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pH-dependent Catalytic Reaction Pathway for Water Splitting at the BiVO-water Interface From the Band Alignment 4

Francesco Ambrosio, Julia Wiktor, and Alfredo Pasquarello ACS Energy Lett., Just Accepted Manuscript • Publication Date (Web): 07 Mar 2018 Downloaded from http://pubs.acs.org on March 7, 2018

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ACS Energy Letters

pH-dependent Catalytic Reaction Pathway for Water Splitting at the BiVO4-Water Interface from the Band Alignment Francesco Ambrosio,∗ Julia Wiktor, and Alfredo Pasquarello Chaire de Simulation à l’Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland E-mail: [email protected] Phone: +41 21 6933423. Fax: +41 21 693 5419

∗

To whom correspondence should be addressed

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Abstract We align the band edges of BiVO4 at the interface with liquid water by combining advanced electronic-structure calculations, molecular dynamics simulations, and a computational hydrogen electrode. After accounting for spin-orbit coupling, thermal and nuclear quantum motions, we achieve good agreement with experiment, particularly with one-shot GW calculations and semi-empirically tuned hybrid functionals. The pH-dependent mechanism of the water oxidation reaction is discussed in consideration of the pH at the point of zero charge, the pKa of adsorbed water molecules, and the redox levels of the rate determining step of the reaction. The mechanism pertaining to acidic conditions is found to dominate over a large pH range. The kinetically more favorable oxidation of hydroxyl ions is favored only in highly alkaline conditions and could be hampered by corrosion processes. Advanced electronic-structure methods are shown to be instrumental to overcome the erroneous physical picture achieved at the semilocal level of theory.

Graphical Table of Contents Artificial photocatalysis at the semiconductor-water interface may represent a viable solution for the clean production of fuel. 1–6 The main hindrance to the success of this promising technology is represented by the slow kinetics of the multi-step water oxidation reaction induced by the photogenerated holes in the semiconductor (2H2 O+4h+ → 2O2 + 4H+ ). 7 Large efforts have been devoted to identify the ideal photocatalyst among the vast plethora of semiconducting materials. 8–13 However, semiconductors catalyzing efficiently both the hydrogen 2


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ACS Energy Letters

reduction and the water oxidation reaction are currently not available. For this reason, the two half-reactions are carried out on separate p-type and n-type electrodes (photoanode and photocatode) through a device architecture known as Z-scheme. 14 In this context, monoclinic bismuth vanadate m-BiVO4 is one of the most promising materials to be used as photoanode for the water oxidation reaction. 15–19 However, the intrinsic photocatalytic properties of this material have not yet been clarified. 20 BiVO4 has a band gap of 2.4-2.5 eV which allows one to capture a large portion of the visible spectrum, and its band edges are favourably aligned with respect to the redox levels of the water splitting reaction. 21,22 However, the band gap of this material has long eluded a consistent theoretical description. In fact, electronic band gaps obtained with semilocal functionals and hybrid functionals with a reduced fraction of nonlocal Fock exchange have been found to be in much better agreement with experiment than standard hybrid functionals. 23–25 This puzzling observation has been recently explained as a consequence of error cancellation. 26 In fact, by properly accounting for spin-orbit, thermal, and nuclear quantum effects, a band gap renormalization of ∼1 eV has been calculated. 26,27 This indicates that these aspects should be taken under consideration when carrying out high-throughput searches to discover materials with the desired electronic properties. In this context, it is of interest to determine the effect of the sizable band gap renormalization on the band edges at the BiVO4 surface and at the BiVO4 -water interface. Band gap renormalization due to thermal vibrations are generally moderate (usually below 0.1-0.2 eV) and comparable to other sources of error in the calculation. 28 Therefore, it is fundamental to verify the robustness of the proposed benchmark against materials where this effect is substantial, such as BiVO4 , which is currently considered as one of the most promising photoanodes. The band alignment at the semiconductor-water interface is usually employed in the screening of materials to assess whether the band edges are favourably aligned to the redox levels of hydrogen reduction and water oxidation. 8,9 However, the oxidation of water

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to molecular oxygen is a multi-step process and, therefore, the alignment of the valence band edge of the semiconductor to the redox levels pertaining to the proton-coupled electron transfers is even more important. In particular, the reaction is initiated through the dehydrogenation of H2 O or the oxidation of OH− in acidic and alkaline conditions, respectively. 7 Therefore, since both the band alignment and the coverage of the semiconductor surface are pH-dependent, 28,29 the preference of one pathway over the other is not obvious. In this Letter, we determine the band edges of BiVO4 at its surface and at its interface with water. By comparing the band alignment calculated at various levels of theory, oneshot GW calculations and semi-empirically tuned hybrid functionals are found to provide the closest agreement with the experimental characterization, provided the band edges of the materials are corrected to account for the huge band gap renormalization of this material. By coupling the results achieved for the band alignment with the insights from the pH-dependent coverage of the BiVO4 surface and with the potentials of the water splitting reaction, we then discuss the effectiveness of BiVO4 as a photoanode at varying pH conditions. The fundamental band gap of a semiconductor at room temperature (i.e. the temperature at which the photocatalytic device is operated) Egtheory (T ) is defined from theory as follows: Egtheory (T ) = εtheory (T ) − εtheory (T ), c v

(1)

where εtheory (T ) and εtheory v−sc (T ) are the valence and conduction band edge of the semiconducc tor, respectively. εtheory (T ) and εtheory (T ) read as follows: c v εtheory (T ) = εtheory (0) + ∆εSOC + ∆εNQE + ∆εTv , v v v v

(2)

εtheory (T ) = εtheory (0) + ∆εSOC + ∆εNQE + ∆εTc , c c c c

(3)

and

(0) are the valence and conduction band edges calculated at 0 K (0) and εtheory where εtheory c v

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ACS Energy Letters

at a level of theory not including spin-orbit coupling and aligned with respect to the average electrostatic potential of the bulk semiconductor. ∆εSOC , ∆εSOC , ∆εNQE , ∆εNQE , ∆εTv , and v c v c ∆εTc are the shifts of the band edges due to spin-orbit coupling (SOC), nuclear quantum effects (NQEs), and thermal effects, respectively. In this Letter, we calculate the band edges at 0 K at various levels of theory. First, we consider computationally cheap schemes such as the semilocal PBE functional, 30 the standard hybrid functional PBE0, 31 and the simplest GW scheme, 32 i.e. the one-shot G0 W0 (0) method with starting wave functions achieved at the PBE level. We also employ the G0 W0 (0.25) method, in which the starting point is achieved at the PBE0 level, and the semi-empirical hybrid functional PBE0(α), in which the fraction of Fock exchange is set to reproduce the f method, which inexperimental gap. Finally, we also consider the self-consistent QSGW cludes vertex corrections in the screened interaction 33 and has been found to provide the band gap of BiVO4 in excellent agreement with experiment. 26 All these calculations 26 have been performed with the freely-available abinit code. 34–36 To achieve the individual shifts of the valence and conduction band edges, we follow the scheme proposed in Ref. 26 for the band gap renormalization. In particular, SOC effects are evaluated from fully relativistic calculations, thermal effects from molecular dynamics simulations with classical nuclei at room temperature, and NQEs from path-integral molecular dynamics simulations at the same temperature. 26 The shifts calculated for the valence and conduction band edge are listed in Table 1. In the Supporting Information, we verify that the band gap renormalization calculated for the bulk semiconductor is essentially unchanged with respect to the semiconductor in aqueous environment 37 and that the shifts reported in Table 1 can therefore be adopted for the band alignment at the BiVO4 -water interface. 37 We model the (010) surface of BiVO4 using an orthorhombic supercell to achieve the interface with vacuum. 37 Through the line-up of the electrostatic-potential across the interface, we align the band edges with respect to the vacuum level and calculate the ionization poten-

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Table 1: Calculated shifts for the valence band and conduction band edge due to spin orbit coupling (SOC), nuclear quantum effects (NQEs) and thermal vibrations at 300 K (T ), respectively. The band gap renormalization ∆Eg 26 is also reported. SOC NQE T Total renorm.

∆εv −0.02 0.11 0.45 0.54

∆εc −0.15 −0.11 −0.25 −0.51

∆Eg −0.13 −0.22 −0.70 −1.05

tial and the electron affinity of BiVO4 . The neutral BiVO4 -water interface, corresponding to the pH at the point of zero charge pHPZC , is composed of an orthorhombic supercell, which includes 56 water molecules corresponding to the experimental density of liquid water. 37 Upon molecular dynamics simulations, interfacial water molecules are found to be molecularly adsorbed on the surface through weak bonds between the O atom of the molecule and the surface Bi atoms. 37 All the interface calculations have been performed with the cp2k code, 38 as described in Refs. 29 and 37. The band alignment at the BiVO4 -water interface is achieved with respect to a computational standard hydrogen electrode µSHE , defined by the reduction of the hydronium ion to gaseous hydrogen. 39,40 The band edges of the semiconductor and µSHE are aligned at the semiconductor-water interface through the line-up of the plane-averaged electrostatic potential. 28,41,42 In particular, we define the potential shift of the semiconductor ∆Vsc and of liquid water ∆Vw , as follows:

∆Vsc = Vsc (bulk) − Vsc (int),

(4)

∆Vw = Vw (bulk) − Vw (int),

(5)

where Vsc (int) and Vw (int) are the average electrostatic potentials in the bulk-like region of the interface for the semiconductor and for liquid water, respectively. ∆Vsc (int) and ∆Vsc (int) are calculated from a 10-ps long molecular dynamics simulation of the BiVO4 (010)-water

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ACS Energy Letters

interface, which is sufficient to achieve converged values. A schematic representation of the alignment scheme used in this work for the BiVO4 (010)-water interface is given in Fig. 1.

Figure 1: Schematic representation of the band alignment at the BiVO4 -water interface. In the left panel, the conduction and valence band edges (ǫc and ǫv in red) of the semiconductor are shown with respect to the electrostatic potential (grey) and its average Vsc (bulk). Similarly, on the right, the SHE level (green) is given with respect to the electrostatic potential (grey) and its average Vw (bulk) in liquid water. The line-up between the electrostatic potentials Vsc (int) and Vw (int) is illustrated in the middle panel. The calculation of the band alignment at the BiVO4 (010)-water interface is performed through the neutral interface model, which corresponds to the pH value at the point of zero charge (pHPZC ). 28 This is defined as the pH for which the concentration of adsorbed protons is equal to that of adsorbed hydroxyl ions and hence no net charge is found at the surface. 29,37 The position of the valence band edge of a semiconductor at pHPZC with respect to µSHE (at pH=0 by definition) reads as follows:

εSHE (PZC) = εtheory (T ) − µSHE − ∆Vsc + ∆Vw , v v

(6)

Consequently, the conduction band edge ǫSHE (PZC) is obtained as follows: c εSHE (PZC) = ǫSHE (PZC) + Egtheory (T ). c v

(7)

Following recent experimental work, 43 we assume Nernstian behaviour for the band edges of BiVO4 in aqueous environment. Hence, the conduction band edge measured at a given pH,

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ǫSHE (pH), can be shifted to its value at pHPZC as follows: c ǫSHE (PZC) = ǫSHE (pH) + (0.059 eV) · (pHPZC − pH). c c

(8)

The experimental range for the pHPZC of the BiVO4 (010)-water interface is 2.5−3.5. 44,45 In particular, the value achieved from the most recent experimental characterization (3.5 in Ref. 45) is close to the one recently calculated (3.46) within a grand-canonical formulation of adsorbates at the semiconductor-water interface. 29 Therefore, to make contact with the bandalignment at the BiVO4 -water interface measured for an electrode immersed in a solution at pH=7, 22 we use Eq. (8) with a value of pHPZC equal to 3.46. 29,46 We now discuss the band alignment at the BiVO4 (010)-vacuum and BiVO4 (010)-water interfaces. The values of the IP and the EA achieved at various levels of theory are illustrated in Fig. 2(a), while those for εSHE and εSHE are in Fig. 2(b). The results are also collected in v c Table 2. For each level of theory, we also report the mean absolute error (MAE) from the individual errors on IP, EA, εSHE , and εSHE . We notice that the trends among electronicv c structure methods observed in Fig. 2(a) and (b) are very similar, indicating a clear correlation between the description of the band edges in the two systems. We first focus on the semilocal PBE functional, which clearly fails in describing the position of the band edges of BiVO4 . In particular, the errors are as large as ∼0.7 eV for the position of the conduction band edge. It is noteworthy to pinpoint that if the corrections to the band edges listed in Table 1 are neglected, the results at the PBE level misleadingly appear to match the experimental characterization closely (cf. Fig. 2). The standard PBE0 functional does not provide a satisfactory agreement with experiment, with a MAE of 0.31 eV. The G0 W0 (0) and G0 W0 (0.25) results are found to be closer to experiment, with average ˜ gives the fundamental band errors of only 0.10 and 0.22 eV, respectively. The QSGW gap of BiVO4 in excellent agreement with experiment, 26 but does not improve the band alignment with respect to less computationally demanding methods, in line with previous

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ACS Energy Letters

Figure 2: Band alignment of BiVO4 at the interface with (a) vacuum and (b) liquid water, as calculated at various levels of theory. IP and EA are referred to the vacuum level, band edges at the semiconductor-water interface are given at pH=7 and are referred to the SHE. Dashed lines indicate the band-alignment achieved at the PBE level without considering SOC, thermal, and nuclear quantum effects. Experimental values from Refs. 21 and 22 are reported as dotted lines for comparison.

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observations for other semiconductors. 28 Finally, when the fraction of Fock exchange α is set to reproduce the experimental band gap, an overall good agreement with experiment is reached for all the considered quantities, thus confirming the effectiveness of the PBE0(α) method for the alignment of the band edges of semiconductors at the interfaces with vacuum and liquid water. 28,42 It should be noted that α has to be set to 19% in order to reproduce the experimental band gap of 2.5 eV. This value is remarkably higher than the value of 5% reported in Ref. 25, which has been obtained ignoring the sizable band-gap renormalization induced by SOC, thermal, and nuclear quantum effects. Table 2: Calculated Egtheory (T ), IP, EA, εSHE , and εSHE at various levels of theory. v c SHE SHE εv and εc are given for a pH=7. Experimental values from Refs. 21 and 22 are included for comparison. Mean absolute errors (MAEs) are provided for each level of theory. All values are given in eV. Method PBE PBE0 G0 W0 (0) G0 W0 (0.25) ˜ QSGW PBE0(α) Expt.

Egtheory (T ) 1.48 2.87 2.47 2.92 2.58 2.50 2.48−2.50

IP 6.92 7.82 7.21 7.52 7.67 7.5 7.27

EA 5.44 4.95 4.74 4.60 5.09 5.00 4.79

εSHE v 1.96 2.86 2.25 2.56 2.71 2.50 2.40

εSHE c 0.48 −0.01 −0.22 −0.36 0.13 0.00 −0.10

MAE 0.52 0.37 0.10 0.22 0.31 0.16

We next analyze the effect of the pH on the alignment of redox levels at the BiVO4 (010)water interface by combining the calculated band alignment with the acid-base chemistry of the BiVO4 (010) surface. We consider the first step of the water oxidation reaction, which generally represents the limiting step of the process, due to its high overpotential. This reaction occurs through the dehydrogenation of H2 O and the oxidation of OH− in acidic and alkaline conditions, respectively. 7 While the redox level of the former shows a Nernstian dependence on the pH of the system, that of the latter does not, as no proton transfer is implied in the reaction. The preference of one mechanism over the other for heterogeneous water-splitting depends upon the pH-dependent composition of the semiconductor-water interface. In turn, this is determined by the acidity of the surface sites. 29,37 It has been demonstrated that, when water molecules are adsorbed on surface Bi sites at the BiVO4 (010)10


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ACS Energy Letters

water interface, their acidity is noticeably enhanced as the respective pKa is reduced from 15.74 of the bulk liquid to 8.46. 29 Therefore, for the BiVO4 (010)-water interface we can distinguish three regions of pH: (i) pH9.46, where the adsorption of hydroxyl ions prevails at the surface, thus favouring the kinetically more favourable mechanism occurring under alkaline conditions; 7 (iii) 7.46

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