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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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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
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: and
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

1

© 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 do 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.
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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 2 − 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)
2 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 1 − 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.

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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 0.

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.
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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  1. 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
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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
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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
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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.
8


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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 2 in the conduction regions. Overall, the GGA + U calculations do not seem to
improve the electronic gaps of WS2 as we have expected.
9


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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 3 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

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