DSpace at VNU: A first-principles investigation of various gas (CO, H2O, NO, and O-2) absorptions on a WS2 monolayer: stability and electronic properties

Home Search Collections Journals About Contact us My IOPscience A first-principles investigation of various gas (CO, H2O, NO, and O2) absorptions on a WS2 monolayer: stability and electronic properties This content has been downloaded from IOPscience Please scroll down to see the full text 2015 J Phys.: Condens Matter 27 305005 (http://iopscience.iop.org/0953-8984/27/30/305005) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 129.8.242.67 This content was downloaded on 21/07/2015 at 06:28 Please note that terms and conditions apply Journal of Physics: Condensed Matter J Phys.: Condens Matter 27 (2015) 305005 (11pp) doi:10.1088/0953-8984/27/30/305005 A first-principles investigation of various gas (CO, H2O, NO, and O2) absorptions on a WS2 monolayer: stability and electronic properties Viet Q Bui1, Tan-Tien Pham1, Duy A Le1, Cao Minh Thi1,2 and Hung M Le3,4   Department of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam   Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam   Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam   Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Vietnam E-mail: hung.m.le@hotmail.com and leminhhung@tdt.edu.vn Received 26 February 2015, revised 12 May 2015 Accepted for publication 11 June 2015 Published 14 July 2015 Abstract Using first-principles calculations, we investigate the interactions between a WS2 monolayer and several gas molecules (CO, H2O, NO, and O2) Different sets of calculations are performed based on generalized-gradient approximations (GGAs) and GGA + U (U = 2.87 eV) calculations with D2 dispersion corrections In general, GGA and GGA + U establish good consistency with each other in terms of absorption stability and band gap estimations Van der Waals density functional (vdW-DF) calculations are also performed to validate longrange gas molecule–WS2 monolayer interactions, and the resultant absorption energies of four gas-absorption cases (from 0.21 to 0.25 eV) are significantly larger than those obtained from calculations using empirical D2 corrections (from 0.11 to 0.19 eV) The reported absorption energies clearly indicate van der Waals interactions between the WS2 monolayer and gas molecules The NO and O2 absorptions are shown to narrow the band gaps of the WS2 material to 0.75–0.95 eV and produce small magnetic moments (0.71 μB and 1.62 μB, respectively) Moreover, these two gas molecules also possess good charge transferability to WS2 This observation is important for NO- and O2-sensing applications on the WS2 surface Interestingly, WS2 can also activate the dissociation of O2 with an estimated barrier of 2.23 eV Keywords: DFT + U, WS2, gas adsorption S Online supplementary data available from stacks.iop.org/JPhysCM/27/305005/mmedia (Some figures may appear in colour only in the online journal) 1. Introduction electronic characteristics, which potentially open up vast applications in electronic and spintronic devices, nanomagnetic equipments, and gas sensors 2D lattices with similar geometry and properties to graphene [1] have been studied extensively One type, layered transition-metal compounds, namely dichalcogenide tungsten (WX2), is known as a 2D semiconducting material [2] In a WS2 monolayer with hexagonal configuration, each W atom Along with the continuous development of electronics industry, the research community has spent much effort on searching for new materials with specific properties which may render applications in electronic equipment and components Among the new advanced materials, 2D structures are considered as a breakthrough with ultrathin size and amazing 0953-8984/15/305005+11$33.00 © 2015 IOP Publishing Ltd  Printed in the UK V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 calculations To our knowledge, there have been theoretical investigations describing the influence of gas on an MoS2 surface [25–27], which are mostly based on density function theory (DFT) within local density approximation (LDA) However, we are aware that as a matter of computation for most semiconducting materials, employing DFT is not accurate enough at predicting the electronic behavior surrounding the Fermi level of transition-metal compounds because of the lack of electron–hole interactions in exchange-correlation descriptions Therefore, we also employ in this study a modified DFT-based method to possibly improve the prediction of electronic properties of the WS2 complexes, i.e the DFT + U method [28–32] Traditionally, the interaction parameter U can be empirically determined relying on experimental results (the U parameter is varied so that the theoretical band gap can be reproduced accordingly) and accounted for in the LDA or GGA scheme In our DFT + U approach, the Hubbard U term is determined using a method proposed by Cococcioni and de Gironcoli [33], the so-called ‘linear response’ approach, which does not depend on the experimental results The results of this study can be employed to present a theoretical picture of the nature of homogeneous gas absorptions on WS2, so that gas-sensing applications can be exploited using single-layer WS2 fabrication in experiments is anchored by three pairs of S atoms forming alternating corners (S–W–S) in a honeycomb network, which might be considered as a graphene-like material A single layer of WS2 has been reported to exhibit an ideal direct band gap (Eg) of approximately 1.8 to 2.1 eV, while the band gap of a single layer of MoS2 has been reported as 1.58 eV [3–5], which is an important key for applications in semiconducting electronic components [6–10] Moreover, the conduction-band minimum of single-layer MoS2 at its K point was shown to split to approximately 4 meV by the spin–orbit coupling effect In addition, the exciton binding energy of MoS2 monolayer is also higher than bulk MoS2 [11] According to Klein and coworkers [12], the van der Waals (vdW) interactions between layers was shown to possess significant influence on the band structure of WS2 by means of angle-resolved photoelectron spectroscopy and augmented-spherical-wave calculations Besides, any small variations of the lattice parameter due to applying compressive or tensile stress can even result in the shift of the conduction-band minimum (CBM) and valenceband maximum (VBM), thereby causing a change in its band gap [13, 14] With these interesting features, WS2 is a promising semiconducting material for applications in electronic devices The 1D carbon materials used in field-effect transistor (FET) technology applied to gas sensors exhibit more advantages than classical semiconductive materials [15–18] With a limited surface area, the absorbed gas molecules not cause significant electrical noise or thresholds for detection In terms of chemical reactions, the graphite surface was found to possess interesting features for the absorptions and dissociations of various gas molecules [19] In electronics, the synthesis and utilization of XS2 FETs (X = Mo, W) has attained remarkable achievements [20–22] Ovchinnikov et al [20] used single-layered WS2 to create FETs with similar properties to graphene nanoribbons, and its flexibility at low temperature was reported as 140 cm2 V−1 S−1, while the ratio of Ion /Ioff at room temperature was approximately 106 Furthermore, Radisavljevic and coworkers [23] were successful in synthesizing MoS2 FETs with similar characteristics to graphene nanoribbons, and the reported mobility was at least 200 cm2 V−1 S−1, while Ion /Ioff reached approximately 108 at room temperature These important achievements are very promising and open up a huge potential in electronic applications, especially in gas-sensing technology With these unique electronic properties on a large surface area, MoS2 and WS2 could offer improvements in FETs used in gas sensors For example, Li et al [22] experimentally demonstrated that MoS2 FETs had high sensitivity for NO absorption with a gas detection threshold of 0.8 ppm In another study, Huo et al [24] showed a strong application of WS2 FETs in gas sensors The electronic and magnetic properties of single-layer XS2 with absorption were also studied For example, the nonmetal atoms (H, B, C, N, O and F) absorbed on a single layer of WS2 were shown to alter the total magnetic moment of the layer [4] In this study, we carry out a theoretical investigation to study the effects of gas molecules (CO, H2O, NO, and O2) absorbing on the WS2 surface and evaluate the pictorial insights of electronic structures based on data derived from first-principles 2.  Computational methods 2.1.  Computational details As previously mentioned, we investigate the electronic properties of a WS2 monolayer under the influence of the absorbed gas (CO, H2O, NO, or O2) Our theoretical gas adhesion model consists of the gas of interest on a (2   ×   2) WS2 supercell All models are examined carefully using a GGA-class functional, the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional [34, 35] Five different calculation sets are presented in this study In the first two calculation sets, the calculations are performed using the Vienna ab initio simulation package [36, 37] (VASP) without and with the Hubbard U parameter (GGA + U) while we use the empirical dispersion correction developed by Grimme (D2) to describe vdW interactions [38, 39] In the VASP calculations, the projector-augmented wave (PAW) method [40] is employed, which explicitly describes the valence shells of W (6s5d) and S (3s3p) Then, a third PBE calculation set is performed using the vdW density functional (vdW-DF) [41, 42] for validating purposes In the last two calculation sets, the GGA(PBE) and GGA(PBE) + U calculations are executed with ultrasoft pseudopotentials [43] (describing 5d6s6p for W and 3s3p for S) in the Quantum Espresso (QE) package [44] The main discussion of this paper relies on the results and data obtained from GGA calculations with D2 empirical corrections within VASP To ensure good boundary conditions in lattice circulation, the c-axis amplitude in all models is selected as 15 Å, which is sufficiently large to pass over interlayer interactions In addition, spin polarization is also considered in our first-principles calculations to explore various spin alignments, which may lead to interesting magnetic features V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 W in the WS2 monolayer is quite low (2.87 eV) According to Cococcioni and de Gironcoli [33], the determination of U by employing this linear response approach is basis-set-independent; therefore, the same U will be used for all GGA + U calculations in the entire study In fact, we also show that such a method is also consistent between Perdew–Wang 1991 (PW91) [46, 47] and PBE calculations within GGA because U values resulting from PW91 calculations turn out to be similar to the U term given by PBE 3.  Results and discussion After optimizing a WS2 (2   ×   2) supercell by employing PBE calculations with D2 corrections, the lattice constant is found to be 6.37 Å In particular, the W–S bond length is 2.41 Å while the S–S bond is 3.13 Å and the S–W–S bending angle is 80.8° Meanwhile, the vdW-DF indicates a small structural change, with the lattice constant being 6.43 Å (0.9% larger) In this case, the W–S and S–S bonds are 2.44 Å and 3.16 Å, respectively, while the S–W–S angle remains unchanged In general, the two approaches show small discrepancies in the equilibrium WS2 configuration, which means the vdW interaction does not have a significant impact on the equilibrium configuration of pure WS2 According to the PBE + D2 calculations using VASP, a direct band gap of 1.85 eV is obtained Electron mobility mainly arises from W, as the partial density of state (PDOS) of 5d z 2, 5dxy, and 5d x − y2 subshells are highly distributed contiguously at the VBM and CBM regions, while the 5dzx and 5dzy orbitals are localized at lower energy levels and are barely involved in the conductivity of the material (see supplementary material available at stacks.iop.org/JPhysCM/27/305005/ mmedia) The inclusion of the Hubbard term reduces Eg, but by an insignificant amount (1.80 eV) The density of state (DOS) plots for band gap determination can be consulted in figure 2 Fortunately enough, we realize that the two reported Eg values are close to experimental expectations [3, 4] Moreover, the utilization of the Hubbard Hamiltonian does not seem to broaden the band gap of WS2 as expected As we also discover in the later examination of band structures when gas absorptions take place, the GGA + U method does not seem to offer improvements in predicting electronic band gaps In the case of CO absorption, it is found in the stable configuration that the C atom tends to move toward W, while the O atom points away, as shown in figure 3(a) The distances from O and C to the nearest atoms in the WS2 surface are found to be quite large (3.63 Å and 3.0 Å, respectively) Meanwhile, by mimicking the same CO absorption using vdW-DF in VASP, the shortest distances from O and C to the nearest atoms in WS2 are reduced (3.36 Å and 3.14 Å, respectively) To verify the stability of an absorption model, it is necessary to perform the calculation of absorption energy: Figure 1.  The non-interacting (ℵ0) and interacting (ℵ) linear response curves of 5d electron occupations versus α The relaxations of ions and lattice vectors are attained by adopting the conjugate gradient algorithm in VASP For QE calculations, the Broyden–Fletcher–Goldfarb–Shanno algorithm [45] is employed The general energy convergence threshold for structural optimizations is 10–5 eV The cut-off energy is selected as 550 eV and a k-point mesh of (5   ×   5  ×  1) is used to represent the Brillouin zone for all investigated structures 2.2.  Determining the on-site Hubbard U Before going into the computational simulation of complexes, we actually perform a U-determining step to identify the U potential acting on the 5d site of W based on the linear response approach [33] The Hubbard correction based on U can be quickly introduced in a simplified equation as below: U Eυ = ∑ Tr[nIσ (1 − niσ )], (1) I,σ where Eυ is the Hubbard correction term and nIσ is the electron occupation at site I with spin σ The effective value of U can be determined as U = ℵ−0 − ℵ−1, (2) ∂n ∂n where ℵ0 = ∂α KS and ℵ = ∂α are the bare and self-consistent response coefficients obtained from the linear relationship between orbital occupation n and α, the so-called Lagrange multiplier acting on the 5d site of W (figure 1) Because of this linear relationship, the perturbation of α in a narrow range (i.e.  −0.04 eV to 0.04 eV, 0.02 eV per step) would result in a linear regression of 5d orbital occupations versus α, and thereby allows us to determine ℵ0 and ℵ It can be observed in the linear response plots in figure 1 that the 5d orbitals of W are not fully occupied because the degree of 5d occupation is about 6.6 Therefore, we expect that the level of 5d occupation would respond strongly with respect to perturbed α and produce high linear-response coefficients ℵ0 and ℵ As a result, their inverse values would become small, so that the resultant Hubbard U applying on Ead = E WS2 + Egas − E total, (3) where E WS2 and Egas are the total energies of a periodic WS2 layer and an isolated gas molecule in vacuum, while E total is the total energy of the optimized complex V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 Figure 2.  (a) Total DOS of WS2, PDOS of W, S and (b) PDOS for W 5d subshells given by PBE calculations, (c) total DOS of WS2, PDOS of W, S and (d) PDOS for W 5d subshells given by PBE + U calculations The Fermi level is positioned at The summary of all absorption energies arising from the five calculation sets is presented in table 1 It is observed in most cases that the bonding interaction between a gas molecule and WS2 is weak (ranging from 0.09 to 0.25 eV), which truly expresses the dispersion vdW binding In general, the absorption energies given by vdW-DF calculations seem to be greater than the corresponding absorption energies given by PBE and PBE + U calculations with D2 empirical corrections Also, it should be noted that the absorption energies resulting from PBE and PBE + U with D2 corrections are almost identical as can be seen in table 1 In the particular case of CO, PBE-D2 calculations give an absorption energy of 0.11 eV but the vdW-DF treatment raises it to 0.21 eV The electronic contribution is investigated by interpreting the DOS in figure 4(a) The PDOS of CO can be found in the low-energy occupation level of the valence band and in the high level of the conduction band; as a result, the absorbed CO molecule does not affect the electronic structure properties of WS2 significantly In addition, we also study the charge transfer from WS2 to the CO molecule based on Bader charge analysis [48–50] From such an analysis for the CO case and other cases as well, all gas molecules in this study serve as electronic receiving components, while WS2 acts as an electron donor; i.e we can consider one gas molecule as a p-type structure doped into an n-type semiconductor structure (WS2) This consideration offers reasonable explanations for the interacting configurations of absorbed gas molecules In the CO case, we recall that the natural electronegativity of O is higher than that of C according to the Pauling stair (3.44 versus 2.55, respectively) Therefore, CO tends to exhibit charge polarization, and part of the electron density from C would be attracted to O Absorbing on the surface of WS2, C tends to move toward WS2 while O is pushed away, so that C would be able to receive partial charge from WS2 According to our estimation, the CO molecule can get a positive charge of +0.0078, smaller than that reported in two previous studies considering CO absorptions on MoS2 [25, 26] The charge density difference plot can be constructed using the VESTA package [51] The charge density difference with the unit of electron charge can be simply determined from the following equation: Δρ = ρAB − ρA − ρ B, (4) where ρAB, ρA, and ρ B are the charge densities of the complex and components in the mixture, respectively The differences in charge density between each gas molecule and WS2 are presented in figure 5 The estimated Bader charges of the systems of interest are executed with an accuracy threshold of 10−4 electron charge V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 (1) (2) (3) Figure 3.  Absorption configurations (including top and side views) of (a) CO, (b) H2O(1), (c) H2O(2), (d) NO, (e) O2 , (f) O2 , and (g) O2 Table 1.  Absorption energies (eV) of different gas absorption configurations on the WS2 surface The configurations are identified consistently with the nomenclature given in figure 3 QE Calculation method PBE (D2) VASP PBE  +  U (D2) CO H2O(1) H2O(2) NO 0.14 0.19 0.18 0.14 0.19 0.19 O(21) 0.11 0.11 O(22) O(23) PBE (D2) 0.11 0.15 0.15 0.13 0.09 PBE  +  U (D2) 0.11 0.15 0.15 0.14 0.09 PBE (vdW-DF) 0.21 0.22 0.23 0.25 0.21 0.11 0.12 0.09 0.09 0.22 −  1.97 −  1.95 −  1.89 −  1.89 −  1.92 In an isolated H2O molecule, H is partially positive due to the electron attraction of O with negative polarity Therefore, the two H atoms tend to approach closer to the WS2 surface in order to withdraw more electrons Two different stable configurations can be found on WS2 with very similar electronic properties and energetic stability In one configuration, the O atom seems to locate above the center of a honeycomb unit of WS2 This configuration is denoted as H2O(1) in figure 3(b) In particular, the shortest distances from H and O to the nearest neighboring atom belonging to WS2 are 2.58 Å and 2.65 Å, respectively In the second configuration (denoted as H2O(2) in figure  3(c)), the O atom in H2O is positioned on the top site of W, and the shortest distances from H and O to the WS2 surface are 2.45 Å and 2.90 Å, respectively The absorption energies of both configurations are very similar, as shown in table  At the same time, the DOS interpretation shows that H2O contributes localization at the low level of the valance band (figures 4(b) and (c)); therefore, the H2O absorption does not alter the electronic structure of the WS2 layer, which is similar to the case of CO absorption reported earlier Despite sharing similar absorption energies, the Bader charge analysis suggests two different charge transfer schemes in the V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 (1) two H2O absorption cases In the H2O case, H2O receives partial charge from WS2 (−0.0048), while in the H2O(2) case, it receives a greater quantity of negative charge (−0.0075) The fact that H possesses negative charge can be explained by considering vdW interactions between H and S from WS2 (see figure 5), in which S is capable of donating partial negative charge toward H atoms The NO molecule is found to absorb on the WS2 surface as shown in figure 3(d) The shortest interatomic distances from N and O to the WS2 surface are found to be 2.34 Å and 2.91 Å, respectively Meanwhile, the similar interactions predicted by vdW-DF are 2.89 Å and 2.99 Å, respectively It can be clearly seen that the distance from N to the nearest neighboring atom in WS2 is extended much further by the vdW-DF calculations In addition, the vdW-DF method also gives a relatively small angle of NO with respect to the WS2 surface compared to the angle resulting from the calculations based on D2 corrections The calculation results show several interesting properties which may render applications in gas sensors and electronic devices Since there is a single electron in NO, we expect there exists a magnetic moment for the whole surface complex Actually, our expectation is reasonable when a total magnetic moment of 0.71 μB shows up In particular, the key contribution of this electron spin polarization comes from N 2p (0.44 μB, which accounts for 62% of spin polarization) and O 2p (0.26 μB, accounting for 37%) orbitals Moreover, a further analysis of electronic structure given by PBE-D2 calculations indicates an occupation near the Fermi level constituted by the NO orbitals as shown in figure 6 This interesting result suggests the existence of an intermediate energy level in the restricted area where electrons may reside The electrons may get excited in the valence band, then become localized at the p orbitals of NO prior to the conduction band The gap between the highest-occupied WS2 level and the occupied NO level is about 0.95 eV (we might consider this as an indirect band gap) The Bader charge analysis shows that NO receives electrons from WS2 (−0.0096) as shown in figure 5(d) The validation calculations using the Hubbard U potential also confirm band gap narrowing This is in fact an important finding, which renders a promising application of WS2 in the detection of NO gas For convenience, we summarize the band gap of each gas absorption case given by PBE and PBE + U calculations using VASP in table 2 In the last case, we investigate O2 absorption on the WS2 surface By adopting various optimization methods, we deduce three different configurations in which O2 can attach to the surface of WS2 Among them, two configurations are reported to be thermodynamically stable due to positive absorption energies (see table 1) According to the Bader charge analysis, two O atoms are found to form vdW interactions with the sulfur atoms in the WS2 surface In figure  3(f), we observe that O2 sits on top of a W atom (regarded as the O(22) case) On average, the O2 molecule is 3.17–3.29 Å from the surface Despite adopting different binding modes, the calculated absorption energies of these two stable configurations are found to be almost identical (0.09 eV as given by DFT/DFT + U calculations with D2 corrections or 0.22 eV with vdW-DF), Figure 4.  Total DOS, PDOS for W, S, and gas for the absorption cases: (a) CO, (b) H2O(1), and (c) H2O(2) which are relatively high compared to the absorption of O2 on MoS2 [26] In terms of magnetic alignment, we can refer to these two stable configurations as ‘triplet’ structures because both configurations have two unpaired electrons and exhibit a total magnetic moment of 1.62 μB Recall that the ground state of O2 is triplet Therefore, the interaction between O2 and WS2 does not have an impact on the electronic structure of O2 It can be observed in the electronic structures (revealed by the DOS plots, figures 7(a) and (b)) of the two stable configurations that O2 constitutes an occupation level in the restricted V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 (1) (2) (3) Figure 5.  The isoface plots of charge density difference for (a) CO, (b) H2O(1), (c) H2O(2), (d) NO, (e) O2 , (f) O2 , and (g) O2 on the WS2 − surface (with isovalue varied from  ±0.0001 to  ±0.0004e ) Charge accumulation and depletion are represented by the red and green plots, respectively about 1.36 eV In addition, the Bader charge analysis indicates that O is a charge acceptor receiving even more than one electron (−1.050) Interestingly enough, this unstable configuration possesses a singlet state; in other words, the total magnetic moment vanishes when the O–O bond is broken and two O–S linkages are formed From a different perspective, we also recognize the capability of WS2 for breaking the O–O bond To clarify such a curiosity, we employ the nudged-elastic-band (NEB) method [52] to optimize the transformation pathway from the structure in figure 3(f) to that in figure 3(g) For computational feasibility, we only perform Γ-point calculations The NEB curve in figure 8 indicates that the O–O bond can be dissociated on the WS2 surface with an activation energy of 2.23 eV This energy is lower than that required to activate dissociation of the O–O bond (5.15 eV) [53] At this point, we return to the issue of the calculations based on GGA + U (with Hubbard U being 2.87 eV) In most cases, the Hubbard U model has almost no effect on the band structure of WS2 The overlapping of the 5d orbital of W does not change in comparison with the pure GGA calculations in the absence of Hubbard U More specifically, we believe that the exchangecorrelation effect for WS2 is already well described by the conventional PBE calculation; therefore, the introduction of U is not obligated for improving band-structure quality In terms of area of the spin-down state This behavior is somewhat similar to the NO case presented earlier In our estimation, the band gap is now narrowed to 0.80–0.83 eV using different calculation methods In the conductivity scheme, we can pictorially imagine that O2 (or NO in the previous case) behaves as an ‘agent’ that takes a deposit from the valence band of WS2, and subsequently reinvests an identical amount into the conduction band of WS2 We also survey the charge transfer from the WS2 layer to a gas molecule, and observe that O2 as well as NO can accept more electrons from WS2 This is also a positive sign of good charge transferability In table  3, we summarize all charge transfer quantities from WS2 to the absorbed gas given by PBE and PBE + U calculations There is an unstable configuration of oxygen absorption in which two O atoms and one S atom form an isosceles triangle (figure 3(g)) The O–S bond lengths are 1.69 Å, while the O–O bond is 1.57 Å, which is larger than the equilibrium bond in an isolated oxygen molecule (1.23 Å) The absorption energy given by PBE-D2 calculations is negative (−1.89 eV), which indicates that the structure is highly unstable In a validation check with vdW-DF calculations, we obtain a slightly different absorption energy of  −1.92 eV In the light of electronic structure evidence from interpreting DOS (shown in figure 7(c)), the overlapping of O, W, and S reduces the band gap of WS2 to V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 Figure 6.  Total DOS, PDOS for W, S, and the absorbed NO gas given by (a) PBE and (b) PBE + U calculations Table 2.  Band gaps predicted by PBE and PBE  +  U calculations However, there is one exception in the electronic structure of NO Looking at the DOS plots (figure 6), the PDOS of NO constituted by GGA + U calculations seems to be inverted compared to the PDOS of NO obtained by GGA calculations We learn from figure 6 that the molecular orbital constituted by NO serves as an intermediate residence of conducting electrons Along with the charge transfer calculations, although a slight difference in magnitude is found between GGA and GGA + U, in general, the acceptor/donor predictions are in good accordance with each other At this stage, we observe from all gas-absorption calculations that the GGA and GGA + U calculations establish good self-consistency in total energy calculations because of the small variance in absorption energies (see table  1) When using D2 empirical corrections, the absorption energies established from QE calculations are higher than those given by the same VASP calculations with percent differences varying in the range of 4–24% (with D2 empirical corrections) in VASP for all gas absorption models The configurations are identified consistently with the nomenclature given in figure 3 CO H2O(1) H2O(2) NO O(21) O(22) O(23) PBE PBE  +  U 1.82 1.82 1.82 0.95 0.81 1.72 1.72 1.72 0.85 0.75 0.81 0.81 1.36 1.32 stability analysis, we observe that the absorption energies arising from GGA + U calculations are no different from those corresponding quantities reported by GGA, as summarized in table 1 V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 Table 3.  Charge transfer from the WS2 layer to gas molecules and magnetization of the investigated models obtained from PBE and PBE  +  U calculations in VASP with D2 empirical corrections The configurations are identified consistently with the nomenclature given in figure 3 Charge transfer (e−) CO H2O(1) H2O(2) NO O(21) O(22) O(23) Magnetization (μB) PBE PBE  +  U PBE PBE  +  U 0.0078 0.0048 0.0075 0.0096 0.0134 0.0082 0.0053 0.0065 0.0205 0.0140 0.00 0.00 0.00 0.71 1.62 0.00 0.00 0.00 0.71 1.62 0.0170 0.0159 1.62 1.62 1.0497 1.0498 0.00 0.00 4. Summary In this study, the interactions between WS2 and several gas molecules (CO, H2O, NO, and O2) are extensively studied using first-principles modeling methods Five different sets of calculations are performed based on the PBE functional within GGA Two calculation packages VASP [36, 37] and QE [44], are employed Overall, these two theory-equivalent programs establish good agreements in predicting absorption energies of gas molecules on WS2 (to the order of tens of meV, as shown in table  1) The electronic structure and energetic stability are intentionally validated using GGA + U calculations (with U = 2.87 eV acting on the 5d site of W), which overall establish consistency in absorption stability with the GGA calculations In terms of electronic properties, the utilization of the Hubbard U potential tends to decrease Eg by an insignificant amount in comparison with the Eg predicted by pure GGA calculations Validating the results with GGA + U, we conclude that the conventional PBE calculations actually describe the electronic structure of WS2 well The use of vdW-DF also establishes similar absorption configurations The absorption energies given by the vdW-DF calculations [41, 42] are significantly larger than that given by the use of empirical D2 corrections [38] Still, both methods find good agreement in describing long-range interactions between gas molecules and the WS2 monolayer We observe that the NO and O2 absorptions narrow the band gap of the material While NO reduces the band gap to 0.85–0.95 eV, two stable absorption cases of O2 reduce the band gap to 0.75–0.81 eV In addition, as we performed Bader charge analysis for all structures, we can conclude that NO and O2 are better in charge transfer because they tend to withdraw more electrons from WS2 than the other two gases (H2O and CO) as shown in table 3 These observations are indeed important for gas-sensing applications Additionally, we observe small magnetic moments exhibited by the WS2–NO and WS2–O2 complexes (0.71 μB and 1.62 μB, respectively) Interestingly enough, an unstable configuration of O2 absorption is also observed, in which two O atoms are split and bound to one S atom A numerical estimation of the reaction pathway is subsequently performed, which indicates that Figure 7.  Total DOS, PDOS for W, S, and the absorbed O2 molecule in three absorption configurations: (a) O(21), (b) O(22), and (c) O(23) with data obtained from PBE-D2 When we make comparisons with GGA, GGA + U does not seem to have an effect on the correlation of the W site in conjunction with gas adsorptions (H2O, CO, NO, and O2) In band gap estimations, the use of Hubbard U corrections even shows a general trend of reducing band gaps (as shown in table 2) This behavior is mainly caused by the shift of W 5d z in the conduction regions Overall, the GGA + U calculations not seem to improve the electronic gaps of WS2 as we have expected V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 (2) (3) Figure 8.  NEB optimization to search for the transformation pathway from structure O2 to structure O2 In this optimization, eight intermediate images (configurations) are employed to describe the reaction path The barrier height is obtained as 2.23 eV [12] Klein A, Tiefenbacher S, Eyert V, Pettenkofer C and Jaegermann W 2001 Electronic band structure of singlecrystal and single-layer WS2: influence of interlayer van der Waals interactions Phys Rev B 64 205416 [13] Yun W S, Han S W, Hong S C, Kim I G and Lee J D 2012 Thickness and strain effects on electronic structures of transition metal dichalcogenides: 2H–MX2 semiconductors (M = Mo, W, X = S, Se, Te) Phys Rev B 85 033305 [14] Ghorbani-Asl M, Zibouche N, Wahiduzzaman M, Oliveira A F, Kuc A and Heine T 2013 Electromechanics in MoS2 and WS2: nanotubes versus monolayers Sci Rep 3 2961 [15] Cao Q and Rogers J A 2009 Ultrathin films of single-walled carbon nanotubes for electronics and sensors: a review of fundamental and applied aspects Adv Mater 21 29–53 [16] Pak Y et al 2014 Palladium-decorated hydrogen-gas sensors using periodically aligned graphene nanoribbons ACS Appl Mater Inter 6 13293–8 [17] Shao L, Chen G, Ye H, Niu H, Wu Y, Zhu Y and Ding B 2014 Sulfur dioxide molecule sensors based on zigzag graphene nanoribbons with and without Cr dopant Phys Lett A 378 667–71 [18] Allen B L, Kichambare P D and Star A 2007 Carbon nanotube field-effect-transistor-based biosensors Adv Mater 19 1439–51 [19] Allouche A and Ferro Y 2006 Dissociative adsorption of small molecules at vacancies on the graphite (0 0 0 1) surface Carbon 44 3320–7 [20] Ovchinnikov D, Allain A, Huang Y S, Dumcenco D and Kis A 2014 Electrical transport properties of single-layer WS2 ACS Nano 8 8174–81 [21] Iqbal M W, Iqbal M Z, Khan M F, Shehzad M A, Seo Y and Eom J 2015 Deep-ultraviolet-light-driven reversible doping of WS2 field-effect transistors Nanoscale 7 747–57 [22] Li H, Yin Z, He Q, Li H, Huang X, Lu G, Fam D W, Tok A I, Zhang Q and Zhang H 2012 Fabrication of single- and multilayer MoS2 film-based field-effect transistors for sensing NO at room temperature Small 8 63–7 [23] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and Kis A 2011 Single-layer MoS2 transistors Nat Nanotechnol 6 147–50 [24] Huo N, Yang S, Wei Z, Li S S, Xia J B and Li J 2014 Photoresponsive and gas sensing field-effect transistors based on multilayer WS2 nanoflakes Sci Rep 4 5209 [25] Zhao S, Xue J and Kang W 2014 Gas absorption on MoS2 monolayer from first-principles calculations Chem Phys Lett 595–596 35–42 the O–O bond can be cleaved with a barrier height of 2.23 eV on the WS2 surface Acknowledgments The authors thank the National Foundation for Science and Technology Developments (NAFOSTED) for their financial support (Grant No 103.01–2013.28) References [1] Geim A K and Novoselov K S 2007 The rise of graphene Nat Mater 6 183–91 [2] Xu M, Liang T, Shi M and Chen H 2013 Graphene-like 2D materials Chem Rev 113 3766–98 [3] Kuc A, Zibouche N and Heine T 2011 Influence of quantum confinement on the electronic structure of the transition metal sulfide TS2 Phys Rev B 83 245213 [4] Ma Y, Dai Y, Guo M, Niu C, Lu J and Huang B 2011 Electronic and magnetic properties of perfect vacancydoped and nonmetal absorbed MoSe2, MoTe2 and WS2 monolayers Phys Chem Chem Phys 13 15546–53 [5] Kośmider K and Fernández-Rossier J 2013 Electronic properties of the MoS2–WS2 heterojunction Phys Rev B 87 075451 [6] Wilson J A and Yoffe A D 1969 The transition metal dichalcogenides: discussion and interpretation of the observed optical electrical and structural properties Adv Phys 18 193–335 [7] Coleman J N et al 2011 2D nanosheets produced by liquid exfoliation of layered materials Science 331 568–71 [8] Wang Q H, Kalantar-Zadeh K, Kis A, Coleman J N and Strano M S 2012 Electronics and optoelectronics of 2D transition metal dichalcogenides Nat Nanotechnol 7 699–712 [9] Gordon R, Yang D, Crozier E, Jiang D and Frindt R 2002 Structures of exfoliated single layers of WS2, MoS2 and MoSe2 in aqueous suspension Phys Rev B 65 125407 [10] Gong K, Zhang L, Liu D, Liu L, Zhu Y, Zhao Y and Guo H 2014 Electric control of spin in monolayer WSe2 field effect transistors Nanotechnology 25 435201 [11] Tawinan C and Lambrecht W R L 2012 Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS2 Phys Rev B 85 205302 10 V Q Bui et al J Phys.: Condens Matter 27 (2015) 305005 [26] Yue Q, Shao Z, Chang S and Li J 2013 Absorption of gas molecules on monolayer MoS2 and effect of applied electric field Nanoscale Res Lett 8 425 [27] Kou L, Du A, Chen C and Frauenheim T 2014 Strain engineering of selective chemical absorption on monolayer MoS2 Nanoscale 6 5156–61 [28] Anisimov V I and Gunnarsson O 1991 Density-functional calculation of effective Coulomb interactions in metals Phys Rev B 43 7570–4 [29] Anisimov V I, Zaanen J and Andersen O K 1991 Band theory and Mott insulators: Hubbard U instead of Stoner I Phys Rev B 44 943–54 [30] Anisimov V I, Solovyev I V and Korotin M A 1993 Densityfunctional theory and NiO photoemission spectra Phys Rev B 48 16929–34 [31] Anisimov V I, Aryasetiawan F and Lichtenstein A I 1997 First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method J Phys.: Condens Matter 9 767–808 [32] Solovyev I V and Dederichs P H 1994 Corrected atomic limit in the local-density approximation and the electronic structure of d impurities in Rb Phys Rev B 50 16861–71 [33] Cococcioni M and de Gironcoli S 2005 Linear response approach to the calculation of the effective interaction parameters in the LDA + U method Phys Rev B 71 035105 [34] Perdew J P, Burke K and Ernzerhof M 1996 Generalized gradient approximation made simple Phys Rev Lett 77 3865–8 [35] Perdew J P, Burke K and Ernzerhof M 1997 Generalized gradient approximation made simple Phys Rev Lett 78 1396 [36] Kresse G 1996 Efficient iterative schemes for ab initio totalenergy calculations using a plane-wave basis set Phys Rev B 54 11169–86 [37] Kresse G and Furthmüller J 1996 Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set Comput Mater Sci 6 15–50 [38] Grimme S 2006 Semiempirical GGA-type density functional constructed with a long-range dispersion correction J Comput Chem 27 1787–99 [39] Barone V, Casarin M, Forrer D, Pavone M, Sambi M and Vittadini A 2009 Role and effective treatment of dispersive forces in materials: polyethylene and graphite crystals as test cases J Comput Chem 30 934–9 [40] Blöchl P E 1994 Projector augmented-wave method Phys Rev B 50 17953–79 [41] Dion M, Rydberg H, Schröder E, Langreth D C and Lundqvist B I 2004 Van der Waals density functional for general geometries Phys Rev Lett 92 246401 [42] Klimeš J, Bowler D R and Michaelides A 2011 Van der Waals density functionals applied to solids Phys Rev B 83 195131 [43] Vanderbilt D 1990 Soft self-consistent pseudopotentials in a generalized eigenvalue formalism Phys Rev B 41 7892–5 [44] Giannozzi P et al 2009 QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials J Phys.: Condens Matter 21 395502 [45] Shanno D F 1985 An example of numerical nonconvergence of a variable-metric method J Optim Theory Appl 46 87–94 [46] Perdew J P, Chevary J A, Vosko S H, Jackson K A, Pederson M R, Singh D J and Fiolhais C 1992 Atoms, molecules, solids and surfaces: applications of the generalized gradient approximation for exchange and correlation Phys Rev B 46 6671–87 [47] Perdew J P, Chevary J A, Vosko S H, Jackson K A, Pederson M R, Singh D J and Fiolhais C 1993 Erratum: Atoms, molecules, solids and surfaces: applications of the generalized gradient approximation for exchange and correlation Phys Rev B 48 4978 [48] Henkelman G, Arnaldsson A and Jónsson H A 2006 Fast and robust algorithm for bader decomposition of charge density Comput Mater Sci 36 354–60 [49] Sanville E, Kenny S D, Smith R and Henkelman G 2007 Improved grid-based algorithm for bader charge allocation J Comput Chem 28 899–908 [50] Tang W, Sanville E and Henkelman G A 2009 Grid-based bader analysis algorithm without lattice bias J Phys Condens Matter 21 084204 [51] Momma K and Izumi F 2011 VESTA for 3D visualization of crystal volumetric and morphology data J Appl Crystallogr 44 1272–6 [52] Sheppard D, Terrell R and Henkelman G 2008 Optimization methods for finding minimum energy paths J Chem Phys 128 134106 [53] Blanksby S J and Ellison G B 2003 Bond dissociation energies of organic molecules Acct Chem Res 36 255–63 11 ... good consistency with each other in terms of absorption stability and band gap estimations Van der Waals density functional (vdW-DF) calculations are also performed to validate longrange gas molecule? ?WS2. .. utilization of the Hubbard Hamiltonian does not seem to broaden the band gap of WS2 as expected As we also discover in the later examination of band structures when gas absorptions take place,... effects of gas molecules (CO, H2O, NO, and O2) absorbing on the WS2 surface and evaluate the pictorial insights of electronic structures based on data derived from first-principles 2.  Computational