materials
Article
First Principles Study on the Interaction Mechanisms
of Water Molecules on TiO2 Nanotubes
Jianhong Dai and Yan Song *
School of Materials Science and Engineering, Harbin Institute of Technology at Weihai, 2 West Wenhua Road,
Weihai 264209, China; [email protected]
* Correspondence: [email protected]; Tel.: +86-631-568-7157
Academic Editor: Walid Daoud
Received: 30 October 2016; Accepted: 8 December 2016; Published: 16 December 2016
Abstract: The adsorption properties of water molecules on TiO2 nanotubes (TiO2 NT) and the
interaction mechanisms between water molecules are studied by first principles calculations.
The adsorption preferences of water molecules in molecular or dissociated states on clean and
H-terminated TiO2 NT are evaluated. Adsorption of OH clusters on (0, 6) and (9, 0) TiO2 nanotubes
are first studied. The smallest adsorption energies are −1.163 eV and −1.383 eV, respectively,
by examining five different adsorption sites on each type of tube. Eight and six adsorption sites
were considered for OH adsorbtion on the H terminated (0, 6) and (9, 0) nanotubes. Water molecules
are reformed with the smallest adsorption energy of −4.796 eV on the former and of −5.013 eV
on the latter nanotube, respectively. For the adsorption of a single water molecule on TiO2 NT,
the molecular state shows the strongest adsorption preference with an adsorption energy of −0.660 eV.
The adsorption of multiple (two and three) water molecules on TiO2 NT is also studied. The calculated
results show that the interactions between water molecules greatly affect their adsorption properties.
Competition occurs between the molecular and dissociated states. The electronic structures are
calculated to clarify the interaction mechanisms between water molecules and TiO2 NT. The bonding
interactions between H from water and oxygen from TiO2 NT may be the reason for the dissociation
of water on TiO2 NT.
Keywords: TiO2 nanotube; water adsorption; first principles
1. Introduction
The demands of energy and the control of environment pollution are factors that inspire us
to develop clean and renewable energy sources. Hydrogen is one of the most promising energy
carriers due to its high energy density and zero pollution. However, the production of hydrogen
with low cost still hinders its application as an energy carrier. Splitting of water on photocatalysts
with solar energy is a desirable way to produce hydrogen without pollution and with low-cost.
Honda and Fujishima proved photocatalytic hydrogen production from water and demonstrated the
decomposition concept using a photo-electrochemical cell [1]. Many studies have been reported in
the literature since their pioneering work. Many photocatalysts have been subsequently developed
with high quantum efficiency for water splitting under UV and visible light illumination [2–4], such as
Pt loaded TiO2 particle system [5], Au/TiO2 [6], platinized SrTiO3 single crystals coated with films
of NaOH [7], RuO2 /TiO2 [8] and NiO/SrTiO3 [9], BaTiO4 loaded with RuO2 [10], K4 Nb6 O17 [11],
and so on. However, photocatalysts with sufficient band gap positions and high chemical stability for
practical applications are still under development. With strongly catalytic activity and high stability,
TiO2 based semiconductors are one of the promising photocatalysts for water-splitting.
The photogenerated electron-hole pairs of TiO2 react with water and produce hydrogen under
illumination. However, the hydrogen production rate is hindered by the quick charge recombination
Materials 2016, 9, 1018; doi:10.3390/ma9121018
www.mdpi.com/journal/materials
Materials 2016, 9, 1018
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and backward reaction [12]. The hydrogen production efficiency is affected by many factors, such as
the incorporating of dopants or other materials that affect charge separation and light harvesting [13].
Generally, the photoactivity of cation-doped titania will be decreased due to the increasing
recombination of the photoexcited electron–hole pairs [14]. Nowadays, several photocatalysts have
been developed. The metal Ag can enhance the hydrogen production using low-energy UV lamps
and maintain the hydrogen production of activity-modified TiO2 [15]. The Ni, Pd, and Pt can
significantly improve the photocatalytic production of H2 from water [16]. The metal oxides, such as
Ni2 O3 and CuO, are also utilized due to their unique plasmon absorption properties using visible
light photo-catalysis [17]. Most recently, the photocatalytic activity of Au@Void@TiO2 yolk-shell
nanostructures were investigated, in which the thicker and bigger shells displayed higher activity of
H2 production [18]. For catalysts of TiO2 in splitting water, one of the important issues is to understand
the interaction mechanisms between water molecules and the TiO2 surface in order to improve the
photocatalytic activity of TiO2 . Many works have studied the interactions between a water molecule
and the TiO2 surface [19–30]. It was shown experimentally that water molecules mainly adsorb on
the clean TiO2 (110) surface with a small amount of dissociations [19–21]. Controversies exist in the
adsorption pathways of water molecules on a TiO2 surface under theoretical works. The selections of
the coverage of water molecules, slab depth, and even the calculation methods can affect the calculation
results [22–29]. Furthermore, defects and impurities greatly affect the hydrolysis efficiency on TiO2 .
The load of Au and Pt can greatly decrease the dissociation barrier of water on TiO2 and therefore
promote hydrolysis efficiency [30].
The water molecule prefers to adsorb on the top of a five-fold coordinated Ti site with a clean rutile
TiO2 (110) surface with an adsorption energy of 0.92 eV under 1 ML (Mono-Layer) coverage, which is
0.14 eV higher than that of dissociated state [21,31,32]. However, the estimated adsorption energy of
water on TiO2 by density functional theory (DFT) calculations is sensitive to the parameters used in the
DFT calculations, which may be the origin of the discrepancy between different works. The adsorption
of water on TiO2 , especially in the dissociated state, can be significantly enhanced by the presence
of fourfold coordinated Ti atoms at the step edge of the surface, due to the easy transfer of charge
from the water molecule to the TiO2 [31]. The photocatalytic properties of TiO2 can be affected by the
adsorption of hydroxyl, and thus it is important to understand the interaction mechanisms between
the water/hydroxyl and the TiO2 surface [33]. There are a variety of distributions of OH groups due
to the influence of complex adsorption states of water molecules. Two types of hydroxyls are found
to adsorb on the TiO2 surface, which could be classified as thermally unstable and thermally stable
(isolate hydroxyl groups) in terms of thermostability [33–36]. The adsorption bands of these hydroxyls
are greatly affected by the crystal structure of TiO2 and the evacuation temperature. The hydroxyls
play different roles in the photo-oxidation process [33], but the chemical environment of hydroxyls on
the TiO2 surface are still deficient.
Water can adsorb on the TiO2 surface in molecular and dissociated states, and therefore,
different hydroxyl clusters can be formed [37]. Herman et al. reported the adsorption of water
on the anatase TiO2 (101) surface in a molecular state [38], and observed three desorption states in
the Temperature Programmed Desorption (TPD) spectra of the multilayer water, adsorbing in sites
of 2-fold-coordinated O and 5-fold-coordinated Ti. Some theoretical calculations are consistent with
the above experiments in that the water molecule adsorbs in a molecular state on the (101) surface
of anatase TiO2 [39], but it will be dissociated on the (001) surface [40,41]. Some theoretical works
predicted that water molecules adsorb in rutile TiO2 surface in the dissociated state, and the OH group
is bonded in the two-coordinated O and five-coordinated Ti sites [42]. The adsorption states are also
affected by the defects in the surface of TiO2 . One O vacancy can capture two OH groups [43,44].
The Highest Occupied Molecular Orbital (HOMO) of the dissociated water on the TiO2 (101) surface is
0.1 eV higher than that of the molecular state. Therefore, the dissociated state of water on the TiO2 has
higher photocatalytic activity than that of the undissociated water [45]. Furthermore, the adsorption
energy of a water molecule on a rutile TiO2 (110) surface is only slightly affected by the relative sites
Materials 2016, 9, 1018
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and orientations of the water molecule. There are repulsive interactions between neighboring OH
groups, causing a decrease of the adsorption energy per H atom from 0.56 eV for isolated OH groups
to 0.40 eV for neighboring OH pairs. The twofold-coordinated O is the preferred adsorption site even
as the coverage increases up to 1 ML [29].
Due to the large surface area and high efficiency of photocatalytic reactions, TiO2 nanotubes
(TiO2 NT) have been attracted great attention since they were discovered in 1996 [46]. The solar water
splitting activity of TiO2 NT increases monotonously with the porosity rather than the wall thickness
and/or inner diameter [47]. Theoretical calculations show that the formation of OH is the rate-limiting
step for the dissociation of the first water molecule on TiO2 nanotube arrays [48]. The adsorption
of water on TiO2 NT is exothermic in both the molecular and dissociated states, and the molecular
adsorption is energetically more favorable [49]. However, the influence of interactions between water
molecules on adsorption states of water molecules are still not well understood. The adsorption
properties of several water molecules on the TiO2 NT are studied in the present work by first principles
calculations. The methods used in this paper are briefly described in Section 2, and the results are
presented in Section 3. Conclusions are summarized in Section 4.
2. Methodology and Models
The (n, 0) and (0, m) of nanotubes are rolled by the anatase (101) sheet along the [101] and
[010] directions, respectively [50]. The numbers of n and m denote the supercell size of the sheet.
The sizes of the simulated boxes of the (n, 0) and (0, m) nanotubes (where n = 6 and 9, and m = 3
and 6) are 30.0 × 30.0 × 10.210 Å3 and 30.0 × 30.0 × 3.776 Å3 , respectively [51]. The Vienna ab initio
simulation package (VASP) was employed to relax the ions and evaluate the total energy and electronic
structures [52,53] with PAW(Projector-Augmented Wave)-GGA (Generalized Gradient Approximation)
potential [54]. The self-consistent convergences of the total energy difference and forces are chosen as
0.01 meV and 0.01 eV/Å, respectively. All ions of the TiO2 nanotube and adsorbates (water molecule
and OH cluster) are allowed to relax to obtain the stable adsorption configurations. The distance
between neighboring nanotubes is verified to avoid the interactions between them. The energy cutoff
is 400 eV, and 1 × 1 × 2 and 1 × 1 × 8 k-meshes were chosen for the (6, 0) and (0, 3) nanotubes,
respectively, to ensure accuracy.
3. Results and Discussion
The adsorption energies of the water molecule and OH cluster on TiO2 NT are evaluated via the
following definition:
Eads = Ent+a − Ent − Ea
(1)
where Ent+a and Ent denote the total energies of the adsorbed water/hydroxyl and clean TiO2 NTs,
respectively. The Ea is the total energy of the adsorbate (water molecule or OH cluster) evaluated using
a 1.0 nm × 1.0 nm ×1.0 nm cell.
3.1. Adsorption of OH on the Clean TiO2 NT
The adsorption of OH on TiO2 NT was studied. Five adsorption sites, at the inner ring (labeled as
“1” and “4”) and the outer ring (labeled as “2” and “3”), and in the center of the tube (labeled as “5”)
are considered as shown in Figure 1a,b. Their adsorption energies are listed in Table 1. For the (0, 6)
nanotube, the OH prefers to locate at site “3” and saturates the closest Ti atom after full relaxation with
an adsorption energy of −1.163 eV, as shown in Figure 1c. The distance between the oxygen of the
OH cluster and its closest Ti atom is 1.915 Å. One Ti atom was dragged out about 0.4 Å by the OH
cluster. For the (9, 0) nanotube, the adsorption of the OH cluster also had negative adsorption energy.
The most stable adsorption of OH cluster was at site “5” with an adsorption energy of −1.383 eV,
and the distance between the OH cluster and the closest Ti atom was 2.111 Å, as shown in Figure 1d.
Therefore, the OH cluster was strongly adsorbed on the nanotube by saturating the five-fold Ti ions.
Materials 2016, 9, 1018
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(a)
(b)
(c)
(d)
Figure1.1. The
Theadsorption
adsorption sites
sites of
ofOH
OHon
onthe
theTiO
TiO2nanotube.
nanotube. (a)
(a) The
The initial
initial adsorption
adsorption sites
sites of
of OH
OH on
on
Figure
2
the
(0,
6);
and
(b)
(9,
0)
nanotube,
respectively;
(c)
the
most
stable
adsorption
sites
of
OH
on
the
(0,
6)
the (0, 6); and (b) (9, 0) nanotube, respectively; (c) the most stable adsorption sites of OH on the (0, 6)
nanotube
after
full
relaxations
and
(d)
(9,
0)
nanotube,
respectively.
The
blue,
red,
and
white
balls
nanotube after full relaxations and (d) (9, 0) nanotube, respectively. The blue, red, and white balls
denotethe
theTi,
Ti,O,
O,and
andH
Hatoms,
atoms,respectively.
respectively.
denote
Table 1. The adsorption energy of the OH cluster on/in the (0, 6) and (9, 0) nanotubes (eV).
Table 1. The adsorption energy of the OH cluster on/in the (0, 6) and (9, 0) nanotubes (eV).
Adsorption Sites
Adsorption
Sites
1
1
2
2
3
3
4
4
5
5
Eads (eV) on (0, 6)
Eads −0.961
(eV) on (0, 6)
−0.961
−0.904
−0.904
−1.163
−1.163
5.007
5.007
0.104
0.104
Eads (eV) on (9, 0)
Eads (eV) on
(9, 0)
−0.883
−0.883
−1.151
−1.151
−1.150
−1.150
−0.388
−0.388
−1.383
−1.383
3.2. Adsorption
Adsorption of
of OH
OH on
on the
the Hydrogen
HydrogenTerminated
TerminatedTiO
TiO2NT
NT
3.2.
2
The dissociation
dissociationof
of water
water will
will produce
produceOH
OHand
andH
Hgroups.
groups. Thus
Thus the
the adsorption
adsorption properties
properties of
of the
the
The
OH
group
on
the
H
terminated
nanotubes
were
further
studied
to
clarify
the
interactions
between
OH group on the H terminated nanotubes were further studied to clarify the interactions between the
the group
OH group
and
on NT.
TiO2Eight
NT. Eight
andsites
six were
sites were
considered
the adsorptions
theonOH
OH
and H
onHTiO
and six
considered
for thefor
adsorptions
of the of
OH
H
2
on
H
terminated
(0,
6)
and
(9,
0)
nanotubes,
respectively.
Figure
2
shows
the
initial
adsorption
terminated (0, 6) and (9, 0) nanotubes, respectively. Figure 2 shows the initial adsorption sites,sites,
and
and their
adsorption
energies
full relaxations
are listed
in Table
For(0,
the6)(0,
6) nanotube,
the
their
adsorption
energies
after after
full relaxations
are listed
in Table
2. For2.the
nanotube,
the OH
OH
cluster
has
negative
adsorption
energy
at
all
considered
adsorption
sites
(around
−4.0
eV
except
cluster has negative adsorption energy at all considered adsorption sites (around −4.0 eV except at
at site
“8”).
most
stable
adsorption
configuration
is when
the
OH cluster
on thering
outer
site
“8”).
TheThe
most
stable
adsorption
configuration
is when
the OH
cluster
adsorbsadsorbs
on the outer
of
ring
of
the
H
terminated
(0,
6)
nanotube,
connecting
its
O
atom
with
the
H
atom
in
the
TiO
2NT,
the H terminated (0, 6) nanotube, connecting its O atom with the H atom in the TiO2 NT, forming a
forming aHO–H
water-like
HO–H
a bond
length
and angle
between
the OH H
and
H of
water-like
group
with agroup
bondwith
length
and angle
between
the OH
and surfacial
of surfacial
the nanotube
the
nanotube
of
1.021
Å
and
105.8°,
as
shown
in
Figure
3a.
However,
the
OH
cluster
at
site
“8”
is
of 1.021 Å and 105.8◦ , as shown in Figure 3a. However, the OH cluster at site “8” is located at the
locatedofatthe
thesimulated
corner of cell
the simulated
cellcontact
and does
contact the
The
adsorption
energy
corner
and does not
thenot
nanotube.
Thenanotube.
adsorption
energy
of −0.777
eV
of
−0.777
eV
may
originate
from
the
calculation
error
of
the
energy
of
the
OH
cluster,
and
this
error
may originate from the calculation error of the energy of the OH cluster, and this error can be ignored
can
be ignored
in terms
of the large
adsorption
energy
of in
theother
OH cluster
in other
For the (9,
0)
in
terms
of the large
adsorption
energy
of the OH
cluster
sites. For
the (9,sites.
0) nanotube,
the
nanotube,
the
OH
cluster
at
site
“6”
shows
the
largest
adsorption
energy,
indicating
the
strong
OH cluster at site “6” shows the largest adsorption energy, indicating the strong bonding interactions
bonding
thenanotube.
OH clusterThe
with
the nanotube.
The strongest
adsorption
the“5”
OH
occurs
of
the OHinteractions
cluster withofthe
strongest
adsorption
of the OH
occurs at of
site
with
an
at
site
“5”
with
an
adsorption
energy
of
−5.013
eV.
At
site
“5”,
the
OH
cluster
is
initially
located
at
adsorption energy of −5.013 eV. At site “5”, the OH cluster is initially located at the center of the
the center of the nanotube (Figure 2b), and moves toward the inner surface, forming a bond with the
H atom on TiO2NT with its O atom with a bond length of 1.052 Å and a H–O–H angle of 109.5°. A
Materials 2016, 9, 1018
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nanotube (Figure 2b), and moves toward the inner surface, forming a bond with the H atom on TiO2 NT
Materials 2016, 9, 1018
5 of 14
Materials
2016,
9, 1018
5 ofis14
with
its O
atom
with a bond length of 1.052 Å and a H–O–H angle of 109.5◦ . A water molecule
therefore
formedis(Figure
3b).formed
Comparing
the3b).
adsorption
energies
of OH on clean
andofHOH
terminated
water molecule
therefore
(Figure
Comparing
the adsorption
energies
on clean
water molecule is therefore formed (Figure 3b). Comparing the adsorption energies of OH on clean
TiO
NTs,
one
can
find
that
the
difference
of
adsorption
energy
is
mainly
caused
by
the
formation
of
and2 H terminated TiO2NTs, one can find that the difference of adsorption energy is mainly caused
and H terminated TiO2NTs, one can find that the difference of adsorption energy is mainly caused
the
water
molecule.
The
H
termination
can
greatly
affect
the
adsorption
ability
of
OH
on
the
surface
by the formation of the water molecule. The H termination can greatly affect the adsorption abilityof
of
by the formation of the water molecule. The H termination can greatly affect the adsorption ability of
the
nanotube,
and
therefore,
the
water-dissociation
efficiency
will
be
limited
in
a
H-rich
environment
OH on the surface of the nanotube, and therefore, the water-dissociation efficiency will be limited in
OH on the surface of the nanotube, and therefore, the water-dissociation efficiency will be limited in
due
to combinations
of due
OH to
and
H clusters atofthe
surface
the TiOat
2 NT.
a H-rich
environment
combinations
OH
and Hofclusters
the surface of the TiO2NT.
a H-rich environment due to combinations of OH and H clusters at the surface of the TiO2NT.
(a)
(a)
(b)
(b)
Figure2.2.The
The initialadsorption
adsorption sitesof
of OHon
on theH
H terminatedTiO
TiO2nanotube.
nanotube. (a) (0,
(0, 6) and
and (b) (9,
(9, 0).
Figure
Figure 2. Theinitial
initial adsorptionsites
sites ofOH
OH onthe
the Hterminated
terminated TiO
(a) (0,6)
6) and(b)
(b) (9,0).
0).
2 2 nanotube.(a)
The
blue,
red,
and
white
balls
denote
the
Ti,
O,
and
H
atoms,
respectively.
The
Theblue,
blue,red,
red,and
andwhite
whiteballs
ballsdenote
denotethe
theTi,Ti,O,O,and
andHHatoms,
atoms,respectively.
respectively.
(a)
(a)
(b)
(b)
Figure 3. The most stable adsorption sites of OH on the TiO2 nanotube after full relaxations; (a) (0, 6);
nanotubeafter
afterfull
fullrelaxations;
relaxations;(a)
(a)(0,
(0,6);
6);
Figure 3.The
Themost
moststable
stableadsorption
adsorptionsites
sitesofofOH
OHon
onthe
the TiO2nanotube
Figure
2 and H atoms,
and (b)3.(9,
0). The blue,
red, and white
balls denote
the TiO
Ti, O,
respectively.
and
(b)
(9,
0).
The
blue,
red,
and
white
balls
denote
the
Ti,
O,
and
H
atoms,
respectively.
and (b) (9, 0). The blue, red, and white balls denote the Ti, O, and H atoms, respectively.
Table 2. The adsorption energy, Eads, of the OH cluster on the H terminated TiO2 nanotube (eV).
theOH
OHcluster
clusteron
onthe
theHHterminated
terminatedTiO
TiO2nanotube
nanotube(eV).
(eV).
Table2.2.The
Theadsorption
adsorptionenergy,
energy,E Eads, ,ofofthe
Table
2
ads
Adsorption Site
(0, 6)
(9, 0)
Adsorption Site
(0, 6)
(9, 0)
1
−
4.490
−
Adsorption Site
(9, 0) −4.885
1
−4.490 (0, 6)
4.885
2
−
4.390 −4.490
−
4.943
1
−
4.885
2
−4.390
−4.943
3
−4.796 −4.390
2
−4.943 −−3.917
3
−4.796
3.917
3
−3.917 −4.332
4
−4.627 −4.796
4
−4.627
−4.332
4
−4.332 −5.013
5
−4.720 −4.627
5
−4.720 −4.720
5
−5.013 −5.013
6
−1.343
−4.207 −4.207
6
6
−1.343 −1.343
−4.207
7
–
−
4.096
7
–
7
–
−4.096 −4.096
8
–
−0.777 −0.777
8
–
8
–
−0.777
3.3.Adsorption
Adsorption of Wateron
on theClean
Clean TiO22NT
NT
3.3.
3.3. AdsorptionofofWater
Water onthe
the CleanTiO
TiO2NT
Theadsorption
adsorption configurationswere
were investigatedby
by comparingthe
the stabilityof
of a watermolecule
molecule
The
The adsorptionconfigurations
configurations wereinvestigated
investigated bycomparing
comparing thestability
stability ofaawater
water molecule
atdifferent
different adsorptionsites
sites of theTiO
TiO22NTs.
NTs. It was
was reported that
that theadsorption
adsorption energy of
of a water
at
at differentadsorption
adsorption sitesofofthe
the TiO
2NTs.It
It wasreported
reported thatthe
the adsorptionenergy
energy ofaawater
water
molecule
on
the
TiO
2
surface
was
almost
not
affected
by
the
relative
site
and
orientation
of
the water
molecule
TiO22 surface
surfacewas
wasalmost
almostnot
not
affected
relative
orientation
the
moleculeon
on the
the TiO
affected
by by
thethe
relative
site site
and and
orientation
of theofwater
[45]. Therefore, only several adsorption configurations of a water molecule on TiO2NT are considered
[45]. Therefore, only several adsorption configurations of a water molecule on TiO2NT are considered
in the present work. Because the influence of the radius of TiO2NT on the adsorption energy of a
in the present work. Because the influence of the radius of TiO2NT on the adsorption energy of a
water molecule is insignificant [48], only the adsorption properties of water molecules on the (0, 3)
water molecule is insignificant [48], only the adsorption properties of water molecules on the (0, 3)
and (6, 0) nanotubes were studied in the following calculations concerning the computation
and (6, 0) nanotubes were studied in the following calculations concerning the computation
Materials 2016, 9, 1018
6 of 14
water [45]. Therefore, only several adsorption configurations of a water molecule on TiO2 NT are
6 of 14
considered in the present work. Because the influence of the radius of TiO2 NT on the adsorption
energy of a water molecule is insignificant [48], only the adsorption properties of water molecules on
consuming. It was reported that the adsorption of single water molecules on TiO2NT was exothermic
the (0, 3) and (6, 0) nanotubes were studied in the following calculations concerning the computation
and energetically favorable [49]. We also obtained results that the adsorption energies of a single
consuming. It was reported that the adsorption of single water molecules on TiO2 NT was exothermic
water molecule on the (0, 3) and (6, 0) nanotubes were −0.660 eV and −0.662 eV, respectively.
Table 3
and energetically favorable [49]. We also obtained results that the adsorption energies of a single water
shows the adsorption energies of different amounts of water molecules in molecular and dissociated
molecule on the (0, 3) and (6, 0) nanotubes were −0.660 eV and −0.662 eV, respectively. Table 3 shows
states (denoted as M and D, respectively) on the (0, 3) and (6, 0) nanotubes.
the adsorption energies of different amounts of water molecules in molecular and dissociated states
(denoted Table
as M and
D,adsorption
respectively)
on the
(0, 3) molecules
and (6, 0)on
nanotubes.
3. The
energies
of water
the (0, 3) and (6, 0) nanotubes (eV).
Materials 2016, 9, 1018
Adsorption
Adsorption
on
Adsorption
Table 3. The adsorption energies
of water molecules
on the (0, 3) and
(6, 0) nanotubes (eV).
Eads (eV)
Eads (eV)
Eads
on (0, 3)
1 × 1 × 3 (0, 3)
on (6, 0)
Adsorption
Adsorption
Adsorption
on −0.660
1M-1
3S-2M-1 on
2M-1 on
−1.083
Eads
(eV)
E−1.128
Eads (eV)
ads
(6,
0)
1
×
1
×
3
(0,
3)
(0,
3)
1M-2
−0.605
3S-2M-2
−0.887
2M-2
−1.055
1M-1
−0.660
3S-2M-1
−−0.964
1.128
2M-1
−
1.083
1M-3
−0.605
3S-2M-3
2M-3
−1.054
1M-2
−
0.605
3S-2M-2
−
0.887
2M-2
−
1.055
1M-4
−0.414
3S-1M-1D
−4.545
2M-4
−1.271
1M-3
−0.605
3S-2M-3
−0.964
2M-3
−1.054
1M-5
−0.411
3S-3M-1
2M-5
−1.272
1M-4
−0.414
3S-1M-1D
−−1.294
4.545
2M-4
−
1.271
3S-3M-2
2M-6
−1.272
1M-5
−0.411
3S-3M-1
−−1.838
1.294
2M-5
−
1.272
3S-3M-2
−−5.430
1.838
2M-6
−
1.272
3S-2M-1D-1
2M-7
−1.277
3S-2M-1D-1
−−5.296
5.430
2M-7
−
1.277
1D
−4.086
3S-2M-1D-2
1M
−0.662
3S-2M-1D-2
−5.296
1M
−0.662
−4.086
1D
1D
−4.067
1D
−4.067
3S-2M-1D-3
−−5.264
5.264
3S-2M-1D-3
1M-1D
−4.693
1M-1D
−
4.693
The
symbols
themolecular
molecular
and
dissociated
states
of water,
respectively.
The numbers
The
symbolsM
Mand
and D
D denote
denote the
and
dissociated
states
of water,
respectively.
The numbers
before
and after
“M”
“D”
indicate
the number
water molecules
the adsorption
respectively.
before
and the
after
theand
“M”
and
“D” indicate
theofnumber
of water and
molecules
and thesite,
adsorption
site,
The symbol 3S
means
the adsorption
of water
on the 1 of
× water
1 × 3 supercell
nanotube. of (0, 3) nanotube.
respectively.
The
symbol
3S means the
adsorption
on the 1of
× 1(0,×3)
3 supercell
For the adsorption
adsorption of a single water molecule on the (0, 3) nanotube, five adsorption sites were
considered as shown in Figure 4, and the calculated adsorption energies are listed in Table 3. The five
sites have similar adsorption energies, varying in a 0.2 eV energy
energy range.
range. The smallest adsorption
0.660eV
eVwith
with the
the relaxed
relaxed configuration
configuration shown
shown in
in Figure
Figure 5a. The
The oxygen
oxygen atom
atom of water
energy is −
−0.660
molecule saturates
saturates the
the five-fold
five-fold Ti, and the angle between H–O–H is slightly increased to 109.7°
109.7◦ by
molecule
To further study the stability of this
the attraction of the neighbouring oxygen atoms in the nanotube. To
adsorption configuration, the OH and H species of water molecules are initially separated as shown
in Figure 5b. After full relaxation, the OH and H species combinated together to the water molecule
(as shown
total
energy
of this
configuration
is almost
identical
to that
theofmost
shown in
inFigure
Figure5c)
5c)and
andthe
the
total
energy
of this
configuration
is almost
identical
to of
that
the
stablestable
adsorption
configuration.
This result
indicates
that the
single
prefers prefers
to adsorb
most
adsorption
configuration.
This result
indicates
that
the water
single molecule
water molecule
to
in the molecular
state compared
to the dissociated
mode on
the TiO
NT.TiO2NT.
adsorb
in the molecular
state compared
to the dissociated
mode
on 2the
(a)
(b)
(c)
(d)
(e)
Figure
Figure 4.
4. The
Theinitial
initial adsorption
adsorption sites
sites of
of water
water molecules
molecules on
on (0,
(0, 3)
3) TiO
TiO22nanotubes.
nanotubes. The
Theblue,
blue,red,
red,brown,
brown,
2NT, O in water, and H atoms, respectively. The indices of
and
white
balls
denote
the
Ti,
O
in
TiO
and white balls denote the Ti, O in TiO2 NT, O in water, and H atoms, respectively. The indices of (a–e)
(a–e)
denote
the different
adsorption
sites
of a water
molecule
the nanotube.
TiO2 nanotube.
denote
the different
adsorption
sites of
a water
molecule
on theon
TiO
2
Materials 2016, 9, 1018
Materials 2016, 9, 1018
Materials 2016, 9, 1018
7 of 14
7 of 14
7 of 14
(a)
(a)
(b)
(b)
(c)
(c)
nanotube. (a)
The
relaxed
Figure5.5.
The
configurations
ofaaawater
water
molecule
adsorbedon
onthe
the(0,
(0,3)
3)TiO
TiO22nanotube.
Figure
5.The
Theconfigurations
configurationsof
of
watermolecule
moleculeadsorbed
adsorbed
on
the
(0,
3)
TiO
(a)The
Therelaxed
relaxed
Figure
2 nanotube.(a)
molecular
state;
(b)
initial;
and
(c)
relaxed
configurations
of
dissociated
states.
The
blue,
red,
brown,
molecularstate;
state;(b)
(b)initial;
initial;and
and(c)
(c)relaxed
relaxedconfigurations
configurationsof
ofdissociated
dissociatedstates.
states.The
Theblue,
blue,red,
red,brown,
brown,
molecular
2NT, O in water, and H atoms, respectively.
and
white
balls
denote
the
Ti,
O
in
TiO
andwhite
whiteballs
ballsdenote
denotethe
theTi,
Ti, O
O in
in TiO
TiO22NT,
NT, O
O in
in water,
water, and H atoms, respectively.
and
In order
order to
to study
study the
the interactions
interactions between
between water
water molecules,
molecules, the
the
adsorption of
of
two and
and three
three
In
In
order
to
study
the
interactions
between
water
molecules,
the adsorption
adsorption
of two
two
and
three
watermolecules
moleculeswere
werestudied
studiedusing
usingaaa11××
×111××
×333supercell
supercell
of
the
(0,
3)
nanotube,
and
theadsorption
adsorption
water
water
molecules
were
studied
using
supercellof
ofthe
the(0,
(0,3)
3)nanotube,
nanotube,and
andthe
the
adsorption
configurations
are
shown
in
Figures
6
and
7,
respectively.
Three
and
two
adsorption
configurations
configurations
configurationsare
areshown
shownin
inFigures
Figures66and
and7,7,respectively.
respectively. Three
Three and
and two
two adsorption
adsorptionconfigurations
configurations
for
the
former
and
latter
cases
were
considered,
respectively.
The
smallest
adsorption
energies are
are
for
forthe
the former
former and
and latter
latter cases
cases were
were considered,
considered, respectively.
respectively. The
The smallest
smallest adsorption
adsorptionenergies
energies
are
−1.128
eV
(−0.564
eV/H
2O) for the former and −1.838 eV (−0.613 eV/H2O) for the latter cases. In the
−1.128
2O)
forforthe
2O)
forforthe
−1.128eV
eV(−0.564
(−0.564eV/H
eV/H
theformer
formerand
and−1.838
−1.838eV
eV(−0.613
(−0.613eV/H
eV/H
thelatter
lattercases.
cases.In
Inthe
the
2 O)
2 O)
multi-water
adsorption
systems,
the
relative
stabilitiesbetween
betweenthe
themolecular
molecularand
anddissociated
dissociatedstates
states
multi-water
multi-wateradsorption
adsorptionsystems,
systems,the
therelative
relativestabilities
stabilities
between
the
molecular
and
dissociated
states
werealso
alsostudied
studiedby
bydissociating
dissociatingone
onewater
watermolecule
moleculeand
andkeeping
keepingthe
theothers
othersin
intheir
their
adsorption
sites
were
were
also
studied
by
dissociating
one
water
molecule
and
keeping
the
others
in
theiradsorption
adsorptionsites
sites
as
shown
in
Figure
8.
For
two
water
molecule
adsorbed
system,
the
initially
dissociated
OH
and
H
as
asshown
shownin
inFigure
Figure8.
8. For
Fortwo
twowater
watermolecule
moleculeadsorbed
adsorbedsystem,
system,the
theinitially
initiallydissociated
dissociatedOH
OHand
andH
H
re-combinated
together
to
the
molecular
state,
however,
they
do
not
reform
a
water
molecule
in
the
re-combinated
re-combinatedtogether
togetherto
tothe
themolecular
molecularstate,
state,however,
however,they
theydo
donot
notreform
reformaawater
watermolecule
moleculein
inthe
the
three
water
molecule
adsorbed
system.
The
total
energy
of
the
system
with
two
molecular
and
one
three
threewater
watermolecule
moleculeadsorbed
adsorbedsystem.
system.The
Thetotal
totalenergy
energyof
ofthe
thesystem
systemwith
withtwo
twomolecular
molecularand
andone
one
dissociatedwater
waterisis
0.032
eV
lower
than
that
with
three
water
molecules,indicating
indicating
that
interactions
dissociated
dissociated
water
is0.032
0.032eV
eVlower
lowerthan
thanthat
thatwith
withthree
threewater
watermolecules,
molecules,
indicatingthat
thatinteractions
interactions
between
water
molecules
prevent
the
re-combination
of
the
dissociated
water
molecule.
between
water
molecules
prevent
the
re-combination
of
the
dissociated
water
molecule.
between water molecules prevent the re-combination of the dissociated water molecule.
(a)
(a)
(b)
(b)
(c)
(c)
nanotubes. Theblue,
blue, red,
Figure 6. Theconfigurations
configurations oftwo
two watermolecules
molecules adsorbedon
on (0,3)
3) TiO22nanotubes.
Figure
Figure6.6.The
The configurationsof
of twowater
water moleculesadsorbed
adsorbed on(0,
(0, 3)TiO
TiO2 nanotubes.The
The blue,red,
red,
brown,
and
white
balls
denote
the
Ti,
O
in
TiO
2NT, O in water, and H atoms, respectively. The indices
brown,
brown,and
andwhite
whiteballs
ballsdenote
denotethe
theTi,
Ti,OOin
inTiO
TiO2NT,
NT,OOininwater,
water,and
andHHatoms,
atoms,respectively.
respectively.The
Theindices
indices
2
of (a–c)denote
denote thedifferent
different adsorptionsites
sites ofaawater
water moleculeon
on theTiO
TiO2 nanotube.
of
of(a–c)
(a–c) denotethe
the differentadsorption
adsorption sitesof
of a water molecule
molecule on the
the TiO2 nanotube.
nanotube.
2
Materials 2016, 9, 1018
Materials 2016, 9, 1018
Materials 2016, 9, 1018
8 of 14
8 of 14
8 of 14
(a)
(a)
(b)
(b)
Figure 7. The configurations
configurations of
of three
three water molecules
molecules adsorbedon
on the (0,
(0, 3) TiO
TiO2 nanotubes. The blue,
Figure
Figure 7. The configurations
three water
water molecules adsorbed
adsorbed on the
the (0, 3)
3) TiO22 nanotubes. The blue,
red,
brown,
and
white
balls
denote
the
Ti,
O
in
TiO
2NT, O in water, and H atoms, respectively. The
red,
and white
whiteballs
ballsdenote
denotethe
theTi,Ti,
TiO
O water,
in water,
H atoms,
respectively.
red, brown, and
OO
in in
TiO
2NT,
O in
andand
H atoms,
respectively.
The
2 NT,
indices
of (a,b)
denote
the different
adsorption
sites of aof
water
molecule
on the
TiO2 nanotube.
The
indices
of (a,b)
denote
the different
adsorption
a water
molecule
on the
indices
of (a,b)
denote
the different
adsorption
sitessites
of a water
molecule
on the
TiOTiO
2 nanotube.
2 nanotube.
(a)
(a)
(b)
(b)
Figure 8. The relaxed configurations of dissociated water molecules adsorbed on the (0, 3) TiO2
Figure 8.
8. The relaxed
relaxed configurations
configurations of
of dissociated
dissociated water
water molecules
molecules adsorbed
adsorbed on the
the (0, 3)
3) TiO
TiO2
Figure
2
nanotubes.The
(a) Two water
molecules and (b)
three water molecules.
The blue, red,on
brown,(0,
and white
nanotubes. (a)
(a) Two
Two water
water molecules
molecules and
and (b)
(b) three
three water
water molecules.
molecules. The
The blue,
blue, red,
red, brown,
brown, and
and white
white
nanotubes.
balls denote the Ti, O in TiO2NT, O in water, and H atoms, respectively.
balls denote
denote the
the Ti,
Ti, O
O in
in TiO
TiO2NT,
NT, O
O in
in water,
water,and
andH
Hatoms,
atoms,respectively.
respectively.
balls
2
For the
the (6,
(6, 0)
0) nanotube,
nanotube, only
only one
one adsorption
adsorption site
site for
for the
the single
single water
water molecule
molecule adsorption
adsorption was
was
For
For considering
the (6, 0) nanotube,
onlythe
oneadsorption
adsorptionbehavior
site for the
singleiswater
molecule
adsorption
was
studied
the
fact
that
of
water
less
sensitive
to
the
diameter
of
studied considering the fact that the adsorption behavior of water is less sensitive to the diameter of
studied
considering
the
fact
that
the
adsorption
behavior
of
water
is
less
sensitive
to
the
diameter
the tube
tube [48].
[48]. Similar
Similar adsorption
adsorption energies
energies when
when the
the water
water molecule
molecule adsorbs
adsorbs at
at different
different sites
sites on
on the
the
the
of
the
tube [48].were
Similar
adsorption
energies
when theThe
water
molecule
adsorbs energy
at different
sites
on
(0,
3)
nanotube
shown
in
the
above
calculations.
estimated
adsorption
of
one
water
(0, 3) nanotube were shown in the above calculations. The estimated adsorption energy of one water
the
(0,
3)
nanotube
were
shown
in
the
above
calculations.
The
estimated
adsorption
energy
of
one
molecule on
on the
the (6,
(6, 0)
0) nanotube
nanotube is
is −0.662
−0.662 eV,
eV, which
which is
is very
very close
close to
to that
that of
of aa water
water molecule
molecule adsorbed
adsorbed
molecule
water
molecule
on the (6,
0)total
nanotube
isof−a0.662
eV,water
which
is very adsorption
close to thaton
ofthe
a water
molecule
on
the
(0,
3)
nanotube.
The
energy
single
molecule
(6,
0)
nanotube
on the (0, 3) nanotube. The total energy of a single water molecule adsorption on the (6, 0) nanotube
adsorbed
on the (0,
3) (Figure
nanotube.
total 0.02
energy
of a single
adsorption
the (6,
0)
in the
the molecular
molecular
state
9a)The
is about
about
eV lower
lower
than water
that in
inmolecule
the dissociated
dissociated
state on
(Figure
9b).
in
state
(Figure 9a)
is
0.02 eV
than
that
the
state
(Figure
9b).
nanotube
in
the
molecular
state
(Figure
9a)
is
about
0.02
eV
lower
than
that
in
the
dissociated
state
In order
order to
to clarify
clarify the
the interactions
interactions between
between water
water molecules,
molecules, seven
seven different
different adsorption
adsorption
In
(Figure
9b). In order
to clarify
the interactions
between
water molecules,
seven
different
adsorption
configurations
in
a
two
water
molecule
adsorbed
(6,
0)
nanotube
are
studied,
as
shown
in
Figure 10.
10.
configurations in a two water molecule adsorbed (6, 0) nanotube are studied, as shown in Figure
configurations
inabout
a two water
molecule
adsorbed
(6, 0)energies
nanotubebetween
are studied,
asdifferent
shown inadsorption
Figure 10.
It
also
shows
0.2
eV
difference
in
total
the
It also shows about 0.2 eV difference in total energies between the different adsorption
It
also shows about
eV difference
in total
energies
between
the different
configurations.
configurations.
The0.2
smallest
adsorption
energy
of the
the
two water
water
adsorbedadsorption
(6, 0)
0) nanotube
nanotube
is −1.277
−1.277
configurations.
The
smallest
adsorption
energy
of
two
adsorbed
(6,
is
The
smallest
adsorption
energy
of the
twothat
water
adsorbed
(6, 0)molecules
nanotube adsorbed
is −1.277 on
eV, the
which
is
eV,
which
is
about
0.15
eV
smaller
than
of
the
two
water
(0, 3)
3)
eV, which is about 0.15 eV smaller than that of the two water molecules adsorbed on the (0,
about
0.15
eV
smaller
than
that
of
the
two
water
molecules
adsorbed
on
the
(0,
3)
nanotube.
The
total
nanotube. The
The total
total energy
energy of
of the
the (6,
(6, 0)
0) nanotube
nanotube with
with one
one dissociated
dissociated and
and one
one molecular
molecular water
water is
is
nanotube.
energy
of the
(6,
0) nanotube
with
one
dissociatedof
and
one
molecular
water
isthe
about
0.01 eVstate,
higher
about
0.01
eV
higher
than
that
of
the
adsorption
two
water
molecules
in
molecular
as
about 0.01 eV higher than that of the adsorption of two water molecules in the molecular state, as
than
that
the adsorption
of two to
water
molecules in
molecular
state,
in Figure 9c,d.
shown
in of
Figure
9c,d. It
It is
is similar
similar
the adsorption
adsorption
of athe
a water
water
molecule
on as
theshown
(0, 3)
3) nanotube.
nanotube.
Due
shown
in
Figure
9c,d.
to the
of
molecule
on
the
(0,
Due
It
is
similar
to
the
adsorption
of
a
water
molecule
on
the
(0,
3)
nanotube.
Due
to
the
almost
identical
to the
the almost
almost identical
identical adsorption
adsorption characteristics
characteristics of
of water
water and
and the
the OH
OH cluster
cluster on
on the
the (0,
(0, 3)
3) and
and (6,
(6, 0)
0)
to
adsorption
characteristics
ofof
water
and
the OH
cluster on
the
(0,
3)0)and
(6, 0) nanotubes,
the adsorption
nanotubes,
the
adsorption
three
water
molecules
on
the
(6,
nanotube
is
not
considered
in
the
nanotubes, the adsorption of three water molecules on the (6, 0) nanotube is not considered in the
of
three water
(6, 0) nanotube
not considered
in thestabilities
present study.
It should be
present
study.molecules
It should
shouldon
bethe
pointed
out that
that is
although
the relative
relative
of dissociated
dissociated
or
present
study.
It
be
pointed
out
although
the
stabilities of
or
molecular states
states are
are really
really complex
complex due
due to
to the
the large
large number
number of
of possible
possible adsorption
adsorption configurations
configurations for
for
molecular
Materials 2016, 9, 1018
9 of 14
pointed2016,
out9,that
Materials
1018although
Materials 2016, 9, 1018
the relative stabilities of dissociated or molecular states are really complex
9 of 14
9 of 14
due to the large number of possible adsorption configurations for multiple water molecules on
the
nanotube,water
the interactions
molecules
and the nanotube
are water
the keymolecules
factor determining
multiple
molecules between
on the water
nanotube,
the interactions
between
and the
multiple water molecules on the nanotube, the interactions between water molecules and the
the adsorption
characteristics.
nanotube
are the
key factor determining the adsorption characteristics.
nanotube are the key factor determining the adsorption characteristics.
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
2 nanotubes. (a)
Figure
9.
The
relaxed configurations
configurations of watermolecules
molecules
adsorbed
on
the
(6, 0) TiO
Figure 9.
9. The
The relaxed
adsorbed
onon
thethe
(6, 0)
(a) One
2 nanotubes.
(a)
Figure
configurationsofofwater
water molecules
adsorbed
(6,TiO
0) TiO
2 nanotubes.
One
molecular
state;
(b) one
dissociated
state;
(c) two
molecular
states;
and
(d) one
molecular
state
molecular
state;
(b)
one
dissociated
state;
(c)
two
molecular
states;
and
(d)
one
molecular
state
and
One molecular state; (b) one dissociated state; (c) two molecular states; and (d) one molecular state
O in water,
and
dissociated
state.
The
blue,
red,
brown,
and white
balls
denote
the
Ti,TiO
O inNT,
TiO2NT,
dissociated
state.
The The
blue,blue,
red, red,
brown,
and white
balls balls
denote
the Ti,the
O Ti,
in
in water,
and H
2 TiOO
2NT,
O in water,
and
dissociated
state.
brown,
and white
denote
O in
and
H
atoms,
respectively.
atoms,
respectively.
and
H atoms,
respectively.
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
(e)
(e)
(f)
(f)
(g)
(g)
Figure 10. The initial adsorption sites of water molecules on the (6, 0) TiO2 nanotubes. The blue, red,
Figure 10. The initial adsorption sites of water molecules on the (6, 0) TiO2 nanotubes. The blue, red,
Figure and
10. The
initial
molecules
on the
(6,H0)atoms,
TiO2 nanotubes.
The
red,
O in water,
and
respectively.
Theblue,
indices
brown,
white
ballsadsorption
denote thesites
Ti, Oofinwater
TiO2NT,
2NT, O in water, and H atoms, respectively. The indices
brown,
and
white
balls
denote
the
Ti,
OOin
TiO
brown,
and
white
balls
denote
the
Ti,
in
TiO
NT,
O
in
water,
and
H
atoms,
respectively.
The
indices
(a–g) denote the different adsorption sites of a 2water molecule on the TiO2 nanotube.
(a–g)
(a–g)denote
denotethe
thedifferent
different adsorption
adsorption sites
sites of
of aa water
water molecule
molecule on
on the
the TiO
TiO2 nanotube.
nanotube.
2
3.4. Electronic Structures of Water Adsorbed Nanotubes
3.4. Electronic Structures of Water Adsorbed Nanotubes
3.4. Electronic Structures of Water Adsorbed Nanotubes
The Bader charge analysis was employed to illustrate the charge distributions of atoms in water
The Bader charge analysis was employed to illustrate the charge distributions of atoms in water
The Bader
charge
was employed
to illustrate
the charge
distributions
of atoms in
water
adsorbed
TiO2NT
[55]. analysis
For the clean
(0, 3) nanotube,
the charges
of two-fold
and three-fold
oxygen
adsorbed TiO2NT [55]. For the clean (0, 3) nanotube, the charges of two-fold and three-fold oxygen
adsorbed
TiO
NT
[55].
For
the
clean
(0,
3)
nanotube,
the
charges
of
two-fold
and
three-fold
oxygen
atoms are 6.862 e and 7.04 e, respectively, and the value is 2.11 e for Ti, indicating that Ti donates
atoms are 6.86 e and 7.04 e, respectively, and the value is 2.11 e for Ti, indicating that Ti donates
atoms areto6.86
e and 7.04
e, respectively,
themolecule
value isadsorbed
2.11 e forsystem
Ti, indicating
that Ti
electrons
the oxygen
atoms.
For the two and
water
(Figure 11a),
thedonates
Bader
electrons to the oxygen atoms. For the two water molecule adsorbed system (Figure 11a), the Bader
electrons
to
the
oxygen
atoms.
For
the
two
water
molecule
adsorbed
system
(Figure
11a),
the
charges of the indexed ‘Ti’ and ‘O3’ atoms of the nanotube are 2.06 e and 6.88 e, respectively.Bader
The
charges of the indexed ‘Ti’ and ‘O3’ atoms of the nanotube are 2.06 e and 6.88 e, respectively. The
charges
of the
indexed
‘O3’ molecules
atoms of the
nanotube are
e and 6.88 e,are
respectively.
total
total
Bader
charges
of ‘Ti’
twoand
water
‘H3–O1–H’
and2.06
‘H1–O2–H2’
7.93 e andThe
7.91
e,
total Bader charges of two water molecules ‘H3–O1–H’ and ‘H1–O2–H2’ are 7.93 e and 7.91 e,
Bader charges
of two water
molecules
and
‘H1–O2–H2’
arewater
7.93 emolecule,
and 7.91 e,
respectively.
respectively.
Therefore,
a small
amount‘H3–O1–H’
of electrons
transfer
from the
especially
the
respectively. Therefore, a small amount of electrons transfer from the water molecule, especially the
Therefore, amolecule,
small amount
electrons transfer from the water molecule, especially the H1–O2–H2
H1–O2–H2
to the of
nanotube.
H1–O2–H2 molecule, to the nanotube.
molecule, to the nanotube.
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200
tot
Density of states (states/eV)
100
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
Ti s
Ti p
Ti d
O1 s
O1 p
O2 s
O2 p
O3 s
O3 p
H1 s
H2 s
H3 s
H4 s
-10
-8
-6
-4
-2
0
2
4
6
Energy relative to Fermi energy level (eV)
(a)
(b)
Figure11.11.Density
Density
of states
oftwo
thewater
two water
molecule
adsorbed
(0, 3) nanotube.
(a) (b)
Structure;
Figure
of states
of the
molecule
adsorbed
(0, 3) nanotube.
(a) Structure;
DOSs.
(b) DOSs.
For the three water adsorbed nanotube in an energetically stable state (Figure 12a), the Bader
For the three water adsorbed nanotube in an energetically stable state (Figure 12a), the Bader
charges of the indexed ‘Ti’ and ‘O4’ of the nanotube are 2.04 e and 7.19 e, respectively. The total
charges of the indexed ‘Ti’ and ‘O4’ of the nanotube are 2.04 e and 7.19 e, respectively. The total Bader
Bader charges of the H1–O1–H2, H3–O–H4, and H5–O3–H6 ‘molecules’ are 7.94 e, 7.87 e, and 7.91 e,
charges of the H1–O1–H2, H3–O–H4, and H5–O3–H6 ‘molecules’ are 7.94 e, 7.87 e, and 7.91 e,
respectively. Specifically, the Bader charge of H4 is about 0.06 e less than that of H3, which may imply
respectively. Specifically, the Bader charge of H4 is about 0.06 e less than that of H3, which may imply
a stronger bonding interaction between H4 and its neighboring oxygen atoms. The Bader charge of
a stronger bonding interaction between H4 and its neighboring oxygen atoms. The Bader charge of
H2 neighbored by two oxygen atoms is about 0.03 e smaller than that of H1 with one neighboring
H2 neighbored by two oxygen atoms is about 0.03 e smaller than that of H1 with one neighboring
oxygen atom, causing less charge transfer with respect to H2. The total Bader charge of the H3–O2–H4
oxygen atom, causing less charge transfer with respect to H2. The total Bader charge of the H3–O2–
‘molecule’ is the smallest between the considered three water molecules due to the dissociation of H.
H4 ‘molecule’ is the smallest between the considered three water molecules due to the dissociation
The “H–O–H–O–H” cluster will then be formed after the dissociation to stabilize the adsorption.
of H. The “H–O–H–O–H” cluster will then be formed after the dissociation to stabilize the adsorption.
The densities of states (DOSs) are further studied to reveal the interactions between water
The densities of states (DOSs) are further studied to reveal the interactions between water
molecules and the TiO2 nanotube. Figures 11b and 12b shown the DOSs of the most stable adsorption
molecules and the TiO2 nanotube. Figures 11b and 12b shown the DOSs of the most stable adsorption
configurations of two and three water molecules on the (0, 3) nanotube (Figure 8). It is worth noting
configurations of two and three water molecules on the (0, 3) nanotube (Figure 8). It is worth noting
that the DFT calculations underestimate the band-gap of the oxides as shown in our calculations.
that the DFT calculations underestimate the band-gap of the oxides as shown in our calculations. For
For the two water molecule adsorbed system as shown in Figure 11b, the bonding peaks of H 1s are
the two water molecule adsorbed system as shown in Figure 11b, the bonding peaks of H 1s are
mainly concentrated in the energy region of (−7.0, −8.0) eV, in which they strongly overlap with
mainly concentrated in the energy region of (−7.0, −8.0) eV, in which they strongly overlap with the
the oxygen atoms from the neighboring water (O2 p orbitals) causing strong bonding interactions.
oxygen atoms from the neighboring water (O2 p orbitals) causing strong bonding interactions. No
No overlaps between O3 from the nanotube and hydrogen from the water can be detected, implying a
overlaps between O3 from the nanotube and hydrogen from the water can be detected, implying a
vanished weak interaction between them. The O p orbitals from water molecules overlap with the Ti d
vanished weak interaction between them. The O p orbitals from water molecules overlap with the Ti
orbitals in the energy region of (−5.5, −1.0) eV. Therefore, the adsorptions of water on TiO2 NT are
d orbitals in the energy region of (−5.5, −1.0) eV. Therefore, the adsorptions of water on TiO2NT are
mainly controlled through the bonding interactions between the oxygen atom in the water molecule
mainly controlled through the bonding interactions between the oxygen atom in the water molecule
and the Ti atom from TiO2 NT. For the three water molecule adsorbed system, the total DOS of the
and the Ti atom from TiO2NT. For the three water molecule adsorbed system, the total DOS of the
adsorbed nanotube are similar with that of the two water molecule adsorbed nanotube as shown in
adsorbed nanotube are similar with that of the two water molecule adsorbed nanotube as shown in
Figure 12b. The bonding peaks of the dissociation hydrogen atom (H4) are mainly distributed in the
Figure 12b. The bonding peaks of the dissociation hydrogen atom (H4) are mainly distributed in the
energy region of (−6.6, −7.6) eV, and forms bonds with the oxygen atom (O4) from TiO2 NT only.
energy region of (−6.6, −7.6) eV, and forms bonds with the oxygen atom (O4) from TiO2NT only. Other
Other hydrogen atoms do not escape from the water, i.e., they mainly bond with their neighboring
hydrogen atoms do not escape from the water, i.e., they mainly bond with their neighboring oxygen
atoms in water molecules. The ‘Ti’ also slightly bonds with oxygen atoms from water molecules.
Materials
Materials2016,
2016,9,9,1018
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1111ofof1414
Therefore, the bonding interactions between the hydrogen from water molecule and the oxygen from
oxygen atoms in water molecules. The ‘Ti’ also slightly bonds with oxygen atoms from water molecules.
the nanotube may be helpful for the water dissociation on TiO2NT.
Therefore, the bonding interactions between the hydrogen from water molecule and the oxygen from
The light irradiation and isoelectronic point are important parameters to evaluate the
the nanotube may be helpful for the water dissociation on TiO2 NT.
photocatalysis. Presently, the optical properties, such as the adsorption coefficient, are calculated to
The light irradiation and isoelectronic point are important parameters to evaluate the
evaluate the influence of light on the materials. Most recently, we have calculated the adsorption
photocatalysis. Presently, the optical properties, such as the adsorption coefficient, are calculated to
coefficient of nanotubes along and perpendicular to the tube axis, and achieved similar results with
evaluate the influence of light on the materials. Most recently, we have calculated the adsorption
experiments [56]. Our calculations show that the large adsorption coefficients occur in the high
coefficient of nanotubes along and perpendicular to the tube axis, and achieved similar results with
energy area (~5.0 eV). The O–H may be easy to dissociate under light irradiation with high energy.
experiments [56]. Our calculations show that the large adsorption coefficients occur in the high energy
Recently, Huang et al. studied the electrochemical phase diagrams combining the density functional
area (~5.0 eV). The O–H may be easy to dissociate under light irradiation with high energy. Recently,
calculations and the thermodynamics results [57], in which the experimental chemical potentials for
Huang et al. studied the electrochemical phase diagrams combining the density functional calculations
ions in solution were employed. The electrode potentials for the oxidation of water to O2 and the
and the thermodynamics
results [57], in which the experimental chemical potentials for ions in solution
reduction of H+ to H2 were located between the Valence Band Maximum (VBM) and Conduction
were employed. The electrode potentials for the oxidation of water to O2 and the reduction of H+ to H2
Band Minimum (CBM) of TiO2 under most of pH values. The electronic structures of the nanotube
were located between the Valence Band Maximum (VBM) and Conduction Band Minimum (CBM) of
are similar with the bulk TiO2, and therefore, the TiO2NT should be a promising photocatalyst, as
TiO2 under most of pH values. The electronic structures of the nanotube are similar with the bulk TiO2 ,
shown by experimental results.
and therefore, the TiO2 NT should be a promising photocatalyst, as shown by experimental results.
200
tot
Density of states (states/eV)
100
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
Ti s
Ti p
Ti d
O1 s
O1 p
O2 s
O2 p
O3 s
O3 p
O4 s
O4 p
H1 s
H2 s
H3 s
H4 s
H5 s
H6 s
-10
-8
-6
-4
-2
0
2
4
6
Energy relative to Fermi energy level (eV)
(a)
(b)
Figure12.
12.Density
Densityofofstates
statesofofaathree
threewater
watermolecule
moleculeadsorbed
adsorbed(0,(0,3)3)nanotube.
nanotube.(a)
(a)Structure;
Structure;(b)
(b)DOSs.
DOSs.
Figure
Conclusions
4.4.Conclusions
Firstprinciples
principlescalculations
calculationsare
arecarried
carriedout
outtotostudy
studythe
theadsorption
adsorptionproperties
propertiesofofwater
watermolecules
molecules
First
on
TiO
2NT. Firstly, the adsorption of OH clusters on clean and H-terminated TiO2NT are studied.
on TiO2 NT. Firstly, the adsorption of OH clusters on clean and H-terminated TiO2 NT are studied.
Thesmallest
smallestadsorption
adsorptionenergy
energy is
is about
about −1.0
adsorption
onon
thethe
clean
tube
andand
−5.0
The
−1.0eV
eVfor
forOH
OHcluster
cluster
adsorption
clean
tube
eV
on
the
H-terminated
tube,
respectively.
A
water
molecule
will
be
easily
formed
for
the
adsorption
−5.0 eV on the H-terminated tube, respectively. A water molecule will be easily formed for the
of an OH cluster
on clean
and
TiO2NT. The
adsorption
properties of single and multiple
adsorption
of an OH
cluster
onH-terminated
clean and H-terminated
TiO
2 NT. The adsorption properties of single
water molecules on TiO2NT are investigated. The single and two water molecules prefer to adsorb in
the molecular state, while the dissociated state is more preferable for the adsorption of three water
Materials 2016, 9, 1018
12 of 14
and multiple water molecules on TiO2 NT are investigated. The single and two water molecules prefer
to adsorb in the molecular state, while the dissociated state is more preferable for the adsorption of
three water molecules, according to the total energy calculations. Water molecules tend to dissociate
into OH and H. The H then bonds with the oxygen from the nanotube, and the OH cluster will form a
‘H–O–H–O–H’ cluster. Therefore, the interactions between molecules can greatly affect the adsorption
of water on the TiO2 nanotube and may bring about the dissociation of water.
Acknowledgments: This work was supported by the National Basic Research Programme of China,
Grant No. 2016YFB0701301, Natural Science Foundation of Shandong, China, Grant No. ZR2014EMM013,
No. ZR2014EMQ009, and the Fundamental Research Funds for the Central Universities Grant No. HIT. KITP.
2014030. Simulations were performed using HPC resources in CAS Shenyang Super-computing Center.
Author Contributions: Yan Song conceived and designed the experiments; Jianhong Dai performed the
experiments; Yan Song and Jianhong Dai analyzed the data; Jianhong Dai wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Fujishima, A.; Honda, K. Electrochemical Photolysis of Water at a Semiconductor Electrode. Nature 1972,
238, 37–38. [CrossRef] [PubMed]
Ismail, A.A.; Bahnemann, D.W. Photochemical Splitting of Water for Hydrogen Production by Photocatalysis:
A Review. Sol. Energy Mater. Sol. Cells 2014, 128, 85–101. [CrossRef]
Ahmad, H.; Kamarudin, S.K.; Minggu, L.J.; Kassim, M. Hydrogen from Photo-catalytic Water Splitting
Process: A Review. Renew. Sustain. Energy Rev. 2015, 43, 599–610. [CrossRef]
Matsuoka, M.; Kitano, M.; Takeuchi, M.; Tsujimaru, K.; Anpo, M.; Thomas, J.M. Photocatalysis for New
Energy Production Recent Advances in Photocatalytic Water Splitting Reactions for Hydrogen Production.
Catal. Today 2007, 122, 51–61. [CrossRef]
Bard, A.J. Photoelectrochemistry. Science 1980, 207, 139–144. [CrossRef] [PubMed]
Primo, A.; Corma, A.; Garcia, H. Titania Supported Gold Nanoparticles as Photocatalyst. Phys. Chem.
Chem. Phys. 2011, 13, 886–910. [CrossRef] [PubMed]
Wagner, F.T.; Somorjai, G.A. Photocatalytic Hydrogen Production from Water on Pt-free SrTiO3 in Alkali
Hydroxide Solutions. Nature 1980, 285, 559–560. [CrossRef]
Kawai, T.; Sakata, T. Reactions of Water with Carbon and Ethylene over Illuminated Pt/TiO2 .
Chem. Phys. Lett. 1980, 70, 131–134.
Domen, K.; Naito, S.; Soma, M.; Onishi, T.; Tamaru, K. Photocatalytic Decomposition of Water Vapour on an
NiO–SrTiO3 catalyst. J. Chem. Soc. Chem. Commun. 1980, 12, 543–544. [CrossRef]
Inoue, Y.; Niiyama, T.; Asai, Y.; Sato, K. Stable Photocatalytic Activity of BaTi4 O9 Combined with Ruthenium
Oxide for Decomposition of Water. J. Chem. Soc. Chem. Commun. 1992, 65, 579–580. [CrossRef]
Kudo, A.; Tanaka, A.; Domen, K.; Maruya, K.; Aika, K.; Onishi, T. Photocatalytic Decomposition of Water
over NiO–K4 Nb6 O17 Catalyst. J. Catal. 1988, 111, 67–76. [CrossRef]
Ni, M.; Leung, M.K.H.; Leung, D.Y.C.; Sumathy, K. A Review and Recent Developments in Photocatalytic
Water–splitting using TiO2 for Hydrogen Production. Renew. Sustain. Energy Rev. 2007, 11, 401–425.
[CrossRef]
Szymanski, P.; El-Sayed, M.A. Some Recent Developments in Photoelectrochemical Water Splitting using
Nanostructured TiO2 : A Short Review. Theor. Chem. Acc. 2012, 131, 1–12. [CrossRef]
Choi, W.; Termin, A.; Hoffmann, M.R. The Role of Metal Ion Dopants in Quantum-Sized TiO2 : Correlation
between Photoreactivity and Charge Carrier Recombination Dynamics. J. Phys. Chem. 1994, 98, 13669–13679.
[CrossRef]
Kannekanti, L.; Jakkidi, K.R.; Venkata, P.S.M.; Durga, K.V.; Machiraju, S. Continuous Hydrogen Production
Activity over Finely Dispersed Ag2 O/TiO2 Catalysts from Methanol: Water Mixtures under Solar Irradiation:
A Atructure–activity Correlation. Int. J. Hydrogen Energy 2010, 35, 3991–4001.
Wu, N.-L.; Lee, M.-S. Enhanced TiO2 Photocatalysis by Cu in Hydrogen Production from Aqueous Methanol
Solution. Int. J. Hydrogen Energy 2004, 29, 1601–1605. [CrossRef]
Park, H.; Park, Y.; Kim, W.; Choi, W. Surface Modification of TiO2 Photocatalyst for Environmental
Applications. J. Photochem. Photobiol. C 2013, 15, 1–20. [CrossRef]
Materials 2016, 9, 1018
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
13 of 14
Lee, Y.J.; Joo, J.B.; Yin, Y.D.; Zaera, F. Evaluation of the Effective Photoexcitation Distances in
the Photocatalytic Production of H2 from Water using Au@Void@TiO2 Yolk–shell nanostructures.
ACS Energy Lett. 2016, 1, 52–56. [CrossRef]
Brinkley, D.; Dietrich, M.; Engel, T.; Engel, T.; Farrall, P.; Gantner, G.; Schafer, A.; Szuchmacher, A. A
Modulated Molecular Beam Study of the Extent of H2 O Dissociation on TiO2 (110). Surf. Sci. 1998, 395,
292–306. [CrossRef]
Henderson, M.A.; Epling, W.S.; Peden, C.H.F.; Perkins, C.L. Insights into Photoexcited Electron Scavenging
Processes on TiO2 Obtained from Studies of the Reaction of O2 with OH Groups Adsorbed at Electronic
Defects on TiO2 (110). J. Phys. Chem. B 2003, 107, 534–545. [CrossRef]
Allegretti, F.; O’Brien, S.; Polcik, M.; Sayago, D.I.; Woodruff, D.P. Adsorption Bond Length for H2 O on
TiO2 (110): A Key Parameter for Theoretical understanding. Phys. Rev. Lett. 2005, 95, 226104. [CrossRef]
[PubMed]
Lindan, P.J.D.; Harrison, N.M.; Holender, M.J. Mixed Dissociative and Molecular Adsorption of Water on the
Rutile (110) Surface. Phys. Rev. Lett. 1998, 80, 762–765. [CrossRef]
Stefanovich, E.V.; Truong, T.N. Ab initio Study of Water Adsorption on TiO2 (110): Molecular Adsorption
versus Dissociative Chemisorption. Chem. Phys. Lett. 1999, 299, 623–629. [CrossRef]
Langel, W. Car–Parrinello Simulation of H2 O Dissociation on Rutile. Surf. Sci. 2002, 496, 141–150. [CrossRef]
Zhang, C.; Lindan, P.J.D. Multilayer water adsorption on rutile TiO2 (110): A first-principles study.
J. Chem. Phys. 2003, 118, 4620–4630. [CrossRef]
Lindan, P.J.D.; Zhang, C. Exothermic Water Dissociation on the Rutile TiO2 (110) Surface. Phys. Rev. B 2005,
72, 075439. [CrossRef]
Harris, L.A.; Quong, A.A. Molecular Chemisorption as the Theoretically Preferred Pathway for Water
Adsorption on Ideal Rutile TiO2 (110). Phys. Rev. Lett. 2004, 93, 086105. [CrossRef] [PubMed]
Kamisaka, H.; Yamashita, K. The Surface Stress of the (110) and (100) Surfaces of Rutile and the Effect of
Water Adsorbents. Surf. Sci. 2007, 601, 4824–4836. [CrossRef]
Kowalski, P.M.; Meyer, B.; Marx, D. Composition, Structure, and Stability of the Rutile TiO2 (110) Surface:
Oxygen Depletion, Hydroxylation, Hydrogen Migration, and Water Ddsorption. Phys. Rev. B 2009, 79,
115410. [CrossRef]
Peng, S.F.; Ho, J.J. The adsorption and Dissociation of H2 O on TiO2 (110) and M/TiO2 (110) (M = Pt, Au)
Surfaces–A Computational Investigation. Int. J. Hydrogen Energy 2010, 35, 1530–1536. [CrossRef]
Hong, F.; Ni, Y.H.; Xu, W.J.; Yan, Y.F. Origin of Enhanced Water Adsorption at Step Edge on Rutile TiO2 (110)
surface. J. Chem. Phys. 2012, 137, 114707. [CrossRef] [PubMed]
Tilocca, A.; Valentin, C.D.; Selloni, A. O2 Interaction and Reactivity on a Model Hydroxylated Rutile(110)
Surface. J. Phys. Chem. B 2005, 109, 20963–20967. [CrossRef] [PubMed]
Lin, H.X.; Long, J.L.; Gu, Q.; Zhang, W.X.; Ruan, R.S.; Li, Z.H.; Wang, X.X. In situ IR Study of Surface Hydroxyl
Species of Dehydrated TiO2 : Towards Understanding Pivotal Surface Processes of TiO2 Photocatalytic
Oxidation of Toluene. Phys. Chem. Chem. Phys. 2012, 14, 9468–9474. [CrossRef] [PubMed]
Yates, D.J.C. Infrared Studies of the Surface Hydroxyl Group on Titanium Dioxide, and of the Chemisorption
of Carbon Monoxide and Carbon Dioxide. J. Phys. Chem. 1961, 65, 746–753. [CrossRef]
Lin, H.X.; Deng, W.H.; Long, J.L.; Wang, X.X. In situ IR study of Surface Hydroxyl and Photocatalytic
Oxidation of Toluene of Rutile TiO2 . Spectrosc. Spectr. Anal. 2014, 34, 1229–1233.
Lin, H.X.; Wang, X.X.; Fu, X.Z. Properties and Distributionof the Surface Hydroxyl Groups of TiO2 .
Prog. Chem. 2007, 19, 665–670.
Vittadini, A.; Casarin, M.; Selloni, A. Chemistry of and on TiO2 -anatase Surfaces by DFT Calculations:
A Partial Review. Theor. Chem. Acc. 2007, 117, 663–671. [CrossRef]
Herman, G.S.; Dohnálek, Z.; Ruzycki, N.; Diebold, U. Experimental Investigation of the Interaction of Water
and Methanol with Anatase-TiO2 (101). J. Phys. Chem. B 2003, 107, 2788–2795. [CrossRef]
Vittadni, A.; Selloni, A.; Rotzinger, F.P. Structure and Energetics of Water Adsorbed at TiO2 Anatase 101 and
001 Surfaces. Phys. Rev. Lett. 1998, 81, 2954–2957. [CrossRef]
Bredow, T.; Jug, K. Theoretical Inverstigation of Water–adsorption at Rutile and Anatase Surfaces. Surf. Sci.
1995, 327, 398–408. [CrossRef]
Selloni, A.; Vittadini, A.; Gratzel, M. The adsorption of Small Molecules on the TiO2 Anatase (101) Surface
by First-principles Molecular Dynamics. Surf. Sci. 1998, 402, 219–222. [CrossRef]
Materials 2016, 9, 1018
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
14 of 14
Henderson, M.A. Structural Sensitivity in the Dissociation of Water on TiO2 Single-Crystal Surfaces. Langmuir
1996, 12, 5093–5098. [CrossRef]
Henrich, V.E.; Dresselhaus, G.; Zeiger, H.J. Chemisorbed Phases of H2 O on TiO2 and SrTiO3 .
Solid State Commun. 1977, 24, 623–626. [CrossRef]
Wang, L.Q.; Baer, D.R.; Engelhard, M.H.; Shultz, A.N. The Adsorption of Liquid and Vapor Water on
TiO2 (110) Surfaces: The Role of Defects. Surf. Sci. 1995, 344, 237–250. [CrossRef]
Sun, H.J.; Mowbray, D.J.; Migani, A.; Zhao, J.; Petek, H.; Rubio, A. Comparing Quasiparticle H2 O Level
Alignment on Anatase and Rutile TiO2 . ACS Catal. 2015, 5, 4242–4254. [CrossRef]
Hoyer, P. Formation of a Titanium Dioxide Nanotube Array. Langmuir 1996, 12, 1411–1413. [CrossRef]
Liang, S.Z.; He, J.F.; Sun, Z.H.; Liu, Q.H.; Jiang, Y.; Cheng, H.; He, B.; Xie, Z.; Wei, S.Q. Improving
Photoelectrochemical Water Splitting Activity of TiO2 Nanotube Arrays by tuning Geometrical Parameters.
J. Phys. Chem. C 2012, 116, 9049–9053. [CrossRef]
Meng, Q.-Q.; Wang, J.-G.; Xie, Q.; Dong, H.-Q.; Li, X.-N. Water Splitting on TiO2 Nanotube Arrays.
Catal. Today 2011, 165, 145–149. [CrossRef]
Liu, H.; Tan, K. Adsorption of Water on Single-walled TiO2 Nanotube: A DFT Investigation.
Comput. Theor. Chem. 2012, 991, 98–101. [CrossRef]
Bandura, A.V.; Evaresto, R.A. From Anatase (101) Surface to TiO2 Nanotubes: Rolling Procedure and First
principles LCAO Calculations. Surf. Sci. 2009, 603, L117–L120. [CrossRef]
Dai, J.H.; Song, Y. First Principles Calculations on the Hydrogen Atom Passivation of TiO2 Nanotube.
RSC Adv. 2016, 6, 19190–19198. [CrossRef]
Kresse, G.; Hafner, J. Ab initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558. [CrossRef]
Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for ab initio Total-energy Calculations using a
Plane-wave Basis Set. Phys. Rev. B 1996, 54, 11169. [CrossRef]
Blöchl, P.E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953.
Tang, W.; Sanville, E.; Henkelman, G. A Grid-based Bader Analysis Algorithm without Lattice Bias. J. Phys.
Condens. Matter 2009, 21, 084204. [PubMed]
Dai, J.H.; Song, Y. Electronic Structure Controlling of Assembly and Optical Properties of TiO2 Nanotube
Arrays. ChemistrySelect 2016, 1, 3661–3666. [CrossRef]
Huang, L.F.; Rondinelli, J.M. Electrochemical Phase Diagrams for Ti Oxides from Density Functional
Calculations. Phys. Rev. B 2015, 92, 245126. [CrossRef]
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