Two-Dimensional Hexagonal Sheet of TiO2 - Chemistry of Materials

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A two-dimensional hexagonal sheet of TiO

Hossein Asnaashari Eivari, S. Alireza Ghasemi, Hossein Tahmasbi, Samare Rostami, Somayeh Faraji, Robabe Rasoulkhani, Stefan Goedecker, and Maximilian Amsler Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b02031 • Publication Date (Web): 02 Aug 2017 Downloaded from http://pubs.acs.org on August 2, 2017

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Chemistry of Materials

A 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, Iran ‡University of Zabol, P.O. Box 98615-538, Zabol, Iran ¶Department of Physics, Universit¨ at Basel, Klingelbergstr. 82, 4056 Basel, Switzerland §Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA E-mail: [email protected]; [email protected]

Abstract We report on the ab initio discovery of a novel putative ground state for quasi two-dimensional TiO2 through a structural search using the minima hopping method with an artificial neural network potential. The structure is based on a honeycomb lattice and is energetically lower than the experimentally reported lepidocrocite sheet by 7 meV/atom, and merely 13 meV/atom higher in energy than the rutile bulk structure. According to our calculations, the hexagonal sheet is stable against mechanical stress, chemically inert, and can be deposited on various substrates without disrupting the structure. Its properties differ significantly from all known TiO2 bulk phases with a large gap of 5.05 eV that can be tuned through strain and defect engineering.

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Introduction Low dimensional materials have attracted significant interest in the recent years, especially since the discovery of graphene in 2004 through its exfoliation from graphite. 1 Due to its extraordinary properties, ranging from high mechanical strength 2 and the presence of massless Dirac electrons 3 to excellent thermal conductivity, 4 many other 2D materials have been considered and isolated for potential applications in electronics and energy conversion. 5 Buckled graphene analogues like silicene 6–8 have been grown on silver substrates, 9 and germanene 6 was synthesized on gold. 10 Similarly, the theoretically predicted boron counterpart 11–14 with a partially filled honeycomb lattice was recently realized on silver substrates 15–17 and confirmed to exhibit Dirac fermions. 18 This class of materials however lacks a finite band gap, rendering them unsuitable for transistor electronics. On the other hand, promising 2D semiconductors have been investigated for potential applications in nano electronics, optoelectronics and photonics. 19–23 Besides the wide band gap h-BN monolayer, 4,24 transition metal di-chalcogenides (TDM) 4,24 have been intensely studied, which exhibit gaps that can be readily tuned based on the number of stacked monolayers, 4 and electronic properties that can be fundamentally modified through in-plane 25–29 and vertical heterostructuring. 29–33 More recently, layered metal oxides have emerged as a new family of 2D materials, which exhibit an overall higher stability in air compared to TDMs. 34 Besides monolayers of MoO3 , 35 WO3 , 36 SnO, 37 and perovskite type oxides, 5 TiO2 is considered one of the most promising candidates. As an important multi-functional oxide widely used in industrial products ranging from consumer goods to advanced materials for photovoltaic cells, 38 sensors, 39 hydrogen storage, 40 and rechargeable lithium ion batteries, 41–44 titania based materials have also drawn the focus of research for nanoelectrics due to their structure dependent, high dielectric constant. 45 TiO2 nanosheets and nanostructures are touted to possess enhanced photocatalytic, photovoltaic, electrochemical and dielectric properties, 46–49 and great efforts have been made to improve their performance by fabricating controlled size and/or shape at the nano scale. 40,50 2


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Despite these efforts, the atomistic structures in the majority of studies on 2D TiO2 remains unclear, and its ground state structure is not fully resolved. Only a few studies explicitly investigate the microscopic structure of TiO2 nanosheets, 51–53 and almost all theoretical studies are based on slabs cut out of bulk structures along different crystallographic planes. These include 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 known to date is the lepidocrocite type nanosheet (LNS), 48,51,54,57 which was also found to exhibit the lowest formation energy among all sheets reported so far in the literature. Using density functional theory (DFT) calculations, Orzali et al. 58 showed that the LNS can be readily obtained from a slab of anatase (001) with six atomic layer by a simple structural rearrangement. While the practice of using bulk-like structures as a starting point for theoretical investigations is understandable, it is based on the assumption that atomically thin layers of TiO2 will adopt a structure close to the crystalline phase. However, physical epitaxy experiments have shown that many 2D materials often exhibit structural motifs that strongly differ from any bulk polymorphs. 17,59 To address this issue, we performed an extensive global search specifically aimed at screening 2D structures of TiO2 and report on the discovery of a new layered ground state with hexagonal symmetry. According to our calculations, this material is chemically and mechanically stable, and its electronic structure can be modified by strain and defect engineering, leading to a tunable band gap covering a wide energy range.

Methods The structural search was conducted with the minima hopping method (MHM), 60,61 which implements an efficient algorithm to explore the energy landscape of a system by performing consecutive molecular dynamics (MD) escape steps followed by local geometry relaxations. The Bell-Evans-Polanyi principle is exploited to accelerate the search by aligning the initial

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MD velocities preferably along soft mode directions. 62 In order to perform predictions for quasi-2D materials the functionality of the MHM was modified to model 2D and layered materials. For this purpose, the target function to be optimized was extended by including 2-dimensional confining potentials Ci (ei , rαj ), where α denotes the axis α = {x, y, z} along the non-periodic direction, rj are the cartesian coordinates of the N atoms in the system, and ei are the equilibrium positions along α at which the potentials are centered. Our confinement functions are sums of atomic contributions and is zero within a cutoff region rc around ei , P α while it has a polynomial form of order n with amplitude Ai beyond rc : Ciα = N j=1 c(ei , rj ) where c(ei , rαj ) = Ai (|ei − rαj | − rc )n for |ei − rαj | ≥ rc and zero otherwise. During the local geometry optimization and the MD escape trials the additional forces acting on the atoms fj =

∂Ci ∂rj

and on the cell vectors σj =

∂Ci ∂hj

were 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 our calculations, a single confinement potential C1 was used with e1 centered along the lattice vector c, with a cutoff rc = 1 ˚ A, n = 4 and A1 = 0.1 eV. Multiple MHM structure prediction runs were performed, starting from a variety of random initial seeds using 2-10 f.u./cell in conjunction with the charge equilibrated neural network technique (CENT) potential. To accelerate the structural search, we prescreened the energy landscape using a recently developed high dimensional artificial neural network (ANN) potential based on CENT, 63 specifically fit to the TiO2 system. In order to train the CENT potential we first prepared a database containing the DFT energies of about 3000 cluster structures, with sizes ranging from 6 to 70 formula units (f.u.). An approximate potential was obtained by fitting CENT to DFT data of randomly generated structures in an initial step. Subsequently, further structures were added to the training set by performing short MHM simulations with the approximate potential. The resulting low energy structures from these MHM runs were carefully filtered to avoid duplicate structures and to ensure a large diversity in structural motifs within the augmented data set, a task performed by comparing structures with a

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structural fingerprint. 64,65 This procedure was repeated several times until a desired accuracy was reached for a predefined validation dataset. Even though the CENT potential was generated from cluster structures, it provides accurate results for periodic systems. This high transferability of CENT was recently demonstrated for calcium fluoride and ZnO. 66,67 The DFT calculations to generate the training data and to refine the results from the MHM simulations were carried out with the FHI-aims code, 68 using the tier 2 basis set for both the Ti and O elements. The generalized gradient approximation parametrized according to Perdew-Burke-Ernzerhof (PBE) 69 was employed for the exchange-correlation functional. Geometry relaxations were performed until the atomic forces were less than 0.01 eV/˚ A, and Monkhorst-Pack k-point grids with a density of 0.03/˚ A were used, resulting in total energies converged to within 1 meV/atom. For all calculations involving 2D structures a vacuum space of about 12 ˚ A was used in the direction perpendicular to the sheets to suppress the interaction between periodic images of the layers. The chemical bonding was studied by analyzing the crystal orbital Hamilton population (COHP) as implemented in the LOBSTER package, 70–73 based on the wave functions computed with the Vienna Ab Initio Simulation package (VASP). 74 Supercells with 48 atoms were used, together with a plane wave cutoff energy of 450 eV and k-point grids with a density of 0.03/˚ A. Phonon calculations were carried with the finite difference approach as implemented in the PHONOPY code, 75 using atomic displacements of 0.01 ˚ A. The dielectric tensor and the born effective charges were computed with VASP. Large supercells containing 192 atoms were used to ensure sufficient convergence of the force constants.

Results and Discussion We performed a global search for 2D TiO2 materials using the constrained MHM algorithm 60,61 together with the recently developed CENT ANN potential. 63 A plethora of structures were recovered, including the majority of the previously reported sheets discussed in

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the literature, indicating that the structural search was sufficiently converged. The most promising candidate structures were subsequently refined at the DFT level. We discovered a novel nanosheet with hexagonal symmetry to have the lowest energy, hereafter referred to as hexagonal nano sheet (HNS), shown in panel (a) of Figure 1. In particular, the HNS is energetically favorable compared to the LNS, which had been considered to be the most stable 2D structure of TiO2 to date. From the structural point of view, the unit cell of HNS is composed of four-fold coordinated Ti and two-fold coordinated O atoms, arranged in a lattice with P 6/mmm symmetry (see Table 1 for the lattice vectors and atomic coordinates). It is isostructural to a previously reported silicon dioxide sheet grown on a Ru surface. 76 The TiO4 units form tetrahedra in two layers, which are stacked on top of each other and linked by shared corners, as illustrated in the side view in panel (b) of Figure 1. Large, hexagonal pores are formed along the out-of-plane axis and arranged in a honeycomb lattice, as shown from the top view in panel (b) of Figure 1. In strong contrast to the HNS, the LNS has a much denser structure, where each Ti atom is six-fold and the O atoms are two-fold or four-fold coordinated, respectively. The edge-sharing octahedra are arranged in an orthorhombic lattice, forming a sheet which is 0.4 ˚ A thinner than the HNS. Similar to the HNS, many other 2D materials have a hexagonal lattice: the large lattice constant of 6.03 ˚ A in the HNS compares for example with values of 2.46 ˚ A in graphene, 77 3.90 ˚ A in silicene 8 and 3.15 ˚ A in MoS2 , 78 potentially allowing the construction of various (commensurate) 2D heterostructured materials with improved properties. Due to the unique hexagonal nano pores in the HNS we expect it to have a very low atomic density compared to other sheets. To quantify the density we considered as the volume the product of the thickness h of each sheet and the area A of the unit cell along the two periodic directions, where h is given by the distance between the two outmost atoms (column 4 in Table 2). Furthermore, we analyzed the bond lengths in all 2D structures and crystalline polymorphs by comparing the minimum and maximum bonds in each system (column 5 and 6 in Table 2). In general, small maximum bond length indicate strong and stiff

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Table 1: The structural parameters of the HNS with the Wyckoff positions of Ti and O. The values of x and y are given in reduced coordinates, whereas the z is given in cartesian coordinates in units of ˚ A. The equilibrium lattice parameter is a = 6.03 ˚ A. Ti 4h O1 6i O22d

x 1/3 1/2 1/3

y 2/3 0/0 2/3

z 1.82 2.36 0.00

show that rutile is the thermodynamic ground state at least up to 1300 K, 79 but semilocal and hybrid DFT calculations predict a reversed energetic ordering, 80–84 possibly due to the failure to correctly capture high-order correlation effects. 85 Most importantly however, the HNS is 7 meV/atom lower in energy than the LNS, rendering it the most stable nanosheet among all known quasi-2D nano structures. A comparative summary of the quantities discussed above is listed in Table 2, showing that the HNS simultaneously has the lowest density and formation energy ∆E with respect to bulk anatase. Table 2: Table contains the PBE formation energy with respect to anatase (∆E) in meV/atom, surface buckling (SB) in ˚ A, pseudo-density in g/cm3 , maximum Ti-O bond length (dmin ) and minimum Ti-O band length (dmax ) in ˚ A, and HSE06 level band-gap energy (Eg ) in eV. For structures cut from bulk material the last column indicates the number of atomic layers they contain as a measure of the initial slab thickness (Nlayer ). Lattice parameters of rutile and anatase phases in our calculations are a = 4.65 ˚ A and c = 2.97 ˚ A for rutile and a = 3.80 ˚ A and c = 9.70 ˚ A for anatase. These values compare well with experimental data, i.e. a = 4.59 ˚ A and c = 2.95 ˚ A for rutile 86 and a = 3.78 ˚ A and c = 9.50 ˚ A for 86 ˚ ˚ anatase. The calculated lattice parameters of the LNS (a = 3.02 A, b = 3.74 A) are in good agreement with the theoretical values of Sato et al., 87 and close to the experimental values of Orzali et al. 58 (a represent bulk densities), whereas the formation energy are in excellent agreement with the PBE values of Forrer et al. (56 meV/atom). 88 structure ∆E rutile(100) 158 flourite(111) 137 anatase(101) 120 rutile(110) 83 TiO2 (B)(001) 60 LNS 52 HNS 45 rutile 32 anatase 0

SB > 1.06 > 1.30 > 1.10 > 1.06 0.67 1.03 0.54

den. 4.199 5.967 5.967 4.597 4.951 5.481 3.536 4.127a 3.765a 8

dmin 1.83 1.85 1.78 1.78 1.81 1.83 1.82 1.99 1.94

dmax 2.09 2.07 2.10 2.14 2.07 1.97 1.82 2.00 2.00


Eg 4.84 4.54 4.87 3.95 4.16 4.65 5.05 3.40 3.58

Nlayer 6 3 6 6 7 6

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We further studied the electronic properties of the new HNS using hybrid functionals due to the well-known severe underestimation of the band gaps of semilocal DFT. The HSE06 89 and PBE0 90 functionals were employed to assess their accuracy by computing the band gaps of the experimentally well studied rutile and anatase phases. The values for HSE06 with gaps of 3.40 eV and 3.58 eV for rutile and anatase, respectively, are closer to the experimental values (3.0 eV and 3.2 eV 86 ) than PBE0, which significantly overestimates the gap with 4.16 eV and 4.32 eV for rutile and anatase, respectively. Hence, all subsequent electronic structure calculations were performed with HSE06, and the band gaps for the structures considered in this work are compiled in Table 2. The band structure for the pristine HNS and LNS are shown in Figure 2, revealing that the LNS has a direct band gap, in contrast to the HNS. However, the valence band of the HNS exhibits very little dispersion, leading to a quasi-direct gap at the K-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 main contribution 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 larger than any other TiO2 polymorph studied here, and lies well beyond the range of visible light. Even the stacking of several HNS sheets on top of each other does not change its electronic structure, 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 be employed in practice, such as impurity doping, introducing vacancies, elemental substitution, and creating heterostructures with other 2D building blocks. 91–95 Since defects can significantly influence the gap energies, the effect of oxygen vacancies on the electronic band structure of an isolated HNS was investigated. Monovacancies were created in a supercell containing 108 atoms by removing each of the two symmetrically distinct oxygen sites, 6i and 2d. We estimated the oxygen vacancy formation energy according to Ev = E(HNS-O) + 12 E(O2 ) − E(HNS), where the energy of O2 was evaluated in vacuum (gas 9



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phase). Defect energies of Ev6i = 6.49 eV and Ev2d = 6.32 eV were obtained with PBE, and Ev6i = 7.35 eV and Ev2d = 7.07 eV with HSE06. The resulting electronic pDOS for the two types of vacancies, depicted in the two bottom panels of Figure 3, shows that the vacancies create an occupied valence state in the band gap of the pristine HNS and essentially reduces the energy differences between conduction and valence bands. The values of the gaps are thus 2.1 eV 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 photocatalytic activity, but suffers from the consequences of a wide band gap which limits the absorbed light to the ultraviolet portion of the solar spectrum. 96 Although the band gap of the pristine HNS is even larger than other TiO2 phases, the reduced gap energies of the HNS with oxygen vacancies is well suited to absorb in the visible spectrum. In addition to the gaps, the relative positions of the band edges with respect the redox potentials of water splitting are crucial to allow photoinduced 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 above the reduction potential of H+ to produce H2 . 95,97,98 Fig. 4 shows the band alignment of pristine anatase TiO2 , together with the HNS without and with oxygen vacancies. The CBM position of the anatase phase are aligned with respect to the experimental values of the normal hydrogen electrode (NHE), 99 and we used the gap energy to place the VBM. The band edges of the pristine and defect phases of the HNS are shifted such that the unperturbed Ti 1s core levels from our all-electron calculations were correctly aligned among all TiO2 polymorphs. A comparison of the band alignment between the anatase TiO2 and the pristine HNS shows that the strong oxidation ability is retained with a decrease of the VBM by 1.39 eV. At the same time, the CBM is shifted up by merely 0.08 eV, still allowing the electron transfer to reduce H+ . Inducing the 2d and 6i oxygen vacancies does not alter the positions of the CBM, but only introduces the occupied defect states, shown by the pink bars in Fig. 4, which denote the corresponding VBM (see also Fig. 3). Similar intermediate bands

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were reported to emerge within the band gap of Rh and F codoped anatase TiO2 . 95 Since the VBM remain below the water oxidation potential, we conclude that even the HNS with oxygen vacancies are thermodynamically suited for water redox reactions. Together with the reduced band gap energy of around 2 eV to absorb in the optical range, the HNS could be tuned through defect engineering to potentially outperform known TiO2 polymorphs for photocatalytic water splitting applications. Another pathway to modify gaps in 2D materials is strain engineering. 100 Since 2D sheets are the fundamental building blocks for layered heterostructures in functional materials, they are often grown through chemical vapor deposition (CVD) and physical epitaxy on a substrate or as mechanically assembled stacks. 4,17,101 These approaches can lead to strain, and its effect on the band-gap was studied at the HSE06 level by applying three different kind of strains: biaxial strain simultaneously along the two equivalent lattice vectors ~a and ~b, uniaxial strain along ~a only, and along 1 ~a + ~b. As shown in panel (b) of Figure 2, the 2 gap energies increase and decrease upon compressive and tensile strain, respectively, and the change only weakly depends on the direction of uniaxial strain. Although a biaxial tensile strain of 10% leads to a large reduction of the band gap by 20%, the gaps never reaches the range of visible light. Nevertheless, growing the HNS on an appropriate substrate would enable a continuous tuning of the gap in a wide range. Large strains experienced for example during the lithiation process in lithium ion batteries or hydrogenation in hydrogen storage applications can also compromise the mechanical stability of a layered material. Therefore, all internal degrees of freedom were fully relaxed when applying strain. Although the atomic structure of the HNS remains intact even at +10% tensile strain, the outermost layers of O atoms start to buckle at compressive strains below -8% for uniaxial and below -6% for biaxial strain, and the hexagonal voids start to deform slightly. The dynamical stability of the HNS was assessed at its equilibrium lattice parameters by computing the phonon dispersion in the whole 2D Brillouin zone with the frozen phonon approach. The calculated phonon spectrum in Figure 5 shows no imaginary

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modes, indicating that the HNS is indeed a metastable structures corresponding to a local minimum on the energy landscape. Like other 2D materials, two acoustic branches are linear as q → 0. Since force constants related to the transverse motion of the atoms decay rapidly, the lowest acoustic mode shows a quadratic behavior close to the Γ point. 8 In fact, this quadratic dispersion is common to all layered materials, as recently discussed in detail by Carrete et al. 102 In addition to the mechanical properties, a high chemical stability is essential in order for a 2D material to be viable in practical applications. We can deduce a first evidence of the high chemical stability of the HNS from its band gap energy, which is the largest among all TiO2 polymorphs (Table 2). Next, we analyzed the crystal orbital Hamilton population (COHP) and its integral (ICOHP) using the LOBSTER code. 70–73 Negative and positive values of the COHP correspond to bonding and antibonding states, respectively, while the ICOHP is considered here as a measure to compare bond strengths. 72,103 The COHP between neighboring Ti and O atoms were calculated for the HNS, LNS and the anatase (001) slab. No antibonding interactions are present in the LNS and HNS for the occupied states. On the other hand, antibonding states exist for anatase (001) slightly below the Fermi level, indicating an electronic instability. Indeed, the anatase (001) undergoes a structural distortion and transforms to the LNS sheet upon relaxation with a very tight force convergence criterion, thereby alleviating this instability. Furthermore, a comparison of the -ICOHP at the Fermi level between the HNS and LNS results in values of 5.33 eV and 3.54 eV, respectively, indicating stronger Ti–O bonds in the HNS, another evidence for its superior chemical stability. Furthermore, we investigating the potential reactivity of the HNS with the most common molecules in the air, such as N2 , O2 , CO2 , and H2 O. For this purpose, these molecules were placed at different sites of the sheet and local geometry relaxations were performed to check if chemical bonds would form between the sheet and the molecules. Four different sites were investigated as shown in Figure 6: on top of an O atom, Ti atom, and in the center of the

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hexagon at the surface of the sheet, and within the void of the hexagons. In order to induce a chemical reaction, the initial distance from the sheet was chosen to be smaller than the sum s of the covalent radii rcov of the closest two atoms of the adsorbate and the sheet whenever

possible. However, all molecules placed on the surface were repelled immediately, leading to s interatomic distances larger than rcov . Similarly, molecules inside the sheet at the center of

the hexagons remained intact and did not form chemical bonds with any atoms of the host structure. These findings were also supported by essentially no change in the charge density plots of the sheet and the adsorbate. A similar conclusion can be drawn from the COHP of the relevant atomic interactions, i.e. between the host and guest atoms closest to each other. As shown in Figure 6, the interaction between the molecules and the HNS is negligible for O2 , CO2 and N2 . However, a relatively strong interaction is observed for the H2 O molecule placed on a Ti atom, which might be of interest in photocatalytic water-splitting application for hydrogen production. 96 Nevertheless, the magnitude of this interaction is much smaller compared to the Ti–O bonds within the sheet and we can safely conclude that even water will not disrupt the HNS structure. 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 were computed in vacuum, i.e. in the gas phase, using both the PBE functional and HSE06. For HSE06, we also took into account Van der Waals (vdW) interactions based on the Tkatchenko-Scheffler method with Hirshfeld partitioning. 104 A direct comparison of the PBE and HSE06+vdW energies shows overall lower values of Eads by 0.5-2 eV for the HSE06+vdW functional, indicating that the adsorbate-HNS interaction is primarily vdW mediated. CO2 is especially weakly bound to the HNS with Eads > −0.2 eV, rather independent of the adsorption site. Together with the negligible impact on the electronic structure we consider that all above molecules are physisorbed on the HNS. Additionally, we investigated the adsorption of catalytic reaction products of H2 O, namely H, OH, and O, and their adsorption energies are listed at the bottom of Table 3. For these species, the interaction with the HNS

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is overall stronger and the effect of the vdW correction is lower. In fact, the difference between the PBE and HSE06+vdW adsorption energies of H and OH is lower (< 0.5 eV) than for the molecules N2 , O2 , CO2 , and H2 O. Elemental O binds the most strongly to the HNS with adsorption energies of around 6 eV with the HSE06+vdW functional. Table 3: The adsorption energies using the PBE and the HSE06 functional with vdW correction of various molecular species on the HNS. The different adsorption sites are given in the second column and correspond to the geometries shown in the insets of Figure 6. Adsorbate N2

O2

H2 O

CO2

H

OH

O

Site on surface in void on O on Ti on surface in void on O on Ti on surface in void on O on Ti on surface in void on O on Ti on surface in void on O on Ti on surface in void on O on Ti on surface in void on O on Ti

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PBE -0.553 -0.443 -0.565 -0.564 -0.599 -0.604 -0.594 -0.585 -0.671 -0.688 -0.670 -0.833 -0.030 0.469 -0.040 -0.018 -2.279 -0.440 -2.279 -2.278 -0.977 -0.761 -1.028 -1.028 -4.114 -4.115 -3.855 -3.855

HSE06+vdW -1.496 -1.594 -1.497 -1.390 -2.290 -1.565 -2.199 -2.104 -1.497 -1.692 -1.499 -1.691 -0.199 -0.002 -0.102 -0.090 -2.308 -0.418 -2.310 -2.307 -1.458 -1.246 -1.501 -1.502 -6.116 -6.116 -5.900 -5.899



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Table 4: The adsorption properties of the HNS on Au and Ag, and the interaction between the HNS and graphite (C), using the PBE and a vdW corrected exchange correlation functional. The binding energy per unit area (Ei ) is given in units of meV/˚ A2 (corresponding to the well depth of the curves in Fig. 7), while the equilibrium distance di between the HNS and substrates/graphene is given in ˚ A (corresponding to the minimum energy distance of the curves in Fig. 7). Substrate Au Ag C Au Ag C

Functional PBE PBE PBE PBE+vdW PBE+vdW PBE+vdW

di ( ˚ A) 3.83 3.63 4.04 3.06 2.87 3.22

Ei (meV/˚ A2 ) -1.21 -3.64 -0.65 -25.10 -29.59 -18.89

If the HNS were to be grown or adsorbed on a substrate, its crystal and electronic structure will be affected due to the interaction at the interface. To study the effect of this interaction we deposited a layer of HNS on two substrates commonly used in CVD, namely Au (111) and Ag (111).

105,106

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

atoms per cell to model the substrate. All atoms were fully relaxed at the equilibrium lattice constant of the bulk material, using the PBE functional and also by taking into account the vdW interactions, PBE+vdW. The atomic structure of the HNS remains overall unaffected during the relaxation, indicating that the sheet only weakly interacts with the substrates, leading to a final distance between the HNS and the surface slabs of 2.9 ˚ A for Ag(111) and 3.1 ˚ A for Au(111). Fig. 7 shows the interaction energies between the HNS and the various substrates as a function of the interlayer distance with respect to the value computed at a spacing of 20 ˚ A. The difference between the energy curves with and without taking into account dispersion effects shows that the major contribution to the binding energy stems from the vdW interaction. Both the binding energies and the equilibrium distances with the PBE and vdW functionals are listed in Table 4. Our conclusion that the HNS-substrate interaction is mediated through weak vdW forces without the formation of strong chemical bonds is also supported by a careful COHP analysis. Essentially no bonding states between Au–O/Ti and Ag–O/Ti are found in the COHP,

20


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another strong indication that the HNS is chemically inert. We also investigated a heterostructure of a single HNS layer and a graphene sheet. Due to a small lattice mismatch, a supercell containing 16 f.u. of TiO2 and 50 C atoms is required to construct a commensurate ˚2 . The equilibrium distance between graphene cell, covering a large surface area of 130.8 A and the HNS was found to be 3.2 ˚ A. The vdW binding energy of ≈ 19 meV/˚ A2 is comparable to the exfoliation energies of graphene in graphite and other 2D materials, 107–110 and an analysis of the COHP indicates that the HNS interacts only weakly with graphene.

60

2

Energy per area (meV/Å )

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


HNS−Au HNS−Au vdW HNS−Ag HNS−Ag vdW HNS−C HNS−C vdW

40 20 0 −20 −40

2

3

4

5

6

Distance (Å) Figure 7: The binding curves of the HNS on different substrates, using the PBE functional with and without taking into account vdW interactions. The binding energies are given per surface area in meV/˚ A2 .

Conclusion In summary, we predict a novel quasi 2-dimensional sheet of TiO2 by systematically searching for layered structures using an extended minima hopping structure prediction approach 21



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and ab initio calculations. According to our results, this sheet is dynamically stable and energetically favorable to any other previously reported 2D material of TiO2 , even surpassing the well known lepidocrocite sheet. A thorough study with respect to its structural and chemical stability shows that the HNS is chemically inert and highly resistant against a wide range of mechanical stress. In fact, uniform and uniaxial strain as well as defect engineering can be readily used to tune the band gap of the HNS. These findings provide strong evidences that the HNS is viable once synthesized and a promising candidate material for energy applications, especially for photocatalytic hydrogen production due to its large surface area with hexagonal voids and the well suited band alignment with the redox potentials of water splitting. Furthermore, the HNS 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 to materials in photovoltaics. Due to its weak vdW interaction, the HNS could be potentially grown as a single layer on an appropriate substrate.

Acknowledgments M.A. acknowledges support from the Novartis Universität Basel Excellence Scholarship for Life Sciences and the Swiss National Science Foundation (P300P2-158407, P300P2-174475). This work was partially performed within the Swiss National Competence Center for Research, Marvel. We gratefully acknowledge the computing resources from the Swiss National Supercomputing Center in Lugano (project s700 and s707), the Extreme Science and Engineering Discovery Environment (XSEDE) (which is supported by National Science Foundation grant number OCI-1053575), the Bridges system at the Pittsburgh Supercomputing Center (PSC) (which is supported by NSF award number ACI-1445606), the Quest high performance computing facility at Northwestern University, and the National Energy Research Scientific Computing Center (DOE: DE-AC02-05CH11231).

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Two-Dimensional Hexagonal Sheet of TiO2 - Chemistry of Materials

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