33 electrons due to charge transfer. All data are summarized in Table S1. One should notice the reference points for δ(ΣGa) and δ(OH*) is not the same. A result that stands out in our data is that for all the peroxo O* structures on the various surfaces, changes in charges (denoted δ(O1*) for the peroxo O1* species are negligible. There are no open valencies to the surface-bound peroxo O1* species which thus is not able to accommodate further charge. Changes in surface Ga charges δ(ΣGa) for these peroxo O1* structures are also negligible. The same observation applies to the OOH* structures on the various surfaces, for which the changes in charges δ(ΣGa) for all the Ga atoms and changes in OOH* charges, denoted δ(OOH*), are negligible. This is somewhat surprising considering the open valency of OOH*. All together there is essentially no charge transfer from the oxygen-deficient surfaces to the peroxo O* species and OOH* species. Further discussion about conditions for charge transfer is given below. In contrast to the finding above, upon considering the OH* structures, the corresponding δ(ΣGa) values are ~ 0.00, 0.89, 0.00, 0.42, 0.35, 0.33, -0.01, 0.28 for the 100-B surface and its seven Ov systems (Ov1, Ov2, Ov2’, Ov3, Ov4, Ov5, Ov6 respectively). The associated δ(OH*) values are ~ 0.33, 0.00, 0.29, 0.30, 0.27, 0.00, 0.21, as shown in Table 2. Thus, for the 100-B, 100-B-Ov2, and 100-B-Ov5 surfaces, there is no or little charge transfer from the surface to OH*. For 100-B-Ov1, 100-B-Ov2’, 100-B-Ov3, 100-B-Ov4, and 100-B-Ov6, the OH* species and the surface Ga’s see a substantial charge transfer. The largest amount of charge transfer is for 100-B-Ov1, with smaller amounts for the other surfaces. Similar findings are obtained for all the dangling O2* structures, as shown in Table 2. In these cases the δ(ΣGa)’s are ~ 0.06, 0.91, 0.00, 0.36, 0.31, 0.31, -0.01, and 0.33, while the δ(O2*) are ~ 0.29, 0.00, 0.21, 0.17, 0.18, 0.00, and 0.13. As before, we find that essentially no charge transfer to dangling O2* occurs in the case of the 100-B, 100-B-Ov2 and 100-B-Ov5 surfaces, while the other surfaces induce varied amounts of charge transfer to dangling O2*. It is interesting to note that, in most cases the surface Ga atoms acquire substantial fractions of an electron, in particular ~ 0.91 of an electron for the 100-B-Ov1 case. It is already interesting to note that, for both OH* and dangling O2*, 100-B-Ov2, 100-BOv2’, and 100-B-Ov5 arise from O(II)-type vacancies (coordination to three Ga’s), compared to O(III)-type vacancies (coordination to four Ga’s) for 100-B-Ov1, 100-B-Ov3, 100-B-Ov4, and 100-B-Ov6.


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Table 2. Changes in Bader Charges for ΣGa atoms (δ(ΣGa)) and OH* (δ(OH*)) for the OH* and dangling O2 intermediates on 100-B and reduced 100-B’s OH*. Surfaces

δ(ΣGa) (OH*)

δ(OH*)

δ(ΣGa) (O2*)

δ(O2*)

100-B

0.00

0.00

0.06

0.00

100-B -Ov1

0.89

0.33

0.91

0.29

100-B -Ov2

0.00

0.00

0.00

0.00

100-B -Ov2’

0.42

0.29

0.36

0.21

100-B -Ov3

0.35

0.30

0.31

0.17

100-B -Ov4

0.33

0.27

0.31

0.18

100-B -Ov5

-0.01

0.00

-0.01

0.00

100-B -Ov6

0.28

0.21

0.33

0.13

Charge transfer and over-potentials: In what follows we discuss the relationship between over-potential for the OER reaction and surface-to-adsorbate charge transfer arising from the Ov’s and their excess electrons. Charge transfers in the intermediate states result in changes in OER step energies and, consequently, in over-potentials. On the oxygen-deficient surfaces 100-B-Ov2 and 100-B-Ov5, there is essentially no charge transfer from the surface to any of the intermediates. The OER step energies are essentially unchanged and so are the over-potentials of OER on these two oxygen-deficient systems, compared to the over-potential on the clean 100-B surface. For pathways and mechanisms involving the OH*, peroxo O1*, and OOH* intermediates, charge transfer due to Ov electrons occurs only to the OH* species, not to the peroxo O1* and OOH* intermediates of OER. On the 100-B-Ov1 surface, there is ~ 0.89 electron transferred from the surface to OH* which makes the binding of OH* to the surface much stronger. This leads to the relative energy of OH* and to the step energy for step 1 of OER to be much lower than for the clean surface, ~ 1.46 eV vs. ~ 2.50 eV respectively as seen in Table 1 above. Since the O1* intermediate does not accept any excess charge from the surface, the relative energy of step 2 remains unchanged. Indeed, the absolute free energies of O1* are ~ 3.45 eV, ~ 3.49 eV, ~ 3.48 eV, ~ 3.45 eV, ~ 3.47 eV, ~ 3.45 eV, ~ 3.45 eV, and ~ 3.44 eV on the 100-B pure and deficient surfaces. It follows that the step energy for step 2 of OER becomes much larger (~ 2.03 eV vs. ~ 0.95 eV). After ZPE and TS corrections, the OER over-potential shows a decrease of ~ 0.47 V. In contrast, on the 100-B-Ov4 surface, we observe ~ 0.33 electron being transferred from the surface to the OH* species. This charge transfer increases the binding of OH* to the surface but to a lesser extent than on the 100-B-Ov1 surface where the charge transfer was very large. As a result, the step energy for step 1 of OER decreases moderately in the present case (from ~ 2.50



eV to ~ 1.74 eV). As before the relative energy of the O1* intermediate is unchanged, it follows that the increase in step energy for step 2 of OER is moderate. Overall the over-potential decreases rather significantly by ~ 0.76 V. For pathways and mechanisms involving the dangling O2* intermediates, there is charge transfer from the surfaces to OH* and also to the dangling O2* intermediate with its open valencies. Charge transfers to OH* and O2* make the binding energy of these species stronger. They induce changes in step energy for steps 1 and 2 that ultimately may or may not result in a lowering in OER over-potential. From the data about changes in BC’s δ(OH*) and δ(O2*) for OH* and O2* and changes in OER over-potentials, we see that the binding energies of the OH*’s are always larger than that of the O2* intermediates. Although the binding energies of the dangling O2* intermediates increase due to charge transfer, the binding energies of OH* remain stronger than the binding energies of dangling O2*. Accordingly, the over-potential for OER will be determined by the binding energy of OH*. The trend in changes of OER over-potential on oxygen-deficient surfaces with dangling O2* intermediates is thus similar to what was observed with peroxo O1* species. The 100-B-Ov1 surface shows the largest over-potential while 100-B-Ov6 has the smallest overpotential, with other surfaces having intermediate over-potentials. In the end we do find that all of the over-potentials for OER on the oxygen-deficient surfaces (except for the surfaces for which there is no charge transfer) changed very little when considering the O2* pathways and mechanisms. Further, the discussions above illustrate the delicate interplay between stabilization of intermediates by charge transfer (Ov-induced here) and change in overall OER over-potential. Binding energies as descriptors: Because the lowering of the over-potential is seen to be correlated to the changes in absorption energies of the OH* and O* intermediates (either peroxo O1* or dangling O2*), it is desirable to establish a dependence of the over-potential on the difference in O* and OH* binding energies, (∆EO* - ∆EOH*). This quantity has the form:

∆EO* − ∆EOH * = ( EO* − E* − EO ) − ( EOH * − E* − EOH ) = EO* − EOH * + ( EOH − EO ) where EO* and EOH* are the DFT energies of O* and OH*, E* is the energy of the clean surface, EOH* and EO* are the energies of the OH* and O* species. Since we adopt the Nørskov’s protocol19 of the computational hydrogen electrode, it follows that (EOH* – EO*) ~ ½ EH2 is a constant, that we can set to zero for convenience (we ignore ZPE and TS corrections as we approximate them as being constant across the series of reduced surfaces for a given intermediate species). The dependence of the activity (defined as the negative of the over-potential) on the differences in binding energies between ∆EO1* (∆EO2*) and ∆EOH* are displayed in Figure 5, panel (a) for the peroxo O1* intermediate and panel (b) for dangling O2* intermediate. The overpotential of OER via peroxo O1* has a volcano-shaped dependence on the energy difference (∆EO1* - ∆EOH*). So does the over-potential of OER via dangling O2* with a volcano-shaped dependence on the (∆EO2* - ∆EOH*). In Figure 5(a) for the peroxo O1* intermediates, (∆EO1* ∆EOH*) varies as ∆EOH* because there is no charge transfer to peroxo O1* and the binding energy of peroxo O1* is essentially not altered by charge transfer. On the 100-B, 100-B-Ov2 and 100-BOv5, there is no charge transfer to any species, the (∆EO1* - ∆EOH*) value remain unchanged, and


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so are the over-potentials. On the other surfaces, the values of (∆EO1* - ∆EOH*) depend on ∆EOH*, and therefore on the amount of charge transfer from the surfaces to OH* as we remarked above. It is interesting to note then that both, the over-potential of OER and the energy difference (∆EO1* - ∆EOH*), are determined and affected by the excess electron charge transfer. It follows that we obtain a volcano shape in Figure 5(a). For Figure 5(b) dealing with dangling O2* intermediates, (∆EO2* - ∆EOH*) is affected by both ∆EO2* and ∆EOH* but with ∆EOH* being the dominant factor. (∆EO2* - ∆EOH*) increases with charge transfer, so does the over-potential. It is interesting that the final shape for (∆EO2* - ∆EOH*) is still a volcano shape.

Figure 5. The dependence of the computed activity (negative of the over-potential) on (a) ∆EO1* - ∆EOH*, and (b) ∆EO2* - ∆EOH* for the 100-B surface and its oxygen-deficient surfaces.

2. OER on 100-A, 001-B, 010 surfaces and their oxygen-deficient surfaces So far we discussed the 100-B surface and its oxygen-deficient surfaces. We observed a striking dependence between OER activity and Ov’s. Here we discuss results for other surfaces, the 100A, 001-b, and 010 surfaces, albeit we investigated fewer (3, 2, and 2 respectively) cases of Ov’s to validate and generalize the findings. All OER step energies and over-potentials for the various cases are also listed in Table 1 above. For the 100-A surface, the oxygen vacancies were positioned in a ‘dangling’ position of the top layer (100-A-Ov1), the 2d layer (100-A-Ov2), and the 3d layer (100-A-Ov3). For the 001-B surface, the vacancies were positioned on the top layer (001-B-Ov1) and in a deep layer (001-B-Ov2). Lastly for the 010 surface, the vacancies were positioned on the top layer (010-Ov1) and the 4th layer (010-B-Ov2). 2.1 OER on the 100-A surface and its oxygen-deficient surfaces From Table 1, we see that the rate-limiting step for OER is the second (proton + electron) removal step on the clean surface and the defected surfaces except for the 100-A-Ov1 surface via the peroxo O1* pathway where it is the first (proton + electron) removal step. The over-



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potentials are ~ 0.63, 0.80, 1.15 and 0.63 V for the peroxo O1* pathways, while for the dangling O2* pathways, the over-potentials are ~ 1.23, 0.98, 1.38, 1.19 V. Compared to the clean surface, the over-potential on 100-A-Ov1 is lower but on 100-A-Ov2 it is higher, while on 100-A-Ov3 the over-potential is unchanged. The BC analyses are shown in Table S2 in the supporting information while the differences in BC’s, δ(ΣGa) for the Ga’s, δ(OH*) for OH*, and δ(O2*) for O2*, are shown in Table 3. With regard to the OH* species, the changes in BC’s δ(OH*) are ~ 0.30, 0.22, and 0.01 with δ(ΣGa)’s ~0.32, 0.43, 0.00. For the dangling O2* pathways, the δ(O2*) are ~ 0.00, 0.29, and 0.02 and the δ(ΣGa)’s are ~ -0.01, 0.42, -0.02. There is no charge transfer from the surface to the adsorbates on the 100-A-Ov3 surface and the over-potential for OER remains unchanged. On the 100-A-Ov2 surface, a charge transfer contributes to an increase in binding energy of the OH* species, which leads to a higher over-potential. On the 100-A-Ov1 surface, charge transfer occurs from the surface to the OH* species, but, interestingly, not to the dangling O2* species. This leads to an increase in binding energy of OH* but also to a decrease in over-potential. The geometries of the intermediates on all the surfaces are shown in Figure S2 of the supporting information.

Table 3. Differences in Bader Charge ΣGa, OH*, and O2* for 100-A, 001B, 010 and its deficient surfaces. Surfaces

δ(ΣGa) (OH*)

δ(OH*)

δ(ΣGa) (O2*)

δ(O2*)

100-A

0.00

0.00

0.06

0.00

100-A-Ov1

0.32

0.30

-0.01

0.00

100-A-Ov2

0.43

0.22

0.42

0.29

100-A-Ov3

0.00

0.01

-0.02

0.02

001-B

0.00

0.00

0.06

0.00

001-B-Ov1

0.31

0.01

0.13

0.02

001-B-Ov2

0.02

0.00

0.02

0.01

010

0.00

0.00

0.06

0.00

010-Ov1

0.02

-0.02

0.03

0.00

010-Ov2

0.96

0.07

0.96

0.61

2.2 OER on the 001-B surface and its oxygen-deficient surfaces


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Figure 6. The OER intermediates OH* and O2* on 001-B, 001-B-Ov1 and 001-B-Ov2 surfaces. The rate-limiting steps for OER on the 001-B surfaces (clean and defected) are the second (proton + electron) removal step except on the 001-B-Ov2 surface where it is the first (proton + electron) removal step. The over-potential is ~ 1.58 V through the peroxo O1* intermediate while it is ~ 1.46 V through the dangling O2* intermediate on a clean 001-B surface. These values are significantly larger than on the other surfaces, such as 100-B and 100-A. A reason for this observation can be found in the structures of the intermediates OH* and O2* displayed in Figure 6. The structures of the OH* and O2* intermediates are unusual as they involve two absorption sites. The increased coordination of the intermediates makes their binding energies larger, to the point that the first and third step energies of OER are very small. As a consequence, the second step energy of OER is much larger and the over-potential is larger also.

On the 001-B-Ov1 surface, the over-potential is ~ 1.48 V through the peroxo O1* intermediate and ~ 1.31 V through the dangling O2* intermediate, a value that is a little smaller than that on the clean surface. As illustrated in Figure 6, the geometries of intermediates are almost the same between the 001-B surface and the 001-B-Ov1 surface. The δ(ΣGa) (OH*) and δ(ΣGa) (O2*) are ~ 0.31 and ~ 0.13 and the δ(OH*) and δ(O2*) are ~ 0.01, ~ 0.02 for the OH* and O2* intermediates as seen in Table 3 and Table S3. As the δ(ΣGa)’s change and the δ(OH*) and δ(O2*) do not change much, the outcome is that there is no charge transfer to the adsorbates and the over-potential remains essentially unchanged. On the 001-B-Ov2, the over-potential are all ~ 0.57 V via the peroxo O1* and dangling O2* species. These values are much lower than that on the other two surfaces. As shown in Table 3, the δ(ΣGa)’s and δ(OH*)’s are almost zero which means there is no charge transfer from



001-B-Ov2 surface to the adsorbates. The over-potential is therefore not affected by this type of vacancy. As seen in Figure 6, we found that the OH* structures do not resemble the structures obtained on the 001-B and 001-B-Ov2 surfaces and that involve only one adsorption site. The doubly-coordinated bonding increases the binding energy of OH* which affects the first step energy of OER. This OH* bonding increase leads to a smaller over-potential for OER as step 1 is the over-potential-determining step. 2.3 OER on the 010 surface and its oxygen-deficient surfaces On the 010 surfaces, the over-potentials are ~ 0.62, ~ 0.54, and ~ 1.83 V for OER via the peroxo O1* species and ~ 1.41, ~ 1.40, and ~ 0.97 V for OER via the dangling O2* species on all the surfaces as shown in Table 1. The rate-limiting steps for OER on the 010 surfaces (clean and defected) are the second (proton + electron) removal step except on the 010-Ov2 surface via O2* species path where it is the third (proton + electron) removal step. The geometries of OH* and O2* are unusual (doubly-coordinated) compared to structures found for other surfaces. Both OH* and O2* for 010-based surfaces are shown in Figure 7. The other geometries are shown in the Figure S4 in the SI. As shown in Table 3 and Table S4, the δ(OH*)’s and δ(ΣGa)’s are negligible on 010Ov1, which means there is no charge transfer from the 010-Ov1 surface to the adsorbates. Compared to the clean surface, the over-potential of OER is essentially the same for the 010-Ov1 surface. It is surprising to find the over-potential larger via the peroxo O1* species on 010-Ov2 and smaller via the dangling O2* species. To rationalize this finding we refer to the fact that the geometries of OH* and O2* on the 001-Ov2 surface (shown in Figure 7) are significantly unusual. OH* forms bonds with two sites (doubly-coordinated binding rather than singly-coordinated binding), and O2* forms bonds with three sites (triply-coordinated binding). This type of binding

Figure 7. The OER intermediates OH* and O2* on the 010, 010-Ov1 and 010-Ov2 surfaces. ACS Paragon Plus Environment

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result in much larger binding energies of OH* and O2*. For OER via peroxo O1* intermediates, only the binding energy of OH* is increased due to charge transfer, so the first step energy of OER is smaller and the 1-to-2 rate-determining over-potential step is higher. For OER with dangling O2* intermediates, although the first step of OER is smaller, the third step of OER is larger, but the over-potential is lower in the end. For these systems, the δ(OH*)’s are ~ -0.02 and ~ 0.07 and the δ(ΣGa) are ~ 0.02, and ~ 0.96; the δ(O2*)’s are ~ 0.00 and ~ 0.61 and the δ(ΣGa)’s are ~ 0.03, and ~ 0.96; the δ(OOH*)’s are ~ 0.04 and ~ 0.26, and δ(ΣGa)’s are ~ 0.01, and ~ 0.95, as shown in Table 3 and Table S4 in the SI. It is clear that a strong charge transfer takes place form the 010-Ov2 surface to O2*, and even OOH*. The charge transfer leads to larger binding energies for these intermediates, which causes the first step energy of OER to be smaller. The second step energy with O2* is now larger, and so is the third step energy. All these changes together make the over-potential larger via O1*, but smaller via O2*. 3. Predicting charge transfer In the above sections, we discussed OER on various clean and oxygen-deficient surfaces and we addressed the question as to whether and how much excess electron charge (formally arising from neutral Ov’s) gets partially transferred to the adsorbates, a feature that results in distinctive effects on the over-potential for OER. Accordingly, understanding the underlying chemical reasons for the charge transfer to the adsorbates is critically important. A neutral oxygen vacancy Ov leaves behind excess electrons that occupy trap states in the band gap. If the energy levels of these trap states are higher than the energy states of an adsorbate, then charge transfer can occur, otherwise, there is no charge transfer. Thus getting the energy levels of the trap states of all the oxygen-deficient surfaces will help in predicting the occurrence of charge transfer.



Figure 8. Energy positions of the vacuum level (VL), the conduction band levels (CB), the valence band levels (VB), and the trap state levels (TS) of the clean surfaces and all the oxygen-deficient surfaces. The surfaces of same parentage 100-B, 100-A, 001-B, and 010 are grouped together along the x-axis. The ticks on the x-axis correspond to the layer where the Ov is located. The nomenclature follows the earlier text. The red and green line corresponds to the top of the valence band and bottom of the conduction band for the clean surfaces. The dash line corresponds to the vacuum level for all clean surfaces. The Ov-induced trap states for all defected surfaces are shown in blue.

To this end we determined densities of states (DOS) and work-functions (WF) of all the oxygen-deficient surfaces (Figue S5-S8 in the SI) to determine the energy levels of the trap states from the hybrid density functional calculations. They are shown in Figure 8. For intrinsic semiconductors, the work function WF is a measure of the energy required to take an electron form the top of the valence band (VB) to the vacuum level (VL). We aligned the VL of all the surfaces (at the zero level of energy). Given the VL level and the WF, the conduction bands CB and valence bands VB of the various surfaces can be positioned on a single energy scale. From the calculated DOS, we get the energy levels of the trap states. They are the energy states (above the VB) populated by the excess electrons. We ought to point out again that we used a hybrid functional as well as dipole correction algorithms for all oxygen deficient surfaces as they have the potential to suffer from artefactual dipole effects. The consistency of results between clean and oxygen-deficient surfaces when considering specific surfaces, suggest that variations in energy


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levels are intrinsic to the various surfaces, and they allow us to derive consistent rules about opportunity for excess charge transfer or not. Focusing on the 100-B surfaces, it is apparent in Figure 8 that the gap states are split along two trend lines, those from 100-B-Ov2, 100-B-Ov2’, and 100-B-Ov5, and those from 100B-Ov1, 100-B-Ov3, 100-B-Ov4, 100-B-Ov6. Since we used a hybrid functional of the density we expect the energy levels to be relatively accurate and reliable. This two-trend observation was pointed out earlier when discussing charge transfer with the 100-B systems. We suggested then that the ‘type’ of vacancy (O(II)-derived for Ov2, Ov2’, and Ov5 compared to O(III)-derived for Ov1, Ov3, Ov4, and Ov6) The correlation applies here as well. The energy levels of the trap states are different among all the oxygen-deficient surfaces. This observation helps explain the differences in the amount of charge transfer. The higher the energy level, the larger the charge transfer. For all the oxygen-deficient 100-B surfaces, the energy levels of the trap states on 100-B-Ov1, 100-B-Ov3, 100-B-Ov4, and 100-B-Ov6 are much higher than those on 100-B-Ov2, 100-B-Ov5, and 100-B-Ov2’. This finding is consistent with the 100-B-Ov1, 100-B-Ov3, 100-B-Ov4, and 100-B-Ov6 surfaces exhibiting charge transfer, while the 100-B-Ov2, 100-B-Ov5, and 100-B-Ov2’ surfaces do not. The energy levels of the trap states on 100-B-Ov1 surface are the highest, a finding consistent with this surface having the largest charge transfer. Among the surfaces we noted that the energy levels of the trap states for 100-B-Ov2 and 100-B-Ov2’ surfaces are about the same, and yet the charge transfer is larger on the 100-B-Ov2’ surface. We believe the reason for this difference is due to the fact that, for 100B-Ov2’ surface, the absorption (reactive) Ga site is next to the oxygen vacancy so that the charge transfer is directly associated with the bonding of the intermediates, in contrast to all other cases where the Ov’s are far from the active site. On all the 100-A oxygen-deficient surfaces, the energy levels of the trap states are all very low, so they are not favorably positioned for charge transfer, except for the 100-A-Ov2 surface, similarly to the 100-B-Ov2 surface. For the 001-B-Ov1 and 001-B-Ov2 surfaces, the energy levels of the trap states are not high enough to allow charge transfer from the surface to the adsorbates. The energy levels of the trap states for the 010-Ov1 and 010-Ov2 surfaces are the highest in all the surfaces and charge transfer should occur. However on the 010-Ov1 surface, there is no charge transfer from surface to adsorbates. We assign this observation to the oxygen vacancy on the 010-Ov1 surface giving rise to under-coordinated Ga atoms that end up forming Ga-Ga bonds with adjacent Ga atoms, as can be clearly seen in Figure 7 and Figure S4 in the supporting information. The length of Ga-Ga bond is ~ 2.5 Ǻ, a short bond length. The excess electrons may be trapped in this Ga-Ga ‘structure’ and are not available for transfer to the adsorbates. For the 010-Ov2 surface, the trap state energy levels are the highest, this surface exhibits charge transfer, including to the OOH* species, a feature not observed with any of the other surfaces. 4. The formation energies of the oxygen vacancies It is of interest to consider the stability of the various oxygen-deficient systems investigated here. The stability of an oxygen vacancy is given by: Ef = Es – Ec + µ0



where Es is the energy of the slab containing the oxygen vacancy, Ec is the energy of the clean slab, and µ0 is the chemical potential of oxygen. The smaller the formation energy, the easier it is to be formed, and the more stable the oxygen vacancy. The formation energies of the oxygen vacancies at different sites are shown in Figure 9. For the 100-A and 010 surfaces the vacancies are much more stable on the surface layer (Ov1) than on the sub-surface layer (Ov2). For 001-B, Ov1 is slightly more stable than Ov2. Trends for 100-B are more complex. The order of the stability is Ov2 ~ Ov2’ > Ov5 > Ov1 > Ov3 > Ov4 ~ Ov6. The two most stable oxygen-deficient surfaces are 100-A-Ov1 and 010-Ov1, and the two most unstable ones are 100-B-Ov4 and 100B-Ov6.

Figure 9. The formation energies of oxygen vacancies at different sites. The index of the horizontal axis corresponds to the “surfaceOvn” labels used throughout. Earlier we noted that 010-Ov1 has low OER over-potential, it also has high stability. The 001-B-Ov2 surface has low OER over-potential, it has moderate stability. The 100-B-Ov4 surface has the lowest over-potential, it has the lowest stability. There results demonstrate a dichotomy between stability and over-potential. Among the oxygen-deficient 100-B surfaces, there appears to be two trend lines. Ov2, Ov2’, and Ov5 have similar oxygen vacancy stability. (For Ov2 and Ov2’, this is expected, both are in the second layer and the difference between them is only with regard to the active site for OER). The over-potentials for 100-B-Ov2 and 100B-O-v5 are very similar and they exhibit no charge transfer to the OER intermediates, and their associated trap states are similarly positioned. In contrast 100-B-Ov1, 100-B-Ov3, 100-B-Ov4, and 100-B-Ov6 align along a different stability trend. They exhibit similar over-potential, charge transfer ability, and trap state levels.


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As indicated earlier, bulk Ga2O3 has three kinds of oxygen atoms differing in their chemical environments. 100B-O-v2, 100-B-Ov2’ and 100-B-Ov5 were found to have been created by removing a O(II)-type oxygen atoms while 100-B-Ov1, 100-B-Ov3, 100-B-Ov4, and 100-B-Ov6 were created by removing a O(III)-type oxygen atoms. We believe the differences in properties and characteristics between the two groups are intrinsically related to the nature of the vacancies, and in fact, of their electronic structure. The structures of clean 100-B, 100-B-Ov2, and 100-BOv3 are highlighted in Figure 10. The most striking feature of Figure 10 is observed for 100-B-Ov2 that arose from an O(II)type vacancy. The two Ga(I) atoms at the vacancy site become three-coordinated from fourcoordinated. In addition the form a Ga(I)-Ga(I) bond with a bond length of ~ 2.57 Å, much shorter than any Ga-Ga in a clean 100-B slab where distances between Ga atoms are ~ 3.08 Å. This type of Ga(I)-Ga(I) bond is also found in 100-B-Ov2’ and in 100-B-Ov5 (structures shown in SI). In contrast, the relaxation of the lattice upon O(III)-type vacancy in 100-B-Ov3 does not exhibit the extent of relaxation seen in 100-B-Ov2 upon O(II)-type vacancy. The Ga(II)…Ga(II) distance is ~ 3.22 Å in 100-B-Ov3, slightly increased compared to the clean slab. The same observation holds for 100-B-Ov1, 100-B-Ov4, 100-B-Ov6, with Ga(II)…Ga(II) distances of ~ 3.1 Å (structures shown in the SI). We believe the Ga-Ga bond-based structure of O(II)-type vacancy is the source of the properties observed for 100-B-Ov2, 100-B-Ov2’, and 100-B-Ov5. The excess electrons arising from the vacancy become strongly trapped into a Ga(I)-Ga(I) bonding state. As a results the excess electrons are no longer able to participate in charge transfer to any of the OER absorbate intermediates. The overpotentials calculated in these cases remain unchanged compared to the clean surface (as seen earlier). The forming of the Ga(I)-Ga(I) bond makes the systems more stable, and the trap states are bonding states close to the VB-max. The stability of these O(II)-type vacancies is stronger and the in-gap trap states levels are lower in energy, as could be seen in Figures 8 and 9. System 100-B-Ov2’ exhibits properties that are not quite the same as 100B-Ov2 and 110-BOb5. We attribute the differences to the position of the vacancy Ov2’ in 100B-Ov2’ to be right near the active site or OER. The structures of the OER intermediates on 100B-Ov2’ are shown in the Supplementary Information.



Figure 10. Clean 100-B, 100-B-Ov2 and 100-B-Ov3 slabs. In clean 100B slab, O(II) and O(Ⅲ) type oxygen atoms are blue and yellow respectively. The Ga atoms connected to the selected O(II) and O(Ⅲ) type O atoms are shown in pink. Key Ga-Ga distances are called out. 5．The theoretical activity of oxygen evolution on β-Ga2O3 Altogether we have calculated OER on 18 Ga2O3 surfaces (clean and oxygen-deficient). As earlier, the theoretical activity (negative of the over-potential) for the four (proton + electron) removal steps in OER is depicted as function of the difference in binding energy (∆EO* - ∆EOH*) in Figure 11. It has a volcano shape, an observation that provides a means to help predict which surfaces could be active toward OER in an experiment. The systems near the top of the volcano are the ‘good’ surfaces. There are eight of them: 100-B-Ov2’, 100-B-Ov3, 100-B-Ov4, 100-A, 001-B-Ov2 (with both peroxo O1 and dangling O2 intermediates), 010, and 010-Ov1. On the clean 100-A, the OER activity is high, and Ov’s appear to decrease the activity and do not help. The clean 010 surfaces has a good OER activity, and Ov on the top layer may lead to a small increase in OER activity. On the 100-B surfaces and 001-B surfaces, Ov’s have potentially an important impact on OER activity, with the 100-B-Ov4 being the most active surface among all these 18 surfaces. It is interesting to note that for 001-B-Ov2 (Ov in the 2d layer), the OER activity is high even for the dangling O2* pathway, an observation that does not happen for the other surfaces.


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Figure 11. The theoretical activity (negative of the over-potential) of the oxygen evolution is depicted as function of the difference in binding energies (∆EO* - ∆EOH*). As mentioned in the introduction, the positive role of Ov’s on the OER have been reported on the hematite14,15, WO318 by DFT calculations and on BaTiO316 by experimental finding. We emphasize then that our finding is likely to be common to different photocatalyst. We also remark that there are no current experimental structural characterization pieces of information about Ov’s for Ga2O3 or for other materials. Accordingly the present work offers insights and knowledge that may serve as seed for increased understanding of controllable physical parameters, such as degree and position of Ov.

Ⅳ. CONCLUSIONS We calculated the step energies for OER on four different surfaces of β-Ga2O3 along with various oxygen-deficient surfaces. We found that the over-potential of OER is affected by the physical location of the Ov’s. Bader Charge analyses show that fractions of the excess electrons arising from the Ov’s get transferred from the surfaces to the adsorbates and strengthen the surface-adsorbate binding. The over-potential of OER is altered accordingly. A lowering of the over-potential for OER is observed only with moderate transfer of the excess electrons. Beyond the amount of excess electrons being transferred to the adsorbates, we observed that the presence of these excess electrons affects also the nature (and structure) of the intermediates. As a result, the Ov excess electrons have an effect on the over-potential for OER. The relative energy levels of the trap states of these excess electrons are good descriptors for predicting whether charge



transfer occurs or not. Our findings reveal a clear relationship between the over-potential of OER and Ov’s. Overall these findings should prove helpful in understanding and predicting the OER activity of oxygen-deficient photo-catalysts. The precise control of the amount and the position of Ov’s is likely to be a synthetic challenge.

ASSOCIATED CONTENT 5 Supporting Information The supporting information includes: 1/ The details of the 100-A, 100-B, 001-B, and 010 slabs of β-Ga2O3 (Table S0); 2/ the free energy calculation scheme for the oxygen evolution reaction (OER); 3/ the Bader charges for the 100-B, 100-A, 001-B, and 010 surfaces, and their oxygen-deficient surfaces (Table S1-S4); 4/ the optimized structures of the OER intermediates on the 100-B, 100-A, 001-B, 010 surfaces and their oxygen-deficient surfaces (Figure S1-S4); 5/ the density of states (DOS) and work-function (WF) data for all clean and oxygen-deficient surfaces (Figure S5-S8). 6. The stability of oxygen vacancy in the 100-B oxygen deficient surfaces. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author: Taifeng Liu: [email protected] Michel Dupuis: [email protected] Present Addresses: Taifeng Liu National & Local Joint Engineering Research Center for Applied Technology of Hybrid Nanomaterials, Collaborative Innovation Center of Nano Functional Materials and Applications of Henan Province, Henan University, Kaifeng, 475004, China. Michel Dupuis Department of Chemical and Biological Engineering, University at Buffalo, State University of New York, Buffalo, NY 14260, USA Funding Sources National Natural Science Foundation of China (grant # 21703054) and Start-up Funds to M.D. by the University at Buffalo. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT


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TOC graphics The theoretical activity of the oxygen evolution reaction (OER) is depicted as function of differences in binding energies (∆EO* - ∆EOH*) of the OH* and O* intermediates in OER

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Role of Oxygen Vacancies on Oxygen Evolution Reaction Activity: Î²

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