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Computational Screening of 2D Materials for Photocatalysis Arunima K. Singh, Kiran Mathew, Houlong L. Zhuang, and Richard G Hennig J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/jz502646d • Publication Date (Web): 26 Feb 2015 Downloaded from http://pubs.acs.org on March 4, 2015

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tion and screening of novel 2D materials for photocatalytic applications can help accelerate the scientific discovery and technological advancement of materials design for photocatalysis. This article emphasizes the role computational approaches play in the discovery of 2D materials and the screening for potential 2D photocatalyst to assist experimental efforts. We first outline the desirable properties for a 2D material to be an efficient photocatalyst for water splitting and suggest strategies for enhancement of their photocatalytic activity. We then discuss how densityfunctional calculations can establish their thermodynamic and mechanical stability, determine their electronic properties, e.g. band gap, band edge positions, and optical absorbance, and finally estimate their solubility in aqueous solution. To enhance the photocatalytic activity, we show how mechanical strain, pH, doping, and applied electrical potential can be used to tune the relevant electronic properties of these materials. Finally, we provide an outlook and discuss possible future work for asserting and optimizing the photocatalytic activity of 2D materials. Photocatalytic Water Splitting. One of the key properties for photocatalytic water splitting is the electronic structure of the photocatalyst, which controls the first steps of photocatalytic water splitting. Incident light of sufficient energy excites an electron across the optical band gap of the semiconducting photocatalysts and generates an electron-hole pair. This exciton then needs to diffuse to the solid/water interface and dissociate into an unbound electron and hole. The excited electron then drives the hydrogen reduction reaction generating hydrogen, 2H+ + 2e− → H2 , and the hole participates in the oxidation reaction to generate oxygen, H2 O + 2h+ → 21 O2 + 2H+ . Required Properties of a Photocatalyst. For a 2D semiconductor to facilitate photocatalytic water-splitting, at least four conditions must be satisfied:

exceed the free energy of water splitting of 1.23 eV and be smaller than about 3 eV to enhance solar absorption. 16 3. Band edges must straddle water redox potentials. The conduction band minimum (CBm) energy is higher than the reduction potential of H+ /H2 and the valence band maximum (VBM) energy is lower than the oxidation potential of O2 /H2 O, i.e., −4.44 and −5.67 eV, respectively. All band edge energies in this article are referenced with respect to the vacuum. 16 4. Insoluble in water. The 2D semiconductor must be insoluble in an aqueous solution. In principle any semiconductor that satisfies these intrinsic materials requirements should display some photocatalytic activity. However, there are several other criteria the material must fulfill to become an efficient and useful photocatalyst for practical applications: 5. Ability to utilize visible light. The material should capture a significant fraction of the visible spectrum as it accounts for more than 40% of the solar energy compared to the ultraviolet spectrum, which accounts for less than 5%. 36 6. Small exciton binding energy. A small exciton binding energy to facilitate the splitting of excitons into free charge carriers. 7. Low exciton recombination rate. Recombinations of the photo-generated electronshole pairs waste energy in the form of heat or light. 8. Low rate of backward reaction. The backward reaction of hydrogen and oxygen to produce water is an energetically favorable process that should be kinetically suppressed. Additionally, the reaction kinetics should be favorable for a fast forward reaction.

1. Low formation energy. A low formation energies relative to bulk material enables easy fabrication from their bulk counterparts as well as extraction of suspended singlelayer flakes.

9. Passivation of edges. The edges of the material must be passivated to minimize reaction with ions in the solution.

2. Sufficient band gap. The band gap must

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and B(g),

Hsolv (kJ/mol)

(a)

An Bm (s) ⇀ ↽ nA(g) + mB(g).

500 Hsolv (kJ/mol)

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400

The enthalpy change of reaction 4, i.e. the cohesive energy of the AB compound, ∆Ecoh , can be calculated efficiently using any solid state DFT code. In the subsequent second reaction,

(b) GaS GaSe

300

(4)

GaTe InS InSe

nA(g) + mB(g) ⇀ ↽ nAp+ (aq) + mBq− (aq), (5)

InTe

the gas atoms are ionized and solvated in water. To calculate the enthalpy of hydration, ∆Hhyd , for this reaction, the energy of the isolated atoms and of the hydrated ions can be efficiently computed using the quantum chemistry codes for molecular and atomic species such as Gaussian09. 79 Here it is important to converge the hydration energy with respect to the number of explicit water molecules used to augment an implicit solvation model for the description of solvation in water. 80 Furthermore, the charges of the dissolved species, p+ and q-, are given by the values that minimize the enthalpy of hydration, ∆Hhyd . In a similar manner, one can take into account the energy for ion association, i.e. a solvated cation-anion pair. A more rigorous treatment of solvation is possible by replacing the implicit solvation model 80,81 with ab-initio molecular dynamics simulations that can capture dynamic solvent effects. 82 Finally, the enthalpy of solvation, ∆Hsolv , is given by the sum of ∆Ecoh and ∆Hhyd . Using this approach, Zhuang et al. have shown that singlelayer GaS, GaSe, GaTe, InS, InSe, InTe, MoS2 , WS2 , PtS2 and PtSe2 are suitable for photocatalytic water splitting as they not only satisfy the band-gap energy and band-edge position requirements shown in Fig. 4(a) and (b), but are also insoluble in water as shown in Fig. 5. 39,41 Optical Absorption. The efficiency of photocatalytic water splitting materials is dependent on their ability to capture a significant fraction of sunlight. It is preferable to capture the visible part of the spectrum as it accounts for more than 40% of the solar energy; in comparison the ultra-violet part of the spectrum accounts for less than 5%. 36 The optical absorption function is given by the imaginary part of the dielectric function and can

200 100 0

Figure 5: Solvation enthalpy of single-layer metal chalcogenides and dichalcogenides in water. Predicted enthalpy of solvation, ∆Hsolv , (a) for transition metal dichalcogenides in comparison with HgS, adapted with permission from Ref. 41, copyright 2013 American Chemical Society, and (b) for the single-layer monochalcogenides, adapted with permission from Ref. 39, copyright 2013 American Chemical Society. The high solvation enthalpies indicate that the single-layer monochalcogenides are insoluble in water. cation of their solubility. When a solid compound AB(s) dissolves in water, the equilibrium concentrations of the dissolved ions is established by the solvation reaction An Bm (s) ⇀ ↽ nAp+ (aq) + mBq− (aq).

(3)

Here, Ap+ (aq) and Bq− (aq) represent A and B ions in an aqueous solution, respectively. Charge balance requires that np = mq. The solubility product, Ksp , of this solvation reaction is given by the Gibbs energy of solvation, ∆Gsolv , or the enthalpy of solvation, ∆Hsolv , if the entropy of solvation is assumed to be small. The enthalpy of solvation, ∆Hsolv , can be computed efficiently by decomposing the reaction 3 into two steps. First, the solid compound is separated into isolated atoms in the gas phase, A(g)


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mission spectroscopy. 86 Further, the second peak at 2.92 eV is due to another exciton, and finally, the third peak corresponds to the direct quasiparticle band gap of 3.16 eV obtained with the G0W0 method. The exciton binding energy of SnS2 is the energy difference between the first and third peak. The BSE value of 0.41 eV is close to the value for bulk SnS2 of 0.4 eV, 87 and also comparable to the exciton binding energy of single-layer MoS2 , 0.96 eV, 74 and WS2 , 0.6 eV. 73 Future Computational Screening. Modelling of exciton diffusion and recombination, kinetics of electron transfer reactions, charge trapping, and corrosion of 2D materials in electrolytes can be pursued in the future to understand the fundamental processes that control stability and efficiency of 2D photocatalyst and to identify better materials for photocatalysis. Exciton Dynamics and Electron Transfer Reactions. The theoretical description of photoinduced electron dynamics is a challenging task as it requires in principle the solution of the time-dependent Schrödinger equation for the many-body system, which has so far only been achieved for small molecules. 88,89 Nonetheless, this non-adiabatic problem can be investigated using a mean-field classical molecular dynamics approach, 90–92 using the so-called Ehrenfest dynamics 93–96 for the nuclei, which is self-consistently coupled with time-dependent DFT for the description of the electronic degrees of freedom. Such an approach has been employed previously to study electron transfer, relaxation dynamics, multiple exciton generation, electron-phonon coupling, wet electron systems, etc. For a detailed description of this approach, a discussion of its capabilities and limitations and of various applications, see Refs. 90–93,97,98 and references within. For solar energy conversion applications, such a technique allows to identify relaxation times as a means to find materials which increase electron-hole recombination times. Such a modeling is feasible and should be performed for 2D materials to study the effect of dimensionality on exciton dynamics. However, the high computational expense of this approach makes it currently impractical for high-throughput screening of materials. Corrosion and Pourbaix Diagrams. The immersion of 2D materials in an aqueous solution

1

BSE RPA

15 0.5

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2.5

3

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3

Energy (eV)

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Figure 6: Imaginary part of the permittivity of single-layer SnS2 calculated with the BSE and RPA scheme. The inset shows a closeup of the first three BSE peaks. To compensate for the band-gap underestimation using the PBE functional in the RPA calculation, we shift the spectra by 1.0 eV, which is the difference between the HSE06 and PBE band gaps. Reprinted figure with permission from Ref. 42. Copyright 2013 by the American Physical Society. be computed using DFT or the GW approximation. However, to obtain an accurate dielectric function and optical absorption spectrum, one has to include excitonic effects and solve the BSE. As input to the BSE, the quasi-particle energies are usually obtained from GW calculations and the wave functions from standard DFT. 83,84 A large optical absorption for a candidate 2D material indicates that it could exhibit a high efficiency for photocatalytic water splitting. The optical absorption spectrum of 2D materials, such as SnS2 42 and MoS2 , 73,85 are dominated by excitonic states which are well described by the BSE. The BSE spectrum provides a good approximation for the exciton energies and the optical band gap of 2D materials. For example, Fig. 6 shows the imaginary part of the permittivity for SnS2 calculated from the BSE and the random phase approximation (RPA), respectively. In contrast with the RPA, which lacks a description of electron-hole pairs, three absorption peaks are observed in the low-energy region below 3.2 eV of the BSE spectrum. The first peak at an energy of 2.75 eV corresponds to the direct optical band gap of SnS2 and agrees well with the experimental optical gap of 2.55 eV measured by UV-visible trans-


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ity, combinations of simplified interaction models, e.g. electrostatic or empirical energy models, 105,106 and structure search algorithms, e.g. genetic algorithms, particle-swarm optimization, minima-hopping, etc., 107–110 have the potential to quickly screen configurations and identify lowenergy candidates. Furthermore, kinetic effects that are not accounted for in Pourbaix diagrams can in practice prevent certain reactions and stabilize species that are shown as unstable. The reaction overpotential, the additional potential above the equilibrium potential required for a reaction to occur, depends significantly on the choice of the solvent and its composition. 111 Photo-generated holes and electrons on the surfaces could also induce formation of reactive intermediates on the surface. The stability of such species and the amount of photocurrent generated depend on the type and the quantity of chemical species present in the solution that could react with the reactive species on the surface. 112 To determine what species are present in the solution and to understand how local variations of the interface potential affect the presence of a particular species, it is important to consider the interactions between the interface and the solution and its constituents simultaneously. Implicit solvation models can provide an efficient description of the effects of solvent on surfaces, adsorption energies, and reaction energy barriers. A firstprinciples computational treatment of the effect of photo-generated holes and electrons on the stability of adsorbed species and reactions on surfaces requires the study of charged systems in the presence of solvents. Study of charged 2D slabs is problematic in a typical DFT framework due to the usage of periodic boundary conditions and the lack of a proper electrostatic reference potential in such a periodic array of charges. 113,114 One way to address the problem is to couple the DFT calculations to an implicit solvation model that is based on the Poisson-Boltzmann equation. The solution of the Poisson-Boltzmann equation provide a unique reference for the electrostatic potential even in charged systems due to the shielding provided by the ions in the solution. 115 Though it is an implicit approach to treat the solution effects, most of the surface chemistry can be captured by

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introducing one or two layers of explicit solvent molecules and adsorbants on the surface and filling the rest with the implicit solvent. In general, a comprehensive and realistic treatment of complex interface phenomena that occur in 2D photocatalytic systems requires that configurational, kinetic, and environmental effects are properly accounted for. To that end it is important to extend computational methods for structure prediction 107–110 to 2D materials, surfaces, and adsorbates and to complement the computational schemes with the emerging efficient techniques to describe solvation effects. 81,116,117 Enhancement of Photocatalytic activity. Engineering of the band gap, band edges, and optical spectra of materials has been demonstrated by application of external sources such as mechanical strain, application of chemical and electrical bias and doping. 39,41,118 Computational tools such as DFT and GW calculations can efficiently identify which of these strategies best tune the band gap, band edges and absorbency of a promising 2D materials for photocatalysis. Strain. One of the methods of adjusting the band gap and band-edge positions of a semiconductor is the application of mechanical strain. Figure 8 shows that application of 5% compressive strain to single-layer α -TiNBr shifts the CBm above the H+ /H2 energy rendering it useful in spontaneous photocatalytic water splitting. Surprisingly, the majority of 2D materials has significantly softer elastic constants in comparison to their bulk 3D counterpart which assists application of strains without inducing breakage of materials. 53 Notably, small strains can shift band edge positions and band gaps by significant amount. 38,39,42 Experimentally controlled tensile and compressive uniaxial strains of up to 2.2 % have been imparted to single-layer or few-layer flakes of graphene and MoS2 by bending of flakes deposited (or suspended) on flexible substrates. 119–122 Recently, Shioya et al. 123 demonstrated that two different techniques, recrystallization of metal contacts and condensation polymerization of organic films, can be used to impart biaxial and in-plane isotropic compressive strains to graphene in a controlled manner. Neither of these techniques require bending of substrates and can be applied to other two-dimensional materials to achieve controlled


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The use of chemical additives is another promising approach to tune the band-edge positions of 2D materials at a fixed electrolyte pH. Adsorbed species affect the electronic structure of the surface, e.g. band edges, band gap, density of states, etc. For instance, chemical functionalization of GaAs with positively charged porphyrins leads to a shift in GaAs band-edge positions. 126 Moreover, chemical additives can potentially enhance the photocatalytic activity of semiconductor photocatalysts by inhibiting charge recombinations, by improving the photoresponse to visible light through formation of impurity energy levels, and by suppression of backward reactions. 16 Reference 16 elaborates the detailed mechanism, advantages and limitations of using chemical additives for enhancing the photocatalytic activity of TiO2 . Electrical Bias. Misaligned band edges (where one or both of the band edges do not straddle the redox potentials of water) necessitate an external applied bias. While biasing works well, it can have many drawbacks. For instance, an electrical bias potential decreases the efficiency for water splitting. 4 If a part of the output of water splitting is assumed to provide energy to an external power source for electrical biasing, the water splitting efficiency, η , of the photocatalyst can be defined as,

Figure 8: Band edge positions of single-layer α TiNBr at strains of 0% and 5%, as well as pure and 12.5% Ti-doped single-layer α -MNI (M = Zr, Hf). The energy scale is indicated by the vacuum level (left Y-axis) in electron volts as a reference. The CBm (blue color) and VBM (red color) are presented along with the potentials in electron volts. The redox potentials (magenta dashed line) of water splitting are shown for comparison. Adapted from Ref. 118 with permission from The Royal Society of Chemistry. strains of as much as 10%. Under experimental conditions the presence of unintended strains, impurities, and defects can cause similar effects and thus it is advisable to investigate photocatalytic activity for a range of bias voltages. Chemical Bias. Modifications of the electrolyte such as changing the pH can tune the reduction and oxidation potentials of water. This is known as chemical biasing. 22,124 Each unit of pH difference between two electrolytes provides a chemical bias of the water redox potentials of 59 meV; 125 the pH dependent reduction potential of water is EHred+ /H2 = −4.44eV + pH · 0.059 eV and the ox-

η=

j (1.23V −Vbias ) Plight

(6)

where Vbias is the applied bias potential, j the measured current density, Plight the power density from the light source, and 1.23 V is the free energy of water splitting. This shows that the bias potential must be significantly smaller than 1.23 V in order for the photocatalysts to exhibit a significant positive energy output. Single-layer SnS2 is an example for a 2D material requiring a bias potential. Photocatalytic water splitting was achieved for this material in a 0.5 M Na2 SO4 electrolyte (equivalent to pH = 6.6 ) at an applied bias of −1 V. 30 In agreement, HSE06 calculations show that indeed while the VBM energy, −7.42 eV, of SnS2 is well below that of the oxidation potential of water, EOoxd = −5.28 2 /H2 O,pH=6.6 eV; the CBm energy, −4.90 eV, of SnS2 is below that reduction potential of water, EHred2 +/H ,pH=6.6 =

idation potential is EOoxd = −5.67eV + pH · 2 /H2 O 0.059 eV. Adjusting the pH of the solution can tune the alignment of the energy levels between the 2D material and the solvent to optimize the system for photocatalysis. For example, increasing the pH shifts both energy levels of H+ /H2 and O2 /H2 O potentials upward, as illustrated in Fig. 4(b), making MoSe2 and WSe2 possible photocatalysts. However care must be taken before exploring this avenue because the hydroxyl groups attached on the semiconductor surface can lead to the modification of their band edges and band gaps counteracting the increase of the voltage with pH. 4

2

−4.05 eV. 42 In agreement with experimental re-


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sults, an additional bias potential of 0.9 V is required to shift the CBm above the reduction potential of water, thus making it photocatalytically active for water splitting. Predicted 2D Photocatalysts. Based on computational studies investigating the band gap and band edge criterion, scores of 2D materials have been predicted to be capable of spontaneous water splitting. Figure 4 illustrates the band edge alignment for several families of 2D materials. Figure 4(a) shows the prediction by Zhuang et al. that the single layer group-III monochalcogenides, GaS, GaSe, GaTe, InS, InSe and InTe are suitable candidates for spontaneous photocatalytic water splitting. 118 Another class of 2D materials that has received a lot of attention for its potential in photocatalysis are the transition-metal dichalcogenides. 40,41,127–131 Figure 4(b), illustrates that the band edge positions of the single-layer transitionmetal dichalcogenides CrS2 , MoS2 , WS2 , PtS2 , and PtSe2 make them suitable for photocatalytic splitting of water. 40,41 Further, studies on the electronic structure of vacancies and edges of MoS2 show that these defects can provide catalytically active sites. 128–130 Recently, Liu et al. predicted that singlelayer metal-phosphorous-trichalcogenides, MPX3 (M=Zn, Mg, Ag0.5 Sc0.5 , Ag0.5 In0.5 and X=S, Se) exhibit the intrinsic electronic properties suitable for spontaneous photocatalytic water splitting, see Fig. 4(c). 63 Single layer α -MNX (M=Zr,Hf; X=Cl,Br,I) and β -MNX (M=Zr,Hf; X=Cl, Br) have been shown to be yet another class of 2D materials suitable for photocatalytic water splitting. 118 Furthermore, single-layer bismuth oxyhalides including BiOCl, BiOBr, and BiOI are suggested to exhibit photocatalytic activity for water splitting. 132 Another 2D material, 2D oxosulphide, (N2 H4 )2 Mn3 Sb4 S8 (µ3 -OH)2 , is predicted to result in continuous hydrogen evolution under visiblelight irradiation. 133 Also, CdS nanosheets with thickness of about 4 nm exhibit efficient photocatalytic activity with hydrogen production rate of 41.4 mmol h−1 g−1 , about 6 times higher than CdS nanosheet based aggregates. However, they have a small IPCE of 1.38% which was improved to 9.62% by loading with PdS. 34

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Finally, the 2D group-IV monochalcogenides, MX (M=Ge, Sn, Pb; X= O, S, Se, Te), have been predicted to be suitable for photocatalytic water splitting but require a bias potential. 43 In agreement with these results, Liang et al. have experimentally demonstrated that seven atomic layer thick SnO sheets display photocatalytic water splitting under bias potentials of −0.2 to −1 V. 35 In their work they also elucidate the effect of layer thickness on the IPCE where seven atomic layer, 12 atomic layer and bulk SnO sheets displayed IPCE of 20.1%, 10.7% and 4.2%, respectively. Summary and Future Outlook. We described a computational strategy to predict and explore 2D materials for photocatalytic water splitting. We suggest possible techniques for their catalytic activity enhancement. The high-throughput computational screening of materials is powerful tool to rapidly predict promising candidates and eliminate unlikely materials candidates, allowing for more efficient use of experimental resources and accelerating possible applications of 2D photocatalysts. Current ab-inito methods, such as density-functional theory and the GW approximation, combine the accuracy to reduce false positive and negatives with the speed required for a highthroughput approach. This strategy can be applied to many more 2D materials and a repository or database from these predictions will accelerate the innovation of photocatalytic water splitting materials. We see the future challenges for the computational screening of materials for photocatalytic applications mostly in the area of the description of solvation and kinetics. The active development of implicit solvation models and their implementation into widely used software packages is expected to lead to an efficient description of the effect of the electrolyte on electronic properties and stability, including corrosion. A challenge for solvation models and computational studies of corrosion is to overcome the complexity of the interaction and chemical reactions between solvated species and the 2D materials. With regards to kinetics, computational methods that describe nonadiabatic dynamics and can assess the rate of electron transfer reactions and exciton dynamics are still being developed and not yet routinely applied or available in community codes. The enormous


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progress in the fields of 2D materials and computational methods suggests that many of those challenges will be tackled in the near future.

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Biographies Arunima K. Singh is a post-doctoral researcher at the National Institute of Standards and Technology. She received her Ph.D. in Materials Science and Engineering in 2014 from Cornell University under the supervision of Richard G. Hennig. Her research focuses on accelerating 2D materials discovery, synthesis and application using first principles computation. Kiran Mathew is Ph.D. student at Cornell University. His research focuses on multiscale modelling and the development of solvation models. Houlong L. Zhuang is a post-doctoral researcher at Oak Ridge National Laboratory. He received his Ph.D. in Materials Science and Engineering in 2014 from Cornell University under the supervision of Richard G. Hennig. His research focuses on computational discovery and design of novel 2D materials for energy applications. Richard G. Hennig received his Diploma in Physics at the University of GÃ˝uttingen in 1997 and his Ph.D. in Physics from Washington University in St. Louis in 2000. After working as a postdoctoral researcher and research scientist at Ohio State University, he joined the faculty of the Department of Materials Science and Engineering at Cornell in 2006 as an Assistant Professor. In 2014 he moved to the University of Florida as an Associate Pro-fessor.

(4) Walter, M. G.; Warren, E. L.; McKone, J. R.; Boettcher, S. W.; Mi, Q.; Santori, E. A.; Lewis, N. S. Solar Water Splitting Cells. Chem. Rev. 2010, 110, 6446– 6473. (5) Chen, X.; Shen, S.; Guo, L.; Mao, S. S. Semiconductor-Based Photocatalytic Hydrogen Generation. Chem. Rev. 2010, 110, 6503–6570. (6) Katz, J. E.; Gingrich, T. R.; Santori, E. A.; Lewis, N. S. Combinatorial Synthesis and High-Throughput Photopotential and Photocurrent Screening of Mixed-Metal Oxides for Photoelectrochemical Water Splitting. Energy Environ. Sci. 2009, 2, 103–112. (7) Cui, Z.; Zeng, D.; Tang, T.; Liu, J.; Xie, C. Processing-Structure-Property Relationships of Bi2 WO6 Nanostructures As Visible-Light-Driven Photocatalyst. J. Hazard. Mater. 2010, 183, 211–217. (8) Maschmeyer, T.; Che, M. Catalytic Aspects of Light-Induced Hydrogen Generation in Water with TiO2 and Other Photocatalysts: A Simple and Practical Way Towards a Normalization. Angew. Chem. Int. Ed. 2010, 49, 1536–1539.

Acknowledgement This work was supported by the NSF through the Cornell Center for Materials Research under Award No. DMR-1120296 and the CAREER award No. DMR-1056587. This research used computational resources of the Texas Advanced Computing Center under Contract No. TG-DMR050028N.

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