**The Reactivity of Anatase TiO2 (211) Surface and the Bond-Charge Counting Model**

Jing Xu, Li-Fang Xu, Jian-Tao Wang and

Annabella Selloni

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69141

#### **Abstract**

In this chapter, we intend to present a generic understanding of surface reactivity and water dissociation on TiO2 surfaces through a study of anatase TiO2 (211) surface—an idea model surface containing both four-coordinated Ti atom (Ti4 ) and five-coordinated Ti atom (Ti5 ). Our first-principles calculations show that the (211) surface is a high reactivity surface and reveal that water molecule can be easily dissociated on a Ti4 site while it hardly dissociates on Ti5 site. Furthermore, we introduce bond-charge counting model to clarify the mechanism. More generally, after an intensive investigation of literature, we found that the bond-charge counting model is applicable to all anatase and rutile TiO2 surfaces including step edges and vacancies where the reactivity of surfaces enable to dissociate water attribute to the existence of Ti<sup>4</sup> atom or equivalent Ti4 atom.

**Keywords:** TiO2 surfaces, surface reactivity, water dissociation, first-principles calculations, bond-charge counting model

### **1. Introduction**

Titanium dioxide is a semiconductor-based heterogeneous photocatalysis material which received more and more interest. In nature, TiO2 crystallizes in three different structures: rutile, anatase, and brookite, all formed by TiO6 octahedra connected by shared edges and/or corners; rutile is the thermodynamically most stable bulk phase, while anatase is very common and stable in nanomaterials. As a major polymorph of TiO2 , anatase TiO2 is the most widely studied phase and is extensively used in many industrial applications such as photovoltaic

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cells, photo and electrochromics, photocatalysis, photonic crystals, smart surface coatings, and sensors [1–9]. In all applications, the surface structure plays a key role, as the surface reactivity and physicochemical properties depend strongly on the exposed crystallographic facet. Therefore, the search for high reactivity TiO2 surfaces is a topic of great interest and an area of intense activity.

The rutile (110) surface has been investigated early [10–12]. Anatase is less stable than rutile, but more efficient than rutile for applications. Many studies of the anatase TiO<sup>2</sup> surface focus on the (001) and (101) surfaces [13–20]. Theoretical studies [13–17] show that the (101) surface is the thermodynamically most stable surface with a small surface energy of 0.49 J/m2 , while the (001) surface is the highest reactivity surface with a high surface energy of 0.98 J/m2 . More recently, using different dopants, adsorbates, or solvated species, anatase TiO<sup>2</sup> nanocrystals exposing various crystalline facets have been prepared, including low-index facets such as (001) facets [18, 19], (100) [21–24], (010) [25, 26], (101) [27–32], (110) [33], and (111) [34], and high-index facets such as (103), (105), (106), (201), (301), and (401) [35–39]. Besides, many researchers have made extensive investigation on surface defects since those defects, e.g., step edges [40–42] and O vacancy [43, 44] are intrinsic on the surfaces of crystalline materials, which strongly influence the surface chemistry.

Since the discovery of photocatalytic splitting of water on a TiO<sup>2</sup> electrode in 1972 [1], the interaction of TiO2 surfaces with water is of special interest. The structure of the hydrated surfaces is important not only because water is always present on TiO2 surfaces, but also because it can help understand and control the catalytic and (photo) electrochemical properties of this material. In fact, different water adsorption states have been found; for example, water favors molecular adsorption on the anatase (101) surface and dissociative adsorption on the (001) surface [13].

There is still controversy for water adsorption on the TiO2 surface based only on the DFT total energy calculations, e.g., on rutile (110). Despite numerous studies on this topic in literature, the mechanism of water dissociation on TiO2 surfaces remains to be clarified. Moreover, there is still a lack of a generic understanding of different surfaces including surfaces with steps and vacancies.

Due to a recent experiment, a large percentage of exposed (211) facet has been prepared and it is found that the (211) surface can effectively improve the photocatalytic activity of TiO<sup>2</sup> for water dissociation reactions [45, 46]. Since the surface exposes both Ti<sup>4</sup> and Ti5 atoms, the anatase (211) surface is studied in this work as an ideal model surface to illustrate the mechanism of water dissociation on TiO2 surface [47]. The Ti4 atom plays a critical role for splitting water molecule. Furthermore, we introduce a bond-charge counting model according to TiO2 structure and conclude that two unsaturated Ti bonds are the necessary conditions for splitting water on the surface. Then, we examine as much as possible TiO<sup>2</sup> surfaces and find the model is applicable to all surfaces.

The paper is organized as follows: the reactivity of anatase TiO<sup>2</sup> (211) surface is briefly reviewed in Section 2; then, we propose the bond-charge counting model and give some typical examples in Section 3; finally, we present conclusion remakes in Section 4.

#### **2. The reactivity of anatase TiO2 (211) surface**

#### **2.1. Surface structure and stability**

cells, photo and electrochromics, photocatalysis, photonic crystals, smart surface coatings, and sensors [1–9]. In all applications, the surface structure plays a key role, as the surface reactivity and physicochemical properties depend strongly on the exposed crystallographic facet.

The rutile (110) surface has been investigated early [10–12]. Anatase is less stable than rutile,

on the (001) and (101) surfaces [13–20]. Theoretical studies [13–17] show that the (101) surface

exposing various crystalline facets have been prepared, including low-index facets such as (001) facets [18, 19], (100) [21–24], (010) [25, 26], (101) [27–32], (110) [33], and (111) [34], and high-index facets such as (103), (105), (106), (201), (301), and (401) [35–39]. Besides, many researchers have made extensive investigation on surface defects since those defects, e.g., step edges [40–42] and O vacancy [43, 44] are intrinsic on the surfaces of crystalline materials,

it can help understand and control the catalytic and (photo) electrochemical properties of this material. In fact, different water adsorption states have been found; for example, water favors molecular adsorption on the anatase (101) surface and dissociative adsorption on the (001)

energy calculations, e.g., on rutile (110). Despite numerous studies on this topic in literature,

is still a lack of a generic understanding of different surfaces including surfaces with steps and

Due to a recent experiment, a large percentage of exposed (211) facet has been prepared and it is found that the (211) surface can effectively improve the photocatalytic activity of TiO<sup>2</sup>

anatase (211) surface is studied in this work as an ideal model surface to illustrate the mecha-

water molecule. Furthermore, we introduce a bond-charge counting model according to TiO2 structure and conclude that two unsaturated Ti bonds are the necessary conditions for split-

in Section 2; then, we propose the bond-charge counting model and give some typical examples

surface [47]. The Ti4

for water dissociation reactions [45, 46]. Since the surface exposes both Ti<sup>4</sup>

ting water on the surface. Then, we examine as much as possible TiO<sup>2</sup>

The paper is organized as follows: the reactivity of anatase TiO<sup>2</sup>

in Section 3; finally, we present conclusion remakes in Section 4.

surfaces with water is of special interest. The structure of the hydrated sur-

is the thermodynamically most stable surface with a small surface energy of 0.49 J/m2

the (001) surface is the highest reactivity surface with a high surface energy of 0.98 J/m2

but more efficient than rutile for applications. Many studies of the anatase TiO<sup>2</sup>

recently, using different dopants, adsorbates, or solvated species, anatase TiO<sup>2</sup>

surfaces is a topic of great interest and an area of

surface focus

nanocrystals

electrode in 1972 [1], the

surfaces, but also because

surface based only on the DFT total

and Ti5

(211) surface is briefly reviewed

surfaces and find the

atom plays a critical role for splitting

atoms, the

surfaces remains to be clarified. Moreover, there

, while

. More

Therefore, the search for high reactivity TiO2

which strongly influence the surface chemistry.

Since the discovery of photocatalytic splitting of water on a TiO<sup>2</sup>

faces is important not only because water is always present on TiO2

There is still controversy for water adsorption on the TiO2

the mechanism of water dissociation on TiO2

nism of water dissociation on TiO2

model is applicable to all surfaces.

intense activity.

4 Titanium Dioxide

interaction of TiO2

surface [13].

vacancies.

We begin with the experimental result. Recently, a large percentage of exposed (211) facet has been identified by X-ray diffraction (XRD) on N-doped TiO<sup>2</sup> film deposited using RF magnetron sputtering [45]. N-doped TiO<sup>2</sup> films were deposited on quartz glass substrates (2 cm × 4 cm) by RF reactive magnetron sputtering. The crystalline structure of the as-deposited N-doped TiO<sup>2</sup> films was identified by X-ray diffraction (XRD). **Figure 1** shows the XRD patterns of N-doped TiO2 film. Diffraction peaks observed at 2θ = 25.28°, 36.95°, 37.88°, 38.55°, 48.05°, 54.09°, 54.88°, 62.67°, and 68.76°correspond well with (101), (103), (004), (112), (200), (105), (211), (204), and (116) planes of anatase phase of TiO2 . It can be seen that N-doping can greatly influence the growth orientation of anatase TiO2 particles. As shown in **Figure 1**, the intensities of the (004), (112), (200), and especially (211) peaks become stronger, while (101) peak become weaker for the N-doped TiO<sup>2</sup> film, compared with those of the undoped TiO<sup>2</sup> film. Especially, the increase of exposed (211) facets can effectively improve the photocatalytic activity of TiO<sup>2</sup> for water dissociation reactions [46], showing the high reactivity of exposed (211) facets.

**Figure 1.** The X-ray diffraction (XRD) on N-doped TiO<sup>2</sup> film.

Motivated by the above experimental findings, in a recent theoretical work [47], we have made a systematic study of the surface reactivity and water adsorption on anatase (211) using *ab initio* calculations. Calculations have been performed by the Vienna ab initio simulation package (VASP) [48–50] with all-electron projector augmented wave (PAW) method [51]. The generalized gradient approximation (GGA-PW91) [52] is set as the exchange and correlation functional. The valence states 3d2 4s2 for Ti, 2s2 2p4 for O, and 1s1 for H are used with an energy cutoff of 500 eV for the plane wave basis set. The calculated lattice constants for bulk anatase TiO2 are used to construct the diverse facets listed in **Table 1**. The anatase (211) surface was modeled by a slab of six layers with a unit surface cell of 7.706 Å × 5.501Å × 27.677Å (γ = 101.44°) comprising a total of 54 atoms separated by a vacuum region of 12 Å. The Monkhorst-Pack scheme [53] was adopted for the Brillouin zone integration with a 6 × 6 × 1 k-point mesh. All atoms are relaxed during geometry optimizations with the given surface cell. Convergence criteria employed for both the electronic self-consistent relaxation and the ionic relaxation were set to 10−6 eV and 0.01 eV/Å for the total energy and Hellmann-Feynman force, respectively.

We firstly discuss the surface stability. The stoichiometric unrelaxed termination of the (211) surface is shown in **Figure 2(a)** There are five under-coordinated and four fully-coordinated atoms exposed to the vacuum. The five under-coordinated atoms include three inequivalent twofold-coordinated oxygen atoms denoted by O21, O22, and O23, a fourfoldcoordinated Ti4 and a fivefold-coordinated Ti<sup>5</sup> , respectively. The four fully-coordinated atoms are O31, O32, O33, and Ti6 [see **Figure 2(a)**]. Different from (001) and (101) surfaces [12], fourfold-coordinated Ti4 atoms are present on the (211) surface. **Figure 2(b)** shows the optimized anatase (211) surface. After relaxation, the (211) surface shows a very corrugated structure, with a characteristic, saw tooth-like profile along the [1–31] direction. All under-coordinated oxygen (O2i) atoms are displaced outward, while the under-coordinated Ti4 and Ti5 atoms are relaxed inward. Both angles ∠Ti4 −O22−Ti<sup>5</sup> and ∠Ti5 −O31−Ti<sup>6</sup> become smaller, 100.3° and 147.7°, respectively. The largest relaxations are those of the fully-coordinated oxygen O31, which relaxes outward by approximately 0.35 Å, and O32, which relaxes inward by approximately 0.34 Å. Meanwhile, the surface atoms form fourmembered-ring (O-Ti-O-Ti) structures on the surface. These O-Ti-O-Ti rings are slightly deformed and the distances between oxygen atoms in these rings increased from the bulk value of 2.458 Å to 2.492–2.515 Å.


**Table 1.** Calculated surface energies (E in J/m<sup>2</sup> ) and surface densities Ti5 , Ti4 , and oxygen O<sup>2</sup> atoms [n(Ti5 ), n(Ti4 ), and n(O2 )]. Nat is the total number of atoms in the slab.

The Reactivity of Anatase TiO2 (211) Surface and the Bond-Charge Counting Model http://dx.doi.org/10.5772/intechopen.69141 7

**Figure 2.** Structures of the unrelaxed (a) and relaxed (b) anatase (211) surfaces. The O and Ti atoms are in red and grey spheres, respectively, indicated with different coordination numbers.

To investigate the surface stability, we calculated the electronic density of states (DOS) for bare anatase (211) surface after relaxation. The result is shown in **Figure 3** in comparison with the bulk TiO2 . There is a big gap, as large as in bulk, in the DOS of relaxed bare anatase (211) surface, which indicates the chemical stability of the (211) surface.

#### **2.2. Surface energetics**

Motivated by the above experimental findings, in a recent theoretical work [47], we have made a systematic study of the surface reactivity and water adsorption on anatase (211) using *ab initio* calculations. Calculations have been performed by the Vienna ab initio simulation package (VASP) [48–50] with all-electron projector augmented wave (PAW) method [51]. The generalized gradient approximation (GGA-PW91) [52] is set as the exchange and correlation

2p4

are used to construct the diverse facets listed in **Table 1**. The anatase (211) surface

cutoff of 500 eV for the plane wave basis set. The calculated lattice constants for bulk ana-

was modeled by a slab of six layers with a unit surface cell of 7.706 Å × 5.501Å × 27.677Å (γ = 101.44°) comprising a total of 54 atoms separated by a vacuum region of 12 Å. The Monkhorst-Pack scheme [53] was adopted for the Brillouin zone integration with a 6 × 6 × 1 k-point mesh. All atoms are relaxed during geometry optimizations with the given surface cell. Convergence criteria employed for both the electronic self-consistent relaxation and the ionic relaxation were set to 10−6 eV and 0.01 eV/Å for the total energy and Hellmann-Feynman

We firstly discuss the surface stability. The stoichiometric unrelaxed termination of the (211) surface is shown in **Figure 2(a)** There are five under-coordinated and four fully-coordinated atoms exposed to the vacuum. The five under-coordinated atoms include three inequivalent twofold-coordinated oxygen atoms denoted by O21, O22, and O23, a fourfold-

the optimized anatase (211) surface. After relaxation, the (211) surface shows a very corrugated structure, with a characteristic, saw tooth-like profile along the [1–31] direction. All under-coordinated oxygen (O2i) atoms are displaced outward, while the under-coor-

become smaller, 100.3° and 147.7°, respectively. The largest relaxations are those of the fully-coordinated oxygen O31, which relaxes outward by approximately 0.35 Å, and O32, which relaxes inward by approximately 0.34 Å. Meanwhile, the surface atoms form fourmembered-ring (O-Ti-O-Ti) structures on the surface. These O-Ti-O-Ti rings are slightly deformed and the distances between oxygen atoms in these rings increased from the bulk

atoms are relaxed inward. Both angles ∠Ti4

**) n(Ti5**

) and surface densities Ti5

(101) 24 0.52 5.1 5.1 (001) 18 1.08 6.9 6.9 (211) 54 0.97 2.4 2.4 7.2

<sup>14</sup> 48 0.99 3.5 (110)14 42 1.15 3.8

for O, and 1s1

for H are used with an energy

, respectively. The four fully-coordinated

−O22−Ti<sup>5</sup>

**) (10−2Å−2) n(O2**

atoms [n(Ti5

and ∠Ti5

−O31−Ti<sup>6</sup>

**) (10−2Å−2)**

), n(Ti4

), and

[see **Figure 2(a)**]. Different from (001) and (101) surfaces

atoms are present on the (211) surface. **Figure 2(b)** shows

**) (10−2Å−2) n(Ti4**

, Ti4

, and oxygen O<sup>2</sup>

4s2

and a fivefold-coordinated Ti<sup>5</sup>

for Ti, 2s2

functional. The valence states 3d2

tase TiO2

6 Titanium Dioxide

force, respectively.

coordinated Ti4

dinated Ti4

(103)s

n(O2

atoms are O31, O32, O33, and Ti6

[12], fourfold-coordinated Ti4

and Ti5

value of 2.458 Å to 2.492–2.515 Å.

**Facet Nat E (J/m2**

**Table 1.** Calculated surface energies (E in J/m<sup>2</sup>

)]. Nat is the total number of atoms in the slab.

The surface energies for (101), (001), and (211) are estimated using the expression, *E =(Etot–nEbulk)/A*, where *Etot* is the total energy of the slab and *Ebulk* is the energy of TiO2 unit in the bulk, *n* is the number of TiO2 units in the slab, *A* is the total surface area of the slab, including both sides of the slab. The calculated surface energies are listed in **Table 1**. The surface energy of the (001) surface is estimated to be 1.08 J/m2 , which is nearly twice that of the most stable anatase (101) surface (0.52 J/m2 ), in agreement with previous theoretical studies [14]. Similarly, the (211) surface has a high surface energy of 0.97 J/m2 , close to that of the (001) surface.

The value of the surface energy is known to be strongly correlated to the presence of undercoordinated Ti atoms on the surface [14]. The (001) surface energy is large because of the high surface density of Ti5 (see **Table 1**). However, the surface energy of anatase (211) is large even

**Figure 3.** Electronic density of states for the bulk TiO<sup>2</sup> and bare anatase (211) surface after relaxation. The Fermi level is set at 0 eV.

though the total density of under-coordinated Ti4 and Ti5 atoms is smaller than that on the (001) surface [even smaller than on (101)]. This result already suggests that Ti4 atoms, with two unsaturated bonds, have a higher reactivity than Ti5 atoms with one unsaturated bond. A similar behavior was found also for the anatase (110) and (103)s surfaces [14].

From the above calculation results in subsections 2.1 and 2.2, we can see that the (211) surface has a large electronic band gap and high surface energy. It shows those two surface properties, stability and reactivity, seem contradictory, could uniformly hold on the (211) surface.

#### **2.3. Water adsorption**

though the total density of under-coordinated Ti4

**Figure 3.** Electronic density of states for the bulk TiO<sup>2</sup>

set at 0 eV.

8 Titanium Dioxide

two unsaturated bonds, have a higher reactivity than Ti5

similar behavior was found also for the anatase (110) and (103)s

and Ti5

(001) surface [even smaller than on (101)]. This result already suggests that Ti4

From the above calculation results in subsections 2.1 and 2.2, we can see that the (211) surface has a large electronic band gap and high surface energy. It shows those two surface properties, stability and reactivity, seem contradictory, could uniformly hold on the (211) surface.

atoms is smaller than that on the

atoms with one unsaturated bond. A

surfaces [14].

and bare anatase (211) surface after relaxation. The Fermi level is

atoms, with

We next present a detailed picture for the adsorption of water on the TiO<sup>2</sup> (211) surface by considering one, two and three adsorbed water molecules corresponding to various coverages θ = 1/3, 2/3 and 1 ML per surface unit cell, respectively.

For a single water molecule (1/3 ML), there are four possible adsorption modes, corresponding to different adsorption positions (Ti<sup>4</sup> or Ti5 ) and different (molecular or dissociative) adsorption conformations. *For molecular water adsorption on Ti5 site* [see **Figure 4(a)**], the oxygen of water bonds to Ti<sup>5</sup> with bond length of 2.226 Å, and two surface oxygen atoms via

**Figure 4.** Side (left) and top (right) views of the structures for water adsorption on the anatase TiO2 (211) surface. (a) Molecular water on a Ti5 site. (b) Dissociative water on a Ti4 site. (c) Mixed state with one dissociative H<sup>2</sup> O on Ti4 and one molecular H2 O on Ti5 sites at 2/3 ML. (d) Mixed state on Ti<sup>4</sup> and Ti5 sites at 1 ML coverage. The O atom of water is plotted in orange, the H atom is in blue, and the H-bond is indicated by a dashed line.

Ti5 form two bond angles ∠Owater−Ti<sup>5</sup> −O22 = 99.85° and ∠Owater−Ti<sup>5</sup> −O31 = 77.18°, close to the bulk angles of 101.90° and 78.10°, respectively. Upon water adsorption, the Ti5 site becomes sixfold-coordinated: the Ti atom has six Ti-O bonds with their orientations similar to those in the bulk. At the same time, the two hydrogen atoms of water form H-bonds (HBs) with two neighboring surface under-coordinated oxygen atoms, O21 and O23, with bond lengths 2.339 and 1.873 Å, respectively. As a result, the computed molecular adsorption energy on the Ti<sup>5</sup> site is 0.784 eV. For dissociative water adsorption on Ti5 site, the water molecule is dissociated into hydroxyl (OH) and H fragments. The OH group bonds to Ti<sup>5</sup> with a length of 1.857 Å and then further bonds to O23 with a weak HB. The H fragment forms a new OH moiety with a nearby O21. As a result, the adsorption energy for a dissociated water on Ti5 site is 0.77 eV, which is slightly smaller than that of molecular adsorption. Thus, molecular adsorption is preferred on Ti5 site.

On the other hand, for molecular water on a Ti4 site, the oxygen atom of water binds to Ti<sup>4</sup> with a bond length of 2.207 Å, and Ti<sup>4</sup> is located at the position of one of the bulk Ti-O bonds indicating that there is one Ti bond left. The Ti4 adsorption site becomes fivefold-coordinated and the adsorption energy for molecular water on Ti4 site is estimated to be 0.99 eV. Finally, *for dissociative water on Ti4 site* [see **Figure 4(b)**], the O atom of the OH group is strongly bonded to the Ti4 atom with a short bond length of 1.847 Å (as compared to the Ti-O bond length of 2.207 Å in the molecular adsorption case) so that the Ti4 adsorption site becomes fivefold-coordinated. It is worthwhile to point out that the adsorption position of the O atom of the OH group does not correspond to the position of a bulk Ti-O bond, but is in the middle of the two missing bulk Ti-O bonds, and the orientation of Ti4 -OOH bond clearly deviates from its direction in the bulk, as shown by the two bond angles ∠OOH−Ti<sup>4</sup> −O33 = 130.86° and ∠OOH−Ti<sup>4</sup> −O32 = 119.91°. This adsorption geometry with short bond length and a middle position indicates that the dissociated water interacts with two unsaturated Ti4 bonds indeed. Furthermore, the hydrogen atom of OH forms a weak HB with a neighboring O23 atom of length 2.534 Å. The dissociated H from water interacts with a surface oxygen O23 forming a new OH moiety with a bond length of 1.013 Å and further forms an HB of 1.598 Å with O22. As a result, the adsorption energy for dissociated water on Ti4 site is estimated to be 1.28 eV, which is significantly larger than the value of 0.99 eV obtained for molecular adsorption.

To obtain further insight, we show the projected densities of states of the surface with a dissociative water on a Ti4 site and molecular water on Ti5 site in **Figure 5**. We can see that the O-2p orbitals in the OH group are extended to a wide range between −3.2 and −0.9 eV, indicating that the O atom of OH is strongly interacting with the substrate. On the other hand, for the case with a molecular water adsorption on a Ti5 site, all peaks from the water molecule are sharp and are simply superimposed on those of the bare surface, indicating that they interact weakly with the surface.

Combined together the above four calculation results: the adsorption energy, bond length, bond angle, and DOS, we can conclude that dissociative adsorption can *easily* happen at the Ti4 site while *hardly* happens on Ti5 . In fact, these different behaviors can be understood in terms of a simple model based on the bond-charge distribution, which is the key issue in this paper and will be discussed in the next section.

The Reactivity of Anatase TiO2 (211) Surface and the Bond-Charge Counting Model http://dx.doi.org/10.5772/intechopen.69141 11

Ti5

10 Titanium Dioxide

preferred on Ti5

Ti4

form two bond angles ∠Owater−Ti<sup>5</sup>

site.

a bond length of 2.207 Å, and Ti<sup>4</sup>

On the other hand, for molecular water on a Ti4

the adsorption energy for molecular water on Ti4

in the molecular adsorption case) so that the Ti4

bulk, as shown by the two bond angles ∠OOH−Ti<sup>4</sup>

sociated water interacts with two unsaturated Ti4

value of 0.99 eV obtained for molecular adsorption.

case with a molecular water adsorption on a Ti5

site while *hardly* happens on Ti5

paper and will be discussed in the next section.

bulk Ti-O bonds, and the orientation of Ti4

dissociated water on Ti4

ciative water on a Ti4

weakly with the surface.

Ti4

cating that there is one Ti bond left. The Ti4

site is 0.784 eV. For dissociative water adsorption on Ti5

into hydroxyl (OH) and H fragments. The OH group bonds to Ti<sup>5</sup>

−O22 = 99.85° and ∠Owater−Ti<sup>5</sup>

sixfold-coordinated: the Ti atom has six Ti-O bonds with their orientations similar to those in the bulk. At the same time, the two hydrogen atoms of water form H-bonds (HBs) with two neighboring surface under-coordinated oxygen atoms, O21 and O23, with bond lengths 2.339 and 1.873 Å, respectively. As a result, the computed molecular adsorption energy on the Ti<sup>5</sup>

and then further bonds to O23 with a weak HB. The H fragment forms a new OH moiety with

which is slightly smaller than that of molecular adsorption. Thus, molecular adsorption is

*sociative water on Ti4 site* [see **Figure 4(b)**], the O atom of the OH group is strongly bonded to the

It is worthwhile to point out that the adsorption position of the O atom of the OH group does not correspond to the position of a bulk Ti-O bond, but is in the middle of the two missing

This adsorption geometry with short bond length and a middle position indicates that the dis-

atom of OH forms a weak HB with a neighboring O23 atom of length 2.534 Å. The dissociated H from water interacts with a surface oxygen O23 forming a new OH moiety with a bond length of 1.013 Å and further forms an HB of 1.598 Å with O22. As a result, the adsorption energy for

To obtain further insight, we show the projected densities of states of the surface with a disso-

orbitals in the OH group are extended to a wide range between −3.2 and −0.9 eV, indicating that the O atom of OH is strongly interacting with the substrate. On the other hand, for the

sharp and are simply superimposed on those of the bare surface, indicating that they interact

Combined together the above four calculation results: the adsorption energy, bond length, bond angle, and DOS, we can conclude that dissociative adsorption can *easily* happen at the

terms of a simple model based on the bond-charge distribution, which is the key issue in this

site and molecular water on Ti5

atom with a short bond length of 1.847 Å (as compared to the Ti-O bond length of 2.207 Å

bulk angles of 101.90° and 78.10°, respectively. Upon water adsorption, the Ti5

a nearby O21. As a result, the adsorption energy for a dissociated water on Ti5

−O31 = 77.18°, close to the

with a length of 1.857 Å

site, the water molecule is dissociated

site, the oxygen atom of water binds to Ti<sup>4</sup>

adsorption site becomes fivefold-coordinated and

site is estimated to be 0.99 eV. Finally, *for dis-*

adsorption site becomes fivefold-coordinated.

bonds indeed. Furthermore, the hydrogen

site in **Figure 5**. We can see that the O-2p

site, all peaks from the water molecule are

. In fact, these different behaviors can be understood in


−O33 = 130.86° and ∠OOH−Ti<sup>4</sup>

site is estimated to be 1.28 eV, which is significantly larger than the

is located at the position of one of the bulk Ti-O bonds indi-

site becomes

site is 0.77 eV,

−O32 = 119.91°.

with

**Figure 5.** Projected electronic density of states on anatase (211) surface (a) for O-2*s,p* in the OH group on Ti4 site; (b) for O-2*s, p* in water on Ti5 site; The Fermi level is set at 0 eV.

Now, let us consider more water adsorption case. For two adsorbed H<sup>2</sup> O molecules (2/3 ML coverage), the first H<sup>2</sup> O prefers to adsorb at a Ti4 site in dissociative form according to the single water-adsorption results; next, another water molecule should adsorb on a Ti<sup>4</sup> or Ti5 site. *For the structure with one dissociated H2 O on a Ti4 site and one molecular H2 O on a Ti5 site* [see **Figure 4(c)**], the O-Ti5 bond is 2.230 Å, while the O-Ti<sup>4</sup> bond length is much shorter, 1.992 Å. The dissociated H combines with an O23 atom forming a new OH moiety and further forms a strong HB (1.590 Å) with an O22 atom. An additional HB between two water molecules forms with a bond length of 1.775 Å, which makes two water molecules closer and changes the values of the bond angles. In this mixed structure (c), the adsorption energy is 1.045 eV/mol, which is a little larger than the averaged value of 1.034 eV [(1.284 + 0.784)/2] for the single water adsorption on Ti4 and Ti5 sites due to the contribution of the new HB. On the contrary, for the structure with two dissociated H2 O on Ti4 and Ti5 sites, the adsorption energy is estimated to be 0.991 eV/mol, which is about 0.036 eV smaller than the averaged value of 1.027 eV [(1.284 + 0.770)/2] for the single water adsorption and also 0.054 eV lower than that of the mixed configuration. These results confirm that molecular adsorption is preferred on Ti<sup>5</sup> in the mixed structure. Moreover, for a structure with one dissociated H2 O and one associated H2 O on Ti4 sites and structure with two dissociated H2 O on Ti4 sites, the adsorption energy is estimated to be 0.960 and 0.916 eV/mol, respectively. Those are clearly lower than 1.045 eV/mol for the mixed structure. Therefore, with increasing coverage, water molecules prefer to be adsorbed in a mixed form with one dissociated H2 O on a Ti4 site and one molecular H2 O on a Ti5 site.

Finally, we discuss the monolayer coverage where three water molecules are adsorbed per surface unit cell. Following the 2/3 ML result with one dissociated H<sup>2</sup> O on a Ti4 site and one molecular H2 O on a Ti5 site, the third molecule would adsorb molecularly on a Ti4 site [see **Figure 4(d)**]. It is an O atom that binds to Ti4 with a bond length of 2.259 Å, while the two H atoms form HBs with nearby O atoms, where H-O21 is 2.156 Å and H-O22 is 1.907 Å. The bond length for molecular water on a Ti5 atom is 2.221 Å, while for dissociated water on Ti4 it is 1.934 Å. Two bond angles ∠OOH−Ti<sup>4</sup> −O33 and ∠Owater−Ti<sup>4</sup> −O32 are 100.69° and 79.00°, respectively. Thus, all Ti atoms are sixfold-coordinated with orientations similar to those of a bulk Ti atom. The dissociated H is captured by an O23 atom to form an OH moiety and further interacts with an O22 atom forming an HB of 1.835 Å. An additional HB of 1.652 Å also exists between these two adsorbed H<sup>2</sup> O. All surface atoms become saturated. The adsorption energy has a larger value of 0.946 eV/mol for this mixed configuration on Ti<sup>4</sup> sites. For comparison, we also consider configuration with two dissociated water molecules on Ti4 sites and one molecular H2 O on Ti5 . Though all surface atoms are also saturated, its adsorption energy is 0.909 eV/mol, which is lower than that of the mixed configuration with one dissociative and one molecular adsorption on Ti<sup>4</sup> . Thus, molecular adsorption is favored on Ti4 for the second water molecule. Meanwhile, for structure with one intact water on Ti4 and two dissociated water molecules on Ti4 and Ti5 sites, the computed adsorption energy is 0.902 eV/mol; for structure with three dissociated water molecules on Ti4 , Ti4 , and Ti5 sites, the adsorption energy is 0.833 eV/mol (see **Table 2**). These results suggest that a mixed water configuration is formed at monolayer coverage, with one dissociated water on Ti<sup>4</sup> , one molecular water on Ti4 , and one molecular water on Ti5 .

Our results show that Ti4 is an only active site which can dissociate water. Once Ti4 is saturated with a water, there will be no more water can be dissociated. It corresponds well with the experimental observations that the dissociation does occur only at low coverages and the probability of H2 O dissociation is decreased with increasing surface coverage. That is the purpose that we describe adsorption in detail from low water coverage to full coverage in this section.

#### **3. The bond-charge counting model for TiO2 surfaces**

#### **3.1. The mechanism and a simple phenomenological model**

According to the above results, the adsorption energies of water on a Ti4 site are always larger than those on a Ti5 site (see **Table 2**). Moreover, a water molecule can be easily dissociated on a Ti4 site while it hardly dissociates on Ti5 . We use a word "hardly" here because there is still controversy for the adsorption of H2 O on Ti5 site. In our case, the adsorption energy for a molecular adsorption on Ti5 site is only slightly higher than the dissociated one, which is not adequately to convince that water cannot be dissociated on Ti5 . Actually, there are a lot of arguments on this issue in literature. Lindan et al. [12] suggested that dissociative adsorption happened on the rutile


dissociated H2

12 Titanium Dioxide

O on a Ti4

O on a Ti5

lar water on a Ti5

angles ∠OOH−Ti<sup>4</sup>

It is an O atom that binds to Ti4

for this mixed configuration on Ti<sup>4</sup>

lar adsorption is favored on Ti4

one intact water on Ti4

one molecular water on Ti4

Our results show that Ti4

Ti4

, and Ti5

ability of H2

than those on a Ti5

adsorption on Ti5

Ti4

two dissociated water molecules on Ti4

ated H2

lar H2

O on Ti4

site and one molecular H2

face unit cell. Following the 2/3 ML result with one dissociated H<sup>2</sup>

−O33 and ∠Owater−Ti<sup>4</sup>

**3. The bond-charge counting model for TiO2**

site while it hardly dissociates on Ti5

convince that water cannot be dissociated on Ti5

troversy for the adsorption of H2

**3.1. The mechanism and a simple phenomenological model**

According to the above results, the adsorption energies of water on a Ti4

O on Ti5

sites, the adsorption energy is estimated to be 0.960 and 0.916 eV/mol,

O on a Ti4

with a bond length of 2.259 Å, while the two H atoms form HBs

−O32 are 100.69° and 79.00°, respectively. Thus, all Ti atoms

sites. For comparison, we also consider configuration with

for the second water molecule. Meanwhile, for structure with

.

 **surfaces**

. We use a word "hardly" here because there is still con-

site. In our case, the adsorption energy for a molecular

. Actually, there are a lot of arguments on this

O on Ti5

and Ti5

site and one molecu-

site [see **Figure 4(d)**].

. Though all surface

sites, the computed

site are always larger

. Thus, molecu-

is saturated

O.

,

,

site.

atom is 2.221 Å, while for dissociated water on Ti4 it is 1.934 Å. Two bond

respectively. Those are clearly lower than 1.045 eV/mol for the mixed structure. Therefore, with increasing coverage, water molecules prefer to be adsorbed in a mixed form with one dissoci-

O on a Ti5

Finally, we discuss the monolayer coverage where three water molecules are adsorbed per sur-

with nearby O atoms, where H-O21 is 2.156 Å and H-O22 is 1.907 Å. The bond length for molecu-

are sixfold-coordinated with orientations similar to those of a bulk Ti atom. The dissociated H is captured by an O23 atom to form an OH moiety and further interacts with an O22 atom forming an HB of 1.835 Å. An additional HB of 1.652 Å also exists between these two adsorbed H<sup>2</sup>

All surface atoms become saturated. The adsorption energy has a larger value of 0.946 eV/mol

atoms are also saturated, its adsorption energy is 0.909 eV/mol, which is lower than that of the

and two dissociated water molecules on Ti4

, and one molecular water on Ti5

adsorption energy is 0.902 eV/mol; for structure with three dissociated water molecules on Ti4

mixed water configuration is formed at monolayer coverage, with one dissociated water on Ti<sup>4</sup>

with a water, there will be no more water can be dissociated. It corresponds well with the experimental observations that the dissociation does occur only at low coverages and the prob-

that we describe adsorption in detail from low water coverage to full coverage in this section.

issue in literature. Lindan et al. [12] suggested that dissociative adsorption happened on the rutile

mixed configuration with one dissociative and one molecular adsorption on Ti<sup>4</sup>

sites and one molecular H2

sites, the adsorption energy is 0.833 eV/mol (see **Table 2**). These results suggest that a

is an only active site which can dissociate water. Once Ti4

O dissociation is decreased with increasing surface coverage. That is the purpose

site (see **Table 2**). Moreover, a water molecule can be easily dissociated on a

site is only slightly higher than the dissociated one, which is not adequately to

site, the third molecule would adsorb molecularly on a Ti4

**Table 2.** Adsorption energy (ΔH in eV) per H<sup>2</sup> O molecule on anatase (211) at various water coverages θ = 1/3, 2/3, and 1 ML.

(110) surface, while Schaub's result [43] is in contrast to that. However, there is an important case that water is indeed dissociated on anatase (001) surface with only Ti5 atom [13]. Therefore, whether Ti5 atom can dissociate water is still a matter for controversy on TiO<sup>2</sup> surfaces.

Many research works are only concentrated on the total energy calculations in literature. DFT total energy calculations are a definitely powerful tool. But here there is a shortcoming that total energy calculations just tell the total energy of the system, not the local interaction energy. For example, in dissociative adsorption, the total energy includes the adsorption site of the dissociated H as well as H-bond energy at high coverage case. Thus, it is difficult to extract the onsite interaction energy and it is hard to obtain a clear conclusion just from the total energy. All those controversies come from the information of total energy and less considerations for the reaction mechanism. Therefore, it is necessary to think it over from the origin of physics and chemistry beyond total energy calculation.

The water dissociation on surface is a chemical adsorption, which can be regarded as a chemical reaction analogue to a chemical displacement reaction, e.g., 2Na + 2H<sup>2</sup> O = 2NaOH + H<sup>2</sup> ↑. In this displacement reaction, the necessary condition is that more active metal atom can substitute the less active metal atom or hydrogen. Also, from a physical point of view, the O atom in water must gain more electrons that H atom provided so that such a dissociation process happens by losing an H atom. From these considerations, we propose a simple bond-charge counting model based on the charge distribution on Ti bond in TiO2 .

In bulk TiO2 , each Ti atom has six nearest neighboring O atoms and Ti atom has four outmost electrons, i.e., each Ti4+ ion is surrounded by an octahedron of six O2− ions. Thus, on an average, each Ti atom can offer 4/6 electron charge at each Ti-O bond. It holds for both rutile and anatase since they have the same TiO6 octahedra structure. Therefore, we could make a simple bondcharge counting for this system. When a Ti4 atom interacts with the oxygen atom of H<sup>2</sup> O, two unsaturated Ti bonds participate in the interaction and offer about 4/3 electron charge to this O atom by forming a strong bond [see **Figure 4(b)**]. Thus, it satisfies the reaction requirement and Ti4 is more active than H atom. Then, one H atom can be released from the water molecule on a Ti4 site. In fact, one H atom dissociates spontaneously from the water molecule as this adsorbs on a Ti4 atom. On the other hand, Ti5 can only provide about 2/3 electron charge to the water O atom, less than the charge contribution from an H atom. Therefore, Ti5 is less active than H atom and hardly causes dissociation of an H atom. Although there is very little difference in energy (0.014 eV) between molecular and dissociated structures, we can clearly judge that water favors molecular adsorption and is unfavorable on Ti5 site.

The essence of the model is qualitatively taking account of average charge on each Ti bond in TiO2 material. The model is phenomenological and does not intend to provide the precise value of charge transferred during interaction due to the complex of 3d orbitals of Ti atom in TiO6 octahedra. Nevertheless, the bond-charge counting model clarifies the intrinsic charge difference between Ti<sup>4</sup> and Ti5 atoms on surfaces where Ti4 can provide more than one electron and Ti5 much less one electron. The necessary condition for water splitting is that the surface Ti atoms must provide more than one electron to O atom of water. The charge contributed from a single Ti bond is not sufficient for water dissociation. Therefore, two unsaturated Ti bonds satisfy the condition corresponding to the four-coordinated Ti4 atom that has chemical reactivity, while Ti5 atom not.

### **3.2. Typical examples**

In order to verify this model, we have made an intensive investigation for TiO2 surface as much as we could find in literature including steps and vacancies. We found that all reactive surfaces splitting water are associated with Ti<sup>4</sup> atom or equivalent Ti4 atom without any exception. We are not able to exhaust all surfaces here, rather list typical and important surfaces in different geometric categories as follows.

#### *3.2.1. Surfaces with Ti4 atom*

We start the survey from the TiO2 surfaces with Ti4 atoms. At anatase surfaces, the (110) and (103)*s* contain Ti4 atoms. Therefore, their surface energies are 1.15 and 0.99 J/m2 , respectively [14]. Those rather high values indicate that the surfaces have a very high reactivity contributed from Ti4 atoms.

#### *3.2.2. Surface with only Ti5 atom*

The surfaces with only Ti5 atom are more interesting. Whether the surfaces can dissociate water is controversy. We will see it strongly depends on its surface energy. As anatase (001) surface, the surface energy has a rather high value of 0.98 J/m2 indicating a high reactivity. Thus, it is clearly pointed out in Ref. [13] that the structure of the dissociated state (in **Figure 6(a)** same The Reactivity of Anatase TiO2 (211) Surface and the Bond-Charge Counting Model http://dx.doi.org/10.5772/intechopen.69141 15

each Ti atom can offer 4/6 electron charge at each Ti-O bond. It holds for both rutile and anatase

unsaturated Ti bonds participate in the interaction and offer about 4/3 electron charge to this O atom by forming a strong bond [see **Figure 4(b)**]. Thus, it satisfies the reaction requirement and

is more active than H atom. Then, one H atom can be released from the water molecule on a

site. In fact, one H atom dissociates spontaneously from the water molecule as this adsorbs

and hardly causes dissociation of an H atom. Although there is very little difference in energy (0.014 eV) between molecular and dissociated structures, we can clearly judge that water favors

The essence of the model is qualitatively taking account of average charge on each Ti bond

atoms on surfaces where Ti4

surface Ti atoms must provide more than one electron to O atom of water. The charge contributed from a single Ti bond is not sufficient for water dissociation. Therefore, two unsaturated

much as we could find in literature including steps and vacancies. We found that all reactive

tion. We are not able to exhaust all surfaces here, rather list typical and important surfaces in

atoms. Therefore, their surface energies are 1.15 and 0.99 J/m2

[14]. Those rather high values indicate that the surfaces have a very high reactivity contrib-

The surfaces with only Ti5 atom are more interesting. Whether the surfaces can dissociate water is controversy. We will see it strongly depends on its surface energy. As anatase (001) surface,

clearly pointed out in Ref. [13] that the structure of the dissociated state (in **Figure 6(a)** same

site.

 material. The model is phenomenological and does not intend to provide the precise value of charge transferred during interaction due to the complex of 3d orbitals of Ti atom in

much less one electron. The necessary condition for water splitting is that the

atom or equivalent Ti4

octahedra. Nevertheless, the bond-charge counting model clarifies the intrinsic charge

octahedra structure. Therefore, we could make a simple bond-

atom interacts with the oxygen atom of H<sup>2</sup>

can only provide about 2/3 electron charge to the water O

O, two

is less active than H atom

can provide more than one elec-

atom that has chemi-

atom without any excep-

atoms. At anatase surfaces, the (110) and

indicating a high reactivity. Thus, it is

surface as

, respectively

since they have the same TiO6

Ti4

Ti4

on a Ti4

14 Titanium Dioxide

in TiO2

tron and Ti5

difference between Ti<sup>4</sup>

cal reactivity, while Ti5

**3.2. Typical examples**

*3.2.1. Surfaces with Ti4*

(103)*s* contain Ti4

uted from Ti4

TiO6

charge counting for this system. When a Ti4

atom. On the other hand, Ti5

molecular adsorption and is unfavorable on Ti5

and Ti5

atom not.

surfaces splitting water are associated with Ti<sup>4</sup>

 *atom*

 *atom*

the surface energy has a rather high value of 0.98 J/m2

different geometric categories as follows.

We start the survey from the TiO2

atoms.

*3.2.2. Surface with only Ti5*

atom, less than the charge contribution from an H atom. Therefore, Ti5

Ti bonds satisfy the condition corresponding to the four-coordinated Ti4

In order to verify this model, we have made an intensive investigation for TiO2

surfaces with Ti4

**Figure 6.** (**Figure 3** in Ref. [13]) Atomic structure (side view) for adsorbed water molecule(s) on anatase (001). (a) Dissociated state. (b) Molecular state. (c) Mixed state. Gray lines in (b) and (c) indicate hydrogen bonds. Bond lengths are in Å.

as in **Figure 3(a)** in Ref. [13]) is characterized by the breaking of the bond between the bridging 2c oxygen and the Ti<sup>5</sup> atoms involved in the adsorption, i.e., the Ti5 atom actually becomes fourfold-coordinated after breaking its bond to a bridging O atom. Therefore, the dissociative water is absorbed on an equivalent Ti4 site. It is expected that such phenomenon of Ti<sup>5</sup> atom breaking bond with neighboring oxygen becomes an effective Ti<sup>4</sup> atom which would be held for the anatase (103)*<sup>f</sup>* surface with the high surface energy of 0.9 J/m2 .

However, for the other surfaces only containing Ti5 atoms, their surface energies are very small. The values are 0.49 and 0.58, and 0.35 J/m2 for anatase (101) and (100), and rutile (110), respectively. Note that the rutile (110) surface has smallest surface energy. Thus, the anatase (101) [13] and rutile (110) [11] are thermodynamically most stable structures. We can rule out the possibility of water dissociation on those surfaces [10].

Combined with the surface energy, we may estimate which surface with only Ti5 atom can dissociate water by breaking a Ti bond. According to calculations, the surface energy should approach to ~1 J/m2 . For the high reactive surfaces with only Ti5 , the Ti5 atoms eventually become too effective Ti<sup>4</sup> atoms during the interaction.

#### *3.2.3. Surfaces with steps*

Step edges are the most common intrinsic defects on the surface. In this subsection, we give two examples of steps on two most stable surfaces, anatase (101) and rutile (110) surface.

Gong et al. [40] have made an intensive investigation on anatase (101) surface. The structure models of step edges they studied are shown in **Figure 7**. We can divide those surface step structures into two categories with Ti4 (in **Figure 7(a)**, **(d)**, **(e)**, **(f)**, and **(h)**) and without Ti4 atoms (in **Figure 7(b)**, **(c)**, and **(g)**). Then, we recapitulate their surface energy calculation results γ (θ) in unit 10-2eV/Å<sup>2</sup> and rearrange in an order of containing Ti4 and Ti5 atoms as follows:


We omit the labels of vicinal surfaces here for simplicity. The surface energies with Ti4 are larger than that with Ti5 in each column. Gong et al. further studied water adsorption on D, BI, and AII with Ti5 atom (see Supplementary Information in Ref. [40]). On D-type step edge, both molecular and dissociative H2 O adsorption can occur, but energy difference is much smaller than on flat TiO<sup>2</sup> (101). For BI step, the adsorption energies are smaller than that on the

**Figure 7.** Structure models of step edges A–E on anatase (101) (**Figure 2** in Ref. [40]).

(101) surface. Note BI has the smallest surface energy among all step structures. On the least stable AII with the highest surface energy among steps containing Ti5 atom, the water adsorption is found to be similar to the anatase (001) surface where water is dissociatively adsorbed with adsorption energy 1.28 eV. Again, here surface Ti5 atom becomes Ti4 by breaking a bond with neighboring oxygen.

Hong et al. [41] investigated water adsorption behavior step edges on rutile TiO2 (110) surface using DFT calculations. They found that the < 1-10 > edge exhibits significantly enhanced water adsorption, especially dissociative adsorption, as compared to the pristine (110) surface and < 001 > step edge due to the existence of fourfold coordinated Ti<sup>4</sup> atoms at the < 1-10 > step edge, which lead to charge transfer to adsorbates more easily than fivefold coordinated Ti5 atoms on the (110) surface and < 001 > step edge.

Later, Zheng et al. [42] studied the associative and dissociative adsorption of water molecules on rutile TiO2 (110) surface with step defects by DFT calculations. The step structures were created by removing the TiO2 unit along the < 1-11 > direction and exposing the Ti<sup>4</sup> atoms (terminating the Ti rows of the upper terrace) and the Ti5 atoms (see **Figure 1(a)**, **(b)** in Ref. [42]). They only considered the case of Ti bonds fully saturated. Their results show that the molecular and dissociative adsorptions of H2 O can both be observed on Ti4 sites and the molecularly absorbed water is more favorable on the Ti5 sites. The lowest energy corresponds to the configuration where water molecule on Ti<sup>5</sup> site and one dissociated and one molecular water on Ti4 site, same as our result for anatase (211) surface [47].

Thus, dissociative adsorption is also attributed to the existence of Ti<sup>4</sup> atoms and/or equivalent Ti4 atoms exposing at step edges on anatase (101) and rutile (110) surfaces.

### *3.2.4. Surfaces with O vacancy*

*3.2.3. Surfaces with steps*

16 Titanium Dioxide

in unit 10-2eV/Å<sup>2</sup>

larger than that with Ti5

smaller than on flat TiO<sup>2</sup>

both molecular and dissociative H2

BI, and AII with Ti5

structures into two categories with Ti4

Step edges are the most common intrinsic defects on the surface. In this subsection, we give two examples of steps on two most stable surfaces, anatase (101) and rutile (110) surface.

Gong et al. [40] have made an intensive investigation on anatase (101) surface. The structure models of step edges they studied are shown in **Figure 7**. We can divide those surface step

(in **Figure 7(b)**, **(c)**, and **(g)**). Then, we recapitulate their surface energy calculation results γ (θ)

We omit the labels of vicinal surfaces here for simplicity. The surface energies with Ti4

**Figure 7.** Structure models of step edges A–E on anatase (101) (**Figure 2** in Ref. [40]).

and rearrange in an order of containing Ti4

AI(**Figure 7(a)**) 5.36 4.68 4.34 Ti4 CI(**Figure 7(e)**) 5.49 4.81 4.46 Ti4 CII(**Figure 7(f)**) 6.22 5.22 4.78 Ti4 E(**Figure 7(h)**) 6.82 5.86 5.34 Ti4 AII(**Figure 7(b)**) 4.60 4.24 4.06 Ti5 BI(**Figure 7(c)**) 3.66 3.59 Ti5 D(**Figure 7(g)**) 4.52 4.11 3.94 Ti5

(in **Figure 7(a)**, **(d)**, **(e)**, **(f)**, and **(h)**) and without Ti4

and Ti5

in each column. Gong et al. further studied water adsorption on D,

(101). For BI step, the adsorption energies are smaller than that on the

O adsorption can occur, but energy difference is much

atom (see Supplementary Information in Ref. [40]). On D-type step edge,

atoms as follows:

atoms

are

Oxygen vacancy is also one of the most common defects on the surface. Again, in this subsection, we give two examples of O vacancy on two most stable surfaces, rutile (110) and anatase (101).

Schaub et al. [43] investigated the O vacancy on rutile (110) through both experiments and DFT calculation and determined the O vacancies as active sites responsible for the dissociation of water molecules. Their DFT calculation results show that the dissociation of water is only at oxygen vacancies with an adsorption energy of 0.94, while on the perfect (100) surface, water molecule binds to the surface by 0.56 eV and the dissociation of water is even endothermic by 0.23 eV. The dissociative adsorption is unfavorable on the perfect (100) surface. They explained that the large reactivity of the vacancies is associated with the high-energy defect and water dissociation is simply to refill the coordination shell of Ti underneath the vacancy. However, there will be something more than that. Note that the *two* Ti6 atoms underneath the vacancy become Ti5 atoms when O leaves the surface. Thus, when O atom of water is to refill the O vacancy, the *two* Ti5 atoms interact with O of water simultaneously. Then, in this case, we should count two Ti bonds participating in interaction. Therefore, the dissociation of water is due to the combined contribution of two unsaturated Ti atoms.

On the anatase (101) surface, dissociation of water close to the oxygen vacancy is energetically favored compared to molecular adsorption. Tilocca and Selloni [44] have done a detailed calculation of energy barrier between the molecular and dissociated states. When a surface O atom is removed, the Ti6 and Ti5 atoms bridging this O atom tune into Ti5 and Ti4 , respectively. Water oxygen bonds to Ti<sup>4</sup> and then dissociates through a dissociation pathway. Thus, the dissociation of water on O vacancy of anatase (101) is also attributed to that Ti4 atom.

#### *3.2.5. Surfaces with Ti3 atom*

Recently, the three-coordinated Ti atom (Ti<sup>3</sup> ) are found on the (111) anatase TiO2 surfaces. Xu et al [34] reported that they prepared anatase TiO2 single crystals exposed (111) facet. Their DFT calculations showed that the (111) facet has a much higher surface energy of 1.61 J/m2 , which is attributed to the large percentage of under-coordinated atoms. They also found that this material has much higher photocatalytic activity than other surfaces. Here, there are Ti3 and Ti5 atoms with the ratio 1:3 on the (111) surface. According to our model, the Ti<sup>3</sup> atom could contribute two electrons participating interaction. Thus, it is expected that two water molecules could be dissociated on a single Ti3 site. It could explain the (111) surface has much higher photocatalytic activity than other surfaces.
