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

Van der Waals density functional vdW-DF calculations are also performed to validate long-range gas molecule–WS2 monolayer interactions, and the resultant absorption energies of four gas-

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A first-principles investigation of various gas (CO, H2O, NO, and O2) absorptions on a WS2 monolayer: stability and electronic properties

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2015 J Phys.: Condens Matter 27 305005

(http://iopscience.iop.org/0953-8984/27/30/305005)

1 Introduction

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 compo-nents Among the new advanced materials, 2D structures are considered as a breakthrough with ultrathin size and amazing

electronic characteristics, which potentially open up vast applications in electronic and spintronic devices, nanomag-netic equipments, and gas sensors

2D lattices with similar geometry and properties to gra-phene [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

Journal of Physics: Condensed Matter

A first-principles investigation of various

properties

Viet Q Bui1, Tan-Tien Pham1, Duy A Le1, Cao Minh Thi1,2 and Hung M Le3,4

1 Department of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam

2 Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City, Vietnam

3 Computational Chemistry Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

4 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 long-range 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)

V Q Bui et al

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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

min-imum 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

valence-band maximum (VBM), thereby causing a change in its valence-band

gap [13, 14] With these interesting features, WS2 is a

prom-ising semiconducting material for applications in electronic

devices

The 1D carbon materials used in field-effect transistor

(FET) technology applied to gas sensors exhibit more

advan-tages than classical semiconductive materials [15–18] With a

limited surface area, the absorbed gas molecules do not cause

significant electrical noise or thresholds for detection In terms

of chemical reactions, the graphite surface was found to

pos-sess 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

remark-able 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 I Ion off/

at room temperature was approximately 106 Furthermore,

Radisavljevic and coworkers [23] were successful in

synthe-sizing MoS2 FETs with similar characteristics to graphene

nanoribbons, and the reported mobility was at least 200 cm2

V−1 S−1, while I Ion off/ reached approximately 108 at room

tem-perature These important achievements are very promising

and open up a huge potential in electronic applications,

espe-cially 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

elec-tronic structures based on data derived from first-principles

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 func-tion theory (DFT) within local density approximafunc-tion (LDA) However, we are aware that as a matter of computation for most semiconducting materials, employing DFT is not accu-rate 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 modi-fied 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

2 Computational methods

2.1 Computational details

As previously mentioned, we investigate the electronic proper-ties 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

cal-culation sets, the GGA(PBE) and GGA(PBE) + U calcal-culations

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 addi-tion, spin polarization is also considered in our first-principles calculations to explore various spin alignments, which may lead to interesting magnetic features

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The relaxations of ions and lattice vectors are attained by

adopting the conjugate gradient algorithm in VASP For QE

cal-culations, 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

com-plexes, 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:

∑

υ

σ

,

(1)

where E υ is the Hubbard correction term and n Iσ is the electron

occupation at site I with spin σ The effective value of U can

be determined as

= ℵ − ℵ− −

U 01 1,

(2)

where ℵ =∂α∂n

0 KS and ℵ = ∂∂α n 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

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-inde-pendent; 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 inter-action 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 5dz2, 5dxy, and 5dx2−y2 subshells are highly distributed con-tiguously 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 supplemen-tary 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

absorp-tions 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 con-figuration 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:

Ead EWS 2 Egas Etotal,

(3) where EWS2 and Egas are the total energies of a periodic WS2 layer and an isolated gas molecule in vacuum, while Etotal is the total energy of the optimized complex

Figure 1. The non-interacting ( ℵ 0 ) and interacting ( ℵ ) linear

response curves of 5d electron occupations versus α.

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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

cor-responding absorption energies given by PBE and PBE + U

cal-culations 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

investi-gated 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

elec-tronic structure properties of WS2 significantly In addition,

we also study the charge transfer from WS2 to the CO

mol-ecule 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

com-ponents, 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 configura-tions of absorbed gas molecules

In the CO case, we recall that the natural electronega-tivity 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 posi-tive charge of +0.0078, smaller than that reported in two pre-vious 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:

Δ = AB− − ,A B

(4) where ρAB, ρA, and ρB 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

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 0.

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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

con-figurations 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 1 At the same time, the DOS interpretation shows that H2O contributes localization at the low level of the val-ance band (figures 4(b) and (c)); therefore, the H2O absorp-tion 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

Figure 3. Absorption configurations (including top and side views) of (a) CO, (b) H 2 O (1) , (c) H 2 O (2) , (d) NO, (e) O( )2 , (f) O( )2, and (g) O( )2 .

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

Calculation method

( )

( )

( )

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V Q Bui et al

two H2O absorption cases In the H2O(1) 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

contribu-tion of this electron spin polarizacontribu-tion 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

ren-ders 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),

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 configu-rations that O2 constitutes an occupation level in the restricted

Figure 4. Total DOS, PDOS for W, S, and gas for the absorption cases: (a) CO, (b) H 2 O (1) , and (c) H2O (2)

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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

calcula-tion 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

conduc-tion 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

posi-tive sign of good charge transferability In table 3, we

sum-marize 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

struc-ture evidence from interpreting DOS (shown in figure 7(c)),

the overlapping of O, W, and S reduces the band gap of WS2 to

about 1.36 eV In addition, the Bader charge analysis indicates that O is a charge acceptor receiving even more than one elec-tron (−1.050) Interestingly enough, this unstable configura-tion 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 rec-ognize 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 com-putational 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

exchange-correlation effect for WS2 is already well described by the

con-ventional PBE calculation; therefore, the introduction of U is

not obligated for improving band-structure quality In terms of

Figure 5. The isoface plots of charge density difference for (a) CO, (b) H 2 O (1) , (c) H 2 O (2) , (d) NO, (e) O( )2 , (f) O( )2, and (g) O( )2 on the WS 2 surface (with isovalue varied from ±0.0001 to ±0.0004e − ) Charge accumulation and depletion are represented by the red and green plots, respectively.

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stability analysis, we observe that the absorption energies arising

from GGA + U calculations are no different from those

corre-sponding quantities reported by GGA, as summarized in table 1

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 elec-trons 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-con-sistency 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 calcula-tions are higher than those given by the same VASP calculacalcula-tions with percent differences varying in the range of 4–24%

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

(with D2 empirical corrections) in VASP for all gas absorption

models The configurations are identified consistently with the

nomenclature given in figure  3

( )

( )

( )

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V Q Bui et al

When we make comparisons with GGA, GGA + U does not

seem to have an effect on the correlation of the W site in

con-junction 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 5dz2 in the

conduc-tion regions Overall, the GGA + U calculaconduc-tions do not seem to

improve the electronic gaps of WS2 as we have expected

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

calcula-tions (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

utili-zation 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 with-draw 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 reac-tion 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( )2, (b) O( )2 , and

(c) O( )2 with data obtained from PBE-D2.

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 − ) Magnetization (μB )

( )

( )

( )

J Phys.: Condens Matter 27 (2015) 305005