Two-Dimensional Hexagonal Sheet of TiO2

Hossein Asnaashari Eivari,†,‡ S. Alireza Ghasemi,*,† Hossein Tahmasbi,† Samare Rostami,†

Somayeh Faraji,† Robabe Rasoulkhani,† Stefan Goedecker,§ and Maximilian Amsler*,⊥,¶

†Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan 45137-66731, Iran‡University of Zabol, P.O. Box 98615-538, Zabol 98613-35856, Iran§Department of Physics, Universitat Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland⊥Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States

ABSTRACT: We report the ab initio discovery of a novelputative ground state for quasi two-dimensional TiO2 througha structural search using the minima hopping method with anartificial neural network potential. The structure is based on ahoneycomb lattice and is energetically lower than theexperimentally reported lepidocrocite sheet by 7 meV/atomand merely 13 meV/atom higher in energy than the rutile bulkstructure. According to our calculations, the hexagonal sheet isstable against mechanical stress, chemically inert, and can bedeposited on various substrates without disrupting thestructure. Its properties differ significantly from all knownTiO2 bulk phases with a large gap of 5.05 eV that can be tunedthrough strain and defect engineering.

■ INTRODUCTION

Low-dimensional materials have attracted significant interest inthe recent years, especially since the discovery of graphene in2004 through its exfoliation from graphite.1 Due to itsextraordinary properties, ranging from high mechanicalstrength2 and the presence of massless Dirac fermions3 toexcellent thermal conductivity,4 many other two-dimensional(2D) materials have been considered and isolated for potentialapplications in electronics and energy conversion.5 Buckledgraphene analogues such as silicene6−8 have been grown onsilver substrates,9 and germanene6 was synthesized on gold.10

Similarly, the theoretically predicted boron counterpart11−14

with a partially filled honeycomb lattice was recently realized onsilver substrates15−17 and confirmed to exhibit Diracfermions.18 This class of materials, however, lacks a finiteband gap, rendering them unsuitable for transistor electronics.On the other hand, promising 2D semiconductors have been

investigated for potential applications in nanoelectronics,optoelectronics, and photonics.19−23 Besides the wide bandgap h-BN monolayer,4,24 transition-metal dichalcogenides(TMD)4,24 have been intensely studied, which exhibit gapsthat can be readily tuned based on the number of stackedmonolayers4 and electronic properties that can be fundamen-tally modified through in-plane25−29 and vertical heterostructur-ing.29−33 More recently, layered metal oxides have emerged as anew family of 2D materials which exhibit an overall higherstability in air compared to that of TMDs.34 Besidesmonolayers of MoO3,

35 WO3,36 SnO,37 and perovskite type

oxides,5 TiO2 is considered one of the most promisingcandidates. As an important multifunctional oxide widely

used in industrial products ranging from consumer goods toadvanced materials for photovoltaic cells,38 sensors,39 hydrogenstorage,40 and rechargeable lithium-ion batteries,41−44 titania-based materials have also drawn the focus of research fornanoelectrics due to their structure dependent, high dielectricconstant.45 TiO2 nanosheets and nanostructures are touted topossess enhanced photocatalytic, photovoltaic, electrochemical,and dielectric properties,46−49 and great efforts have been madeto improve their performance by fabricating controlled sizeand/or shape at the nanoscale.40,50

Despite these efforts, the atomistic structures in the majorityof studies on 2D TiO2 remain unclear, and its ground statestructure is not fully resolved. Only a few studies explicitlyinvestigate the microscopic structure of TiO2 nanosheets,

51−53

and almost all theoretical studies are based on slabs cut out ofbulk phases along different crystallographic planes. Theseinclude anatase (001)53,54 and (101);51,52,55 fluorite (111);50,51

rutile (011),50 (110),50,51,56 and (100);54 and TiO2(B) (001).57

The only fully reconstructed, truly 2D material of TiO2 knownto date is the lepidocrocite-type nanosheet (LNS),48,51,54,57

which was also found to exhibit the lowest formation energyamong all sheets reported so far in the literature. Using densityfunctional theory (DFT) calculations, Orzali et al.58 showedthat the LNS can be readily obtained from a slab of anatase(001) with six atomic layers by a simple structural rearrange-ment.

Received: May 17, 2017Revised: August 1, 2017Published: August 2, 2017

Article

pubs.acs.org/cm

© 2017 American Chemical Society 8594 DOI: 10.1021/acs.chemmater.7b02031Chem. Mater. 2017, 29, 8594−8603

Cite This: Chem. Mater. 2017, 29, 8594-8603

While the practice of using bulk-like structures as a startingpoint for theoretical investigations is understandable, it is basedon the assumption that atomically thin layers of TiO2 will adopta structure close to the crystalline phase. However, physicalepitaxy experiments have shown that many 2D materials oftenexhibit structural motifs that strongly differ from any bulkpolymorphs.17,59 To address this issue, we performed anextensive global search specifically aimed at screening 2Dstructures of TiO2 and report the discovery of a new groundstate with hexagonal symmetry. According to our calculations,this material is chemically and mechanically stable, and itselectronic structure can be modified by strain and defectengineering, leading to a tunable band gap covering a wideenergy range.

■ METHODSThe structural search was conducted with the minima hopping method(MHM),60,61 which implements an efficient algorithm to explore theenergy landscape of a system by performing consecutive moleculardynamics (MD) escape steps followed by local geometry relaxa-tions.62−65 The Bell−Evans−Polanyi principle is exploited toaccelerate the search by aligning the initial MD velocities preferablyalong soft mode directions.66 To perform predictions for quasi-2Dmaterials, the functionality of the MHM was modified to model 2Dand layered materials. For this purpose, the target function to beoptimized was extended by including 2D confining potentials Ci(ei, rj

α),where α denotes the axis α = {x,y,z} along the nonperiodic direction, rjare the Cartesian coordinates of the N atoms in the system, and ei arethe equilibrium positions along α at which the potentials are centered.Our confinement functions are sums of atomic contributions and arezero within a cutoff region rc around ei, while it has a polynomial formof order n with amplitude Ai beyond rc: Ci

α = ∑j = 1N c(ei, rj

α), where c(ei,rjα) = Ai(|ei − rj

α| − rc)n for |ei − rj

α| ≥ rc and zero otherwise. During the

MD escape trials, the additional forces acting on the atoms = − ∂∂f jCr

i

j

and on the cell vectors σ = − ∂∂j

Ch

i

jwere fully taken into account, where

the atomic positions are expressed in the reduced coordinates ri = hsi,and h = (a, b, c) is the matrix containing the lattice vectors. For ourcalculations, a single confinement potential C1 was used with e1centered along the lattice vector c with a cutoff rc = 1 Å, n = 4 andA1 = 0.1 eV. Multiple MHM structure prediction runs were performed,starting from a variety of random initial seeds using 2−10 formulaunits (fu)/cell in conjunction with the charge equilibrated neuralnetwork technique (CENT) potential.

To accelerate the structural search, we prescreened the energylandscape using a recently developed high dimensional artificial neuralnetwork (ANN) potential based on CENT,67 specifically fit to theTiO2 system. To train the CENT potential, we first prepared adatabase containing the DFT energies of about 3000 cluster structures,with sizes ranging from 6 to 70 fu. An approximate potential wasobtained by fitting CENT to DFT data of randomly generatedstructures in an initial step. Subsequently, further structures wereadded to the training set by performing short MHM simulations withthe approximate potential. The resulting low energy structures fromthese MHM runs were carefully filtered to avoid duplicate structuresand to ensure a large diversity in structural motifs within theaugmented data set, a task performed by comparing structures with astructural fingerprint.68,69 This procedure was repeated several timesuntil a desired accuracy was reached for a predefined validation dataset. Even though the CENT potential was generated from clusterstructures, it provides accurate results for periodic systems. This hightransferability of CENT was recently demonstrated for CaF2 andZnO.70,71

The DFT calculations to generate the training data and to refine theresults from the MHM simulations were carried out with the FHI-aimscode72 using the tier 2 basis set for both the Ti and O elements. Thegeneralized gradient approximation parametrized according toPerdew−Burke−Ernzerhof (PBE)73 was employed for the exchange-correlation functional. Geometry relaxations were performed until theatomic forces were less than 0.01 eV/Å, and Monkhorst−Pack k-pointgrids with a density of 0.03/Å were used, resulting in total energiesconverged to within 1 meV/atom. For all calculations involving 2Dstructures, a vacuum space of about 12 Å was used in the directionperpendicular to the sheets to suppress the interaction betweenperiodic images of the layers.

The chemical bonding was studied by analyzing the crystal orbitalHamilton population (COHP) as implemented in the LOBSTERpackage74−77 based on the wave functions computed with the ViennaAb Initio Simulation package (VASP).78 Supercells with 48 atomswere used together with a plane wave cutoff energy of 450 eV and k-point grids with a density of 0.03/Å. Phonon calculations were carriedwith the finite difference approach as implemented in the PHONOPYcode,79 using atomic displacements of 0.01 Å. The dielectric tensorand the born effective charges were computed with VASP. Largesupercells containing 192 atoms were used to ensure sufficientconvergence of the force constants.

■ RESULTS AND DISCUSSION

We performed a global search for 2D TiO2 materials using theconstrained MHM algorithm60,61 together with the recentlydeveloped CENT ANN potential.67 A plethora of structures

Figure 1. (a) A single layer of the HNS from a perspective view. (b) Projected views along the c direction and along the ab plane, where the Ti−Obonds are represented by gray polyhedra. The green (large) and red (small) spheres represent the Ti and O atoms, respectively.

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was recovered, including the majority of the previously reportedsheets discussed in the literature, indicating that the structuralsearch was sufficiently converged. The most promisingcandidate structures were subsequently refined at the DFTlevel. We discovered a novel nanosheet with hexagonalsymmetry to have the lowest energy, hereafter referred to ashexagonal nanosheet (HNS), shown in panel a of Figure 1. Inparticular, the HNS is energetically favorable compared to theLNS, which had been considered to be the most stable 2Dstructure of TiO2 to date. From the structural point of view, theunit cell of the HNS is composed of fourfold coordinated Tiand twofold coordinated O atoms, arranged in a lattice withP6/mmm symmetry (see Table 1 for the lattice vectors and

atomic coordinates). The HNS is isostructural to a previouslyreported silicon dioxide sheet grown on a Ru surface.80 TheTiO4 units form tetrahedra in two layers, which are stacked ontop of each other and linked by shared corners, as illustrated inthe side view in panel b of Figure 1. Large, hexagonal pores areformed along the out-of-plane axis and arranged in ahoneycomb lattice, as shown from the top view in panel b ofFigure 1. In strong contrast to the HNS, the LNS has a muchdenser structure, where each Ti atom is sixfold and the O atomsare twofold or fourfold coordinated, respectively. The edge-sharing octahedra are arranged in an orthorhombic lattice,forming a sheet which is 0.4 Å thinner than the HNS. Similar tothe HNS, many other 2D materials have a hexagonal lattice: thelarge lattice constant of 6.03 Å in the HNS compares forexample with values of 2.46 Å in graphene,81 3.90 Å in silicene8

and 3.15 Å in MoS2,82 potentially allowing the construction of

various (commensurate) 2D heterostructured materials withimproved properties.Due to the unique hexagonal nanopores in the HNS, we

expect it to have a very low atomic density compared to othersheets. To quantify the density, we considered as the volumethe product of the thickness h of each sheet and the area A ofthe unit cell along the two periodic directions, where h is givenby the distance between the two outmost atoms (column 4 inTable 2). Furthermore, we analyzed the bond lengths in all 2Dstructures and crystalline polymorphs by comparing theminimum and maximum bonds in each system (columns 5and 6 in Table 2). In general, small maximum bond lengthindicate strong and stiff bonds between Ti and O atoms. It issomewhat surprising that, although the HNS exhibits theshortest maximum bond lengths, its pseudodensity is the lowestamong all sheets with a value of only 3.536 g/cm3, 16% lowerthan any other sheet, indicating that the nanopores arestabilized through strong interatomic bonds. Furthermore, wealso quantified the roughness of the surface in terms of theamount of buckling in the outermost atomic layers (SB),essentially corresponding to the out-of-plane distance of thetwo outmost Ti and O atoms (column 3 in Table 2).

From the energetic point of view, we consider the formationenergies per atom as a measure of (meta)stability and comparethem to the LNS and other configurations that have beenreported in the literature (column 2 in Table 2). The energydifferences per atom ΔE were computed with respect to theanatase TiO2 phase. All structures that were directly cut frombulk have ΔE significantly higher than the HNS, at least for theslab thicknesses that we considered in our study. In fact, theHNS is only 45 and 13 meV/atom higher in energy than bulkanatase and rutile, respectively. Note that experimental heatcapacity measurements show that rutile is the thermodynamicground state at least up to 1300 K,83 but semilocal and hybridDFT calculations predict a reversed energetic ordering,84−88

possibly due to the failure to correctly capture high-ordercorrelation effects.89 Most importantly, however, the HNS is 7meV/atom lower in energy than the LNS, rendering it the moststable nanosheet among all known quasi-2D nanostructures. Acomparative summary of the quantities discussed above is listedin Table 2, showing that the HNS simultaneously has thelowest density and formation energy ΔE with respect to bulkanatase.We further studied the electronic properties of the new HNS

using hybrid functionals due to the well-known severeunderestimation of the band gaps of semilocal DFT. TheHSE0693 and PBE094 functionals were employed to assess theiraccuracy by computing the band gaps of the experimentallywell-studied rutile and anatase phases. The values for HSE06with gaps of 3.40 and 3.58 eV for rutile and anatase,respectively, are closer to the experimental values (3.0 and3.2 eV90) than PBE0, which significantly overestimates the gapwith 4.16 and 4.32 eV for rutile and anatase, respectively.Hence, all subsequent electronic structure calculations wereperformed with HSE06, and the band gaps for the structuresconsidered in this work are compiled in Table 2.

Table 1. Structural Parameters of the HNS with the WyckoffPositions of Ti and Oa

x y z

Ti 4h 1/3 2/3 1.82O1 6i 1/2 0/0 2.36O2 2d 1/3 2/3 0.00

aThe values of x and y are given in reduced coordinates, whereas z isgiven in Cartesian coordinates in units of Å. The equilibrium latticeparameter is a = 6.03 Å.

Table 2. PBE Formation Energy with Respect to Anatase(ΔE) in meV/atom, Surface Buckling (SB) in Å, Pseudo-Density in g/cm3, Maximum Ti−O Bond Length (dmax) andMinimum Ti−O Bond Length (dmin) in Å, and HSE06 LevelBand-Gap Energy (Eg) in eVa

structure ΔE SB den. dmin dmax Eg Nlayer

rutile(100) 158 >1.06 4.199 1.83 2.09 4.84 6flourite(111) 137 >1.30 5.967 1.85 2.07 4.54 3anatase(101) 120 >1.10 5.967 1.78 2.10 4.87 6rutile(110) 83 >1.06 4.597 1.78 2.14 3.95 6TiO2(B)(001) 60 0.67 4.951 1.81 2.07 4.16 7LNS 52 1.03 5.481 1.83 1.97 4.65 6HNS 45 0.54 3.536 1.82 1.82 5.05rutile 32 4.127* 1.99 2.00 3.40anatase 0 3.765* 1.94 2.00 3.58aFor structures cut from bulk material, the last column indicates thenumber of atomic layers they contain as a measure of the initial slabthickness (Nlayer). Lattice parameters of rutile and anatase phases inour calculations are a = 4.65 Å and c = 2.97 Å for rutile and a = 3.80 Åand c = 9.70 Å for anatase. These values compare well withexperimental data, i.e. a = 4.59 Å and c = 2.95 Å for rutile90 and a =3.78 Å and c = 9.50 Å for anatase.90 The calculated lattice parametersof the LNS (a = 3.02 Å, b = 3.74 Å) are in good agreement with thetheoretical values of Sato et al.91 and close to the experimental valuesof Orzali et al.58, whereas the formation energies are in excellentagreement with the PBE values of Forrer et al. (56 meV/atom)92 (*represents bulk densities).

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The band structures of the pristine HNS and LNS are shownin Figure 2, revealing that the LNS has a direct band gap, incontrast to the HNS. However, the valence band of the HNSexhibits very little dispersion, leading to a quasi-direct gap at theK-point with a value of 5.17 eV. The partial DOS of the HNS,shown in the top panel of Figure 3, indicates that the maincontribution to the valence band stems from oxygen p-states,while empty d-states of the Ti atoms contribute mainly to the

conduction bands. The magnitude of the HNS gap is largerthan any other TiO2 polymorph studied here and lies wellbeyond the range of visible light. Even the stacking of severalHNS sheets on top of each other does not change its electronicstructure, and in the limit of bulk HNS in a fully periodic cell,the band gap is only marginally reduced to 5.04 eV. However,there are various methods to tune band gaps which could beemployed in practice such as impurity doping, introducingvacancies, elemental substitution, and creating heterostructureswith other 2D building blocks.95−99 Because defects cansignificantly influence the gap energies, the effect of oxygenvacancies on the electronic band structure of an isolated HNSwas investigated. Monovacancies were created in a supercellcontaining 108 atoms by removing each of the two symmetri-cally distinct oxygen sites, 6i and 2d. We estimated theoxygen vacancy format ion energy accord ing to

= − + −E E E E(HNS O) (O ) (HNS)v12 2 , where the energy

of O2 was evaluated in vacuum (gas phase). Defect energies ofEv6i = 6.49 eV and Ev

2d = 6.32 eV were obtained with PBE, andEv6i = 7.35 eV and Ev

2d = 7.07 eV were obtained with HSE06.The resulting electronic PDOS for the two types of vacancies,depicted in the two bottom panels of Figure 3, show that thevacancies create an occupied valence state in the band gap ofthe pristine HNS which essentially reduces the energydifference between conduction and valence bands. The valuesof the gaps are thus 2.1 and 2.3 eV for the 6i and 2d vacancies,respectively.TiO2 is a promising material as a photocatalyst for water-

splitting and hydrogen production due to its high photo-catalytic activity but suffers from the consequences of a wideband gap which limits the absorbed light to the ultravioletportion of the solar spectrum.100 Although the band gap of thepristine HNS is even larger than that of other TiO2 phases, thereduced gap energies of the HNS with oxygen vacancies arewell-suited to absorb in the visible spectrum. In addition to thegaps, the relative positions of the band edges with respect theredox potentials of water splitting are crucial to allowphotoinduced electron transfers: the valence band maximum(VBM) needs to be below the oxidation potential of water,while the conduction band minimum (CBM) has to be abovethe reduction potential of H+ to produce H2.

99,101,102 Figure 4

Figure 2. (a) Electronic band structures of HNS (left) and LNS(right) along a path in the 2D Brillouin zone with the HSE06functional. The red and green arrows indicate the values of the directand indirect band gap, respectively. (b) Band gap energies for differentvalues of strain. The color coded arrows in the inset indicate thedirection of biaxial and uniaxial strain.

Figure 3. Electronic PDOS of the pristine HNS (top panel) and thesheet with oxygen vacancies (two bottom panels) at the HSE06 level.The VBM level of the HNS is shown by the gray vertical line. Theenergy scale of the two vacancy structures was shifted with respect tothe pristine HNS to show the relative alignment of the bands withrespect to the CBM. Hence, the occupied defect states lie in the gap ofthe pristine HNS.

Figure 4. Band edge alignment of the pristine anatase TiO2 phasetogether with the pristine and defect HNS with respect to the water-splitting reduction and oxidation potentials shown as dashed lines. Thepurple and blue regions denote the conduction and valence bands,respectively. The pink regions represent the defect states.

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shows the band alignment of pristine anatase TiO2 togetherwith the HNS without and with oxygen vacancies. The CBMposition of the anatase phase is aligned with respect to theexperimental values of the normal hydrogen electrode(NHE),103 and we used the gap energy to place the VBM.The band edges of the pristine and defect phases of the HNSare shifted such that the unperturbed Ti 1s core levels from ourall-electron calculations were correctly aligned among all TiO2polymorphs.A comparison of the band alignment between the anatase

TiO2 and the pristine HNS shows that the strong oxidationability is retained with a decrease of the VBM by 1.39 eV. Atthe same time, the CBM is shifted up by merely 0.08 eV, stillallowing the electron transfer to reduce H+. Inducing the 2dand 6i oxygen vacancies does not alter the positions of theCBM but only introduces the occupied defect states, shown bythe pink bars in Figure 4, which denote the correspondingVBM (see also Figure 3). Similar intermediate bands werereported to emerge within the band gap of Rh and F codopedanatase TiO2.

99 Because the VBM remain below the wateroxidation potential, we conclude that even the HNS withoxygen vacancies is thermodynamically suited for water redoxreactions. Together with the reduced band gap energy ofaround 2 eV to absorb in the optical range, the HNS could betuned through defect engineering to potentially outperformknown TiO2 polymorphs for photocatalytic water splittingapplications.Another pathway to modify gaps in 2D materials is strain

engineering.104 Because 2D sheets are the fundamental buildingblocks for layered heterostructures in functional materials, theyare often grown through chemical vapor deposition (CVD) andphysical epitaxy on a substrate or as mechanically assembledstacks.4,17,105 These approaches can lead to strain, and westudied its effect on the band gap at the HSE06 level byapplying three different kind of strains: biaxial strainsimultaneously along the two equivalent lattice vectors a andb , uniaxial strain along a only, and along + a b1

2. As shown in

panel b of Figure 2, the gap energies increase and decreaseupon compressive and tensile strain, respectively, and thechange only weakly depends on the direction of uniaxial strain.Although a biaxial tensile strain of 10% leads to a largereduction of the band gap by 20%, the gaps never reach therange of visible light. Nevertheless, growing the HNS on anappropriate substrate would enable a continuous tuning of thegap in a wide range.Large strains experienced, for example, during the lithiation

process in lithium-ion batteries or hydrogenation in hydrogenstorage applications can also compromise the mechanicalstability of a layered material. Therefore, all internal degrees offreedom were fully relaxed when applying strain. Although theatomic structure of the HNS remains intact even at +10%tensile strain, the outermost layers of O atoms start to buckle atcompressive strains below −8% for uniaxial and below −6% forbiaxial strain, and the hexagonal voids start to deform slightly.The dynamical stability of the HNS was assessed at itsequilibrium lattice parameters by computing the phonondispersion in the whole 2D Brillouin zone with the frozenphonon approach. The calculated phonon spectrum in Figure 5shows no imaginary modes, indicating that the HNS is indeed ametastable structure corresponding to a local minimum on theenergy landscape. Like other 2D materials, two acousticbranches are linear as q → 0. Because force constants related

to the transverse motion of the atoms decay rapidly, the lowestacoustic mode shows a quadratic behavior close to the Γ point.8

In fact, this quadratic dispersion is common to all layeredmaterials, as recently discussed in detail by Carrete et al.106

In addition to the mechanical properties, a high chemicalstability is essential for a 2D material to be viable in practicalapplications. We can deduce the first evidence of the highchemical stability of the HNS from its band gap energy, whichis the largest among all TiO2 polymorphs (Table 2). Next, weanalyzed the crystal orbital Hamilton population (COHP) andits integral (ICOHP) using the LOBSTER code.74−77 Negativeand positive values of the COHP correspond to bonding andantibonding states, respectively, while the ICOHP is consideredhere as a measure to compare bond strengths.76,107 The COHPbetween neighboring Ti and O atoms were calculated for theHNS, LNS, and the anatase (001) slab. No antibondinginteractions are present in the LNS and HNS for the occupiedstates. On the other hand, antibonding states exist for anatase(001) slightly below the Fermi level, indicating an electronicinstability. Indeed, the anatase (001) undergoes a structuraldistortion and transforms to the LNS sheet upon relaxationwith a very tight force convergence criterion, thereby alleviatingthis instability. Furthermore, a comparison of the −ICOHP atthe Fermi level between the HNS and LNS results in values of5.33 and 3.54 eV, respectively, indicating stronger Ti−O bondsin the HNS, further evidence for its superior chemical stability.Furthermore, we investigated the potential reactivity of the

HNS with the most common molecules in air such as N2, O2,CO2, and H2O. For this purpose, these molecules were placedat different sites of the sheet, and local geometry relaxationswere performed to check if chemical bonds would formbetween the sheet and the molecules. Four different sites wereinvestigated, as shown in Figure 6: on top of an O atom and Tiatom, in the center of the hexagon at the surface of the sheet,and within the void of the hexagons. To induce a chemicalreaction, the initial distance from the sheet was chosen to besmaller than the sum of the covalent radii rcov

s of the closest twoatoms of the adsorbate and the sheet whenever possible.However, all molecules placed on the surface were repelledimmediately, leading to interatomic distances larger than rcov

s .Similarly, molecules inside the sheet at the center of thehexagons remained intact and did not form chemical bondswith any atoms of the host structure. These findings were alsosupported by essentially no change in the charge density plots

Figure 5. Phonon dispersion of the HNS in the 2D Brillouin zone,together with the partial phonon density of states (PDOS). Theshaded areas indicate the total density of states. The inset shows theacoustic branches along Γ−M, illustrating that the soft, acousticphonon branch does not exhibit any imaginary modes. Furthermore,the dispersion clearly shows the two linear and one quadratic branchesas q → Γ, characteristic for 2D materials.

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of the sheet and the adsorbate. A similar conclusion can bedrawn from the COHP of the relevant atomic interactions, i.e.between the host and guest atoms closest to each other. Asshown in Figure 6, the interaction between the molecules andthe HNS is negligible for O2, CO2, and N2. However, arelatively strong interaction is observed for the H2O moleculeplaced on a Ti atom, which might be of interest inphotocatalytic water-splitting application for hydrogen produc-tion.100 Nevertheless, the magnitude of this interaction is muchsmaller compared to the Ti−O bonds within the sheet, and wesafely conclude that even water will not disrupt the HNSstructure.The adsorption energies according to Eads = E(HNS + M) −

E(HNS) − E(M) of above molecules are listed in Table 3,where the energies of the individual adsorbates M werecomputed in vacuum, i.e. in the gas phase, using both the PBEfunctional and HSE06. For HSE06, we also took into accountvan der Waals (vdW) interactions based on the Tkatchenko−Scheffler method with Hirshfeld partitioning.108 A directcomparison of the PBE and HSE06+vdW energies showsoverall lower values of Eads by 0.5−2 eV for the HSE06+vdWfunctional, indicating that the adsorbate−HNS interaction isprimarily vdW mediated. CO2 is especially weakly bound to theHNS with Eads > − 0.2 eV, rather independent of theadsorption site. Together with the negligible impact on theelectronic structure, we consider that all above molecules arephysisorbed on the HNS. Additionally, we investigated theadsorption of catalytic reaction products of H2O, namely H,OH, and O, and their adsorption energies are listed at thebottom of Table 3. For these species, the interaction with theHNS is overall stronger, and the effect of the vdW correction islower. In fact, the difference between the PBE andHSE06+vdW adsorption energies of H and OH is lower(<0.5 eV) than that for the molecules N2, O2, CO2, and H2O.Elemental O binds the most strongly to the HNS withadsorption energies of around 6 eV with the HSE06+vdWfunctional.If the HNS were to be grown or adsorbed on a substrate, its

atomic and electronic structure will be affected due to theinteraction at the interface. To study the effect of thisinteraction, we deposited a layer of HNS on two substratescommonly used in CVD, namely Au(111) and Ag(111).109,110

A slab with 6 atomic layers of Au and Ag was used with 24

atoms per cell to model the substrate. All atoms were fullyrelaxed at the equilibrium lattice constant of the bulk material,using the PBE functional and also by taking into account thevdW interactions, PBE+vdW. The atomic structure of the HNSremains overall unaffected during the relaxation, indicating thatthe sheet only weakly interacts with the substrates, leading to afinal distance between the HNS and the surface slabs of 2.9 Åfor Ag(111) and 3.1 Å for Au(111). Figure 7 shows the

Figure 6. COHP plots showing the Ti−O bonding interaction of theHNS in red together with the bonds between the HNS and CO2, H2O,N2, and O2 molecules. The geometric location where these moleculesare adsorbed on the sheet is shown by the large, purple sphere in theinsets.

Table 3. Adsorption Energies Using the PBE and HSE06Functionals with vdW Correction of Various MolecularSpecies on the HNSa

adsorbate site PBE HSE06+vdW

N2 on surface −0.553 −1.496in void −0.443 −1.594on O −0.565 −1.497on Ti −0.564 −1.390

O2 on surface −0.599 −2.290in void −0.604 −1.565on O −0.594 −2.199on Ti −0.585 −2.104

H2O on surface −0.671 −1.497in void −0.688 −1.692on O −0.670 −1.499on Ti −0.833 −1.691

CO2 on surface −0.030 −0.199in void 0.469 −0.002on O −0.040 −0.102on Ti −0.018 −0.090

H on surface −2.279 −2.308in void −0.440 −0.418on O −2.279 −2.310on Ti −2.278 −2.307

OH on surface −0.977 −1.458in void −0.761 −1.246on O −1.028 −1.501on Ti −1.028 −1.502

O on surface −4.114 −6.116in void −4.115 −6.116on O −3.855 −5.900on Ti −3.855 −5.899

aThe different adsorption sites are given in the second column andcorrespond to the geometries shown in the insets of Figure 6.

Figure 7. Binding curves of the HNS on different substrates using thePBE functional with and without taking into account vdW interactions.The binding energies are given per surface area in meV/Å2.

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interaction energies between the HNS and the varioussubstrates as a function of the interlayer distance with respectto the value computed at a spacing of 20 Å. The differencebetween the energy curves with and without taking intoaccount dispersion effects shows that the major contribution tothe binding energy stems from the vdW interaction. Both thebinding energies and the equilibrium distances with the PBEand vdW functionals are listed in Table 4.

Our conclusion that the HNS−substrate interaction ismediated through weak vdW forces without the formation ofstrong chemical bonds is also supported by a careful COHPanalysis. Essentially no bonding states between Au−O/Ti andAg−O/Ti are found in the COHP, another strong indicationthat the HNS is chemically inert. We also investigated aheterostructure of a single HNS layer and a graphene sheet.Due to a small lattice mismatch, a supercell containing 16 fu ofTiO2 and 50 C atoms is required to construct a commensuratecell, covering a large surface area of 130.8 Å2. The equilibriumdistance between graphene and the HNS was found to be 3.2 Å.The vdW binding energy of ≈19 meV/Å2 is comparable to theexfoliation energies of graphene in graphite and other 2Dmaterials,111−114 and an analysis of the COHP indicates thatthe HNS interacts only weakly with graphene.

■ CONCLUSIONIn summary, we predict a novel quasi 2D sheet of TiO2 bysystematically searching for layered structures using anextended minima hopping structure prediction approach andab initio calculations. According to our results, this sheet isdynamically stable and energetically more favorable than anyother previously reported 2D material of TiO2, even surpassingthe well-known lepidocrocite sheet. A thorough study withrespect to its structural and chemical stability shows that theHNS is chemically inert and highly resistant against a widerange of mechanical stress. In fact, uniform and uniaxial strainas well as defect engineering can be readily used to tune theband gap of the HNS. These findings provide strong evidencethat the HNS is viable once synthesized and a promisingcandidate material for energy applications, especially forphotocatalytic hydrogen production due to its large surfacearea with hexagonal voids and the well-suited band alignmentwith the redox potentials of water splitting. Furthermore, theHNS can readily serve as a building block for heterostructures(e.g., with graphene) with potential applications in energy

storage and conversion, ranging from metal-ion batteries tomaterials in photovoltaics. Due to its weak vdW interaction, theHNS could be potentially grown as a single layer on anappropriate substrate.

■ AUTHOR INFORMATION

Corresponding Authors*E-mail: aghasemi@iasbs.ac.ir.*E-mail: amsler.max@gmail.com.

ORCIDMaximilian Amsler: 0000-0001-8350-2476Present Address¶M.A.: Laboratory of Atomic and Solid State Physics, CornellUniversity, Ithaca, New York 14853, United States.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

M.A. acknowledges support from the Novartis Universitat BaselExcellence Scholarship for Life Sciences and the Swiss NationalScience Foundation (Grants P300P2-158407 and P300P2-174475). This work was partially performed within the SwissNational Competence Center for Research, Marvel. Wegratefully acknowledge the computing resources from theSwiss National Supercomputing Center in Lugano (Projects700 and s707), the Extreme Science and EngineeringDiscovery Environment (XSEDE) (which is supported byNational Science Foundation Grant OCI-1053575), the Bridgessystem at the Pittsburgh Supercomputing Center (PSC) (whichis supported by NSF Award ACI-1445606), the Quest highperformance computing facility at Northwestern University,and the National Energy Research Scientific Computing Center(DOE DE-AC02-05CH11231).

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Table 4. Adsorption Properties of the HNS on Au and Agand the Interaction between the HNS and Graphene (C)Using the PBE and a vdW Corrected Exchange CorrelationFunctionala

substrate functional di (Å) Ei (meV/Å2)

Au PBE 3.83 −1.21Ag PBE 3.63 −3.64C PBE 4.04 −0.65Au PBE+vdW 3.06 −25.10Ag PBE+vdW 2.87 −29.59C PBE+vdW 3.22 −18.89

aThe binding energy per unit area (Ei) is given in units of meV/Å2

(corresponding to the well depth of the curves in Figure 7), while theequilibrium distance di between the HNS and substrates/graphene isgiven in Å (corresponding to the minimum energy distance of thecurves in Figure 7).

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Chemistry of Materials Article

DOI: 10.1021/acs.chemmater.7b02031Chem. Mater. 2017, 29, 8594−8603

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