The mechanism of H₂ and H₂O desorption from bridging hydroxyls of a TiO₂(110) surface

Abstract

The photocatalytic H₂ production from H₂O over TiO₂ has attracted tremendous attention in recent years, and great progress has been achieved in light adsorption and water dissociation. As a comparison, the H₂ and O₂ production over a pure TiO₂ surface has not been successful yet. Recently, the desorption of bridging hydroxyls (BBOHs) to form H₂ has been found to be possible on a TiO₂(110) surface. However, the yield of H₂ is low, and the majority of BBOHs desorb as H₂O. Here, for the first time, we have systematically studied the mechanism of H₂ desorption and the competition of H₂ and H₂O desorption on a TiO₂(110) surface with DFT methods. We found that the generally believed pathway, the direct coupling of BBOHs, is not the most facile pathway. We propose that the reaction undergoes a Ti–H key intermediate, which then forms an O–H^δ+⋯H^δ−–Ti type dehydrogenation transition state. On a stoichiometric surface, the barriers for H₂ desorption and H₂O desorption are 2.20 eV and 1.09 eV, respectively. However, with an increase in BBO vacancies (O_vs, created by H₂O desorption), the barrier for H₂ desorption decreases, while the barrier for H₂O desorption increases. Specifically, H₂ desorption was found to be easier than H₂O desorption with our two O_vs TiO₂ model. Therefore, our results predict that H₂O desorption is dominant at the beginning, then H₂ desorption becomes more and more competitive. This prediction perfectly fits with the experimental observations. Furthermore, the stability of the key Ti–H intermediates and the possible ways for changing the conditions of H₂ desorption have also been discussed.

---

Introduction

Titania (TiO₂) has emerged as one of the most important metal oxides in a large number of technological areas, including heterogeneous catalysis, electronic devices, photocatalysis, biomaterials, and so on.^1–7 TiO₂-based photocatalysis has grown into a fascinating research field since Fujishima and Honda's first reports on water splitting on TiO₂ and its potential application in clean hydrogen production.⁸ The key problems in water splitting include light adsorption, water dissociation, H₂ production and O₂ production etc. In the past decades, great progress has been achieved in the fields of light adsorption and water dissociation. However, the H₂ production over a TiO₂ surface has not been successful until very recently^14–18 by heating the photocatalyzed methanol/TiO₂(110) surface.¹⁵ As shown in the literature and our previous work (ref. 33), the dissociation of MeOH on TiO₂ affords aldehyde and bridging hydroxyls (BBOHs). The observation of H₂ from MeOH shows that H₂ can be formed by BBOHs, which is not clear before. The dissociation of H₂O also affords BBOHs, together with the hydroxyl group on a five-coordinated titanium (Ti_5c) site. Therefore, the observation of H₂ from MeOH is crucial; it tells us that in principle H₂ can also be formed by the dissociation of H₂O over a TiO₂ surface. However, currently the temperature for H₂ desorption is >500 K, and H₂O is already desorbed at this temperature (in the case of MeOH, the production of aldehyde leaves BBOH on the surface which cannot desorb as MeOH). If we can reduce the H₂ desorption temperature to which the H₂O can adsorb on the surface, the water splitting for hydrogen production could be available (although not catalytically unless the hydroxyl group on Ti_5c can also be removed). Understanding the mechanism is one of the promising ways for designing new systems with better reactivity, and we expected that the mechanistic study of H₂ desorption from a BBOH-covered TiO₂(110) surface could be helpful in increasing the yield of H₂ for the methanol/TiO₂(110) system, as well as in providing valuable ideas to realize the H₂ from the H₂O/TiO₂(110) system.

The most commonly observed and investigated hydrogen adatoms on the rutile TiO₂(110) surface are BBOHs that can be achieved by various methods.^9–15 The largest challenge for the H₂ desorption over TiO₂(110) is the competition of H₂O desorption. Besides that, BBOHs can also migrate into the TiO₂ bulk. DFT calculations have shown that on a stoichiometric surface the barrier for H₂O desorption is 0.9–1.1 eV,^14,18 and the barrier for BBOH migration to bulk is also about 1.1 eV.^12,17,18 However, the direct coupling of two BBOHs to form H₂ is much difficult, with a barrier of 1.6–1.85 eV from nudged elastic band (NEB) calculations.^14,18 These theoretical studies support the findings that it is indeed much easier for the BBOHs to diffuse into the bulk or produce H₂O compared to the formation of H₂ on the surface. On the experimental side, Michael A. Henderson found that BBOHs desorb as H₂O at temperatures between 500 and 550 K.¹⁶ However, Yin et al. used high BBOH coverage samples and no corresponding H₂O (or H₂) temperature-programmed desorption (TPD) signal has been observed; instead, they supported that the BBOHs migrated into the TiO₂ bulk.¹² Afterwards, Y. Du et al. found a H₂O TPD peak at 500 K, and no H₂ product was detected from the highly hydroxylated TiO₂(110) surface.¹⁴

Surprisingly, very recently our colleagues' TPD experiments have shown the desorption of H₂O at about 520 K and the desorption of H₂ at ∼50 K higher.¹⁵ Although the ratio of H₂ is low, it is the first time that H₂ production has been observed on a TiO₂(110) gas–solid interface. The H₂O yield increased very fast at first and then reached a plateau, and after that, the H₂ yield was increasing faster than that of H₂O.¹⁵ Later on, H₂ desorption on an anatase(101) surface has also been observed by our colleagues.¹⁹ Wu et al. found a H₂ peak at 207 K using thermal desorption spectroscopy (TDS) spectra, and they proposed that H–Ti species could be the photoactive species.²¹

These important observations put a big challenge to the mechanistic studies. Previous theoretical calculations have shown that for the 1 ML (1 ML = 5.2 × 10¹⁴ molecules cm⁻²) BBOHs coverage model, using the NEB method with 12 images, the direct coupling of two BBOHs to form H₂ has a barrier of 1.85 eV (ref. 18) which is much higher than the barrier of H₂O desorption. It is known that H₂ desorption is facilitated by the reducing ability of the surface since it requires two electrons to be transferred from the surface to two H⁺ (BBOH) to form H₂, while H₂O desorption does not involve electron transfer between the surface and H₂O, thus is less sensitive to the reducing ability of the surface. With a decrease in BBOH concentration, the surface becomes less reducing, and the H₂ desorption barrier is expected to be higher, while in ref. 14, using the NEB method with 7 images, the barrier for the 1/2 ML BBOHs coverage model is found to be only 1.60 eV. We know that the barrier evaluated by the NEB method is highly sensitive to the number of images used in the calculation. Therefore, we have re-evaluated the direct coupling mechanism using the newly developed climbing-image nudged elastic band (CI-NEB) method^38,39 which is designed to locate the transition state directly. We found that for the 1 ML BBOHs coverage model, the H₂ desorption barrier is 1.80 eV, which is almost the same as that in ref. 18. While for the 1/2 ML BBOHs coverage model, the barrier is 2.00 eV. To further evaluate this mechanism, we have calculated the barrier using the 1/4 ML BBOHs coverage model (which is more close to the experimental conditions), and we obtained an even higher barrier of 2.66 eV (shown in Fig. 1). Based on these results, we think that possibly the H₂ is not formed by the direct coupling of two BBOHs as the communities have thought before, and it undergoes a new mechanism which has not been addressed yet.

Fig. 1 Reaction profiles for H₂ desorption on 1/4 ML BBOHs on a stoichiometric TiO₂(110) surface. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Indeed, it is not surprising that the direct coupling of BBOHs has a very high barrier, since both BBOHs bear strong positive charges. There are many well studied dehydrogenation/hydrogenation systems which happen under mild conditions. In general, these systems bear less polarized M–H bonds or have both H^δ+ and H^δ− coexisting in the system (shown in Scheme 1).^22–30 The dehydrogenation is therefore facilitated by the less electrostatic repulsion between two H atoms. On a TiO₂(110) surface, such mechanisms are also available. Two types of Ti–H species can be candidates for key intermediates of dehydrogenation: the end on Ti_5c–H and the bridging Ti–H–Ti at the BBO vacancies (O_v) where H occupied the place of the missing BBO (Ti_5c-Ov−H).

Scheme 1 Typical mechanisms for dehydrogenation under mild conditions.

In this work, we have systematically investigated the mechanism of H₂ desorption, as well as the competition between H₂ and H₂O desorption on a TiO₂(110) surface. We propose that the reaction undergoes a Ti–H key intermediate, which then forms an O–H^δ+⋯H^δ−–Ti type transition state. The O_v plays an important role in both H₂ desorption and H₂O desorption. Our mechanism successfully explains the experimental observations, especially the competition between H₂ desorption and H₂O desorption. Furthermore, we have also discussed the possible ways to increase the yield of H₂ desorption on the TiO₂(110) surface.

Methods

As shown in our previous studies,^32,33 all of our calculations were performed using the Vienna ab initio simulation package code^34,35 and plane augmented wave potential.³⁶ The wave function was expanded by the plane wave, with a kinetic cut-off of 400 eV and a density cut-off of 650 eV. The generalized gradient approximation with the spin-polarized Perdew–Burke–Ernzerhof functional³⁷ was used to determine the optimized molecular structures of TiO₂(110).

Unless specified, an efficient force reversed method³¹ was used to locate the transition state (TS). The CI-NEB methods (constrained minimization and climbing-image nudged elastic band methods)^38,39 were used for TSs which are challenging using the force reversed method, and in this case the minimum energy pathway for each elementary reaction was discretized by a total of ten images between the initial and final states.

Our surface model was cut out of a six-layer slab TiO₂ crystal to expose the (110) surface^{32,33,40–44} and fixed on the bottom two layers of the atoms. All Ti_5c sites on the bottom layer were saturated with water molecules to maintain the bulk coordination environment.^32,33 The periodically repeated slabs on the surface were decoupled by 15 Å vacuum gaps. A Monkhorst–Pack grid⁴⁵ of (2 × 1 × 2) k-points was used for the 4 × 2 surface unit cell. Isolated gas-phase molecules were optimized in a (15 × 15 × 15) unit cell with a single k-point.

The reaction energy (ΔE), the H₂O desorption energy (ΔE_{H2O_desorption}) and the H₂ desorption energy (ΔE_{H2_desorption}) were defined as follows:

ΔE = E_fin state − E_init state (1)

ΔE_{H2O_desorption} = E_H2O + E_{slab+Ov+(n−2)BBOHs} − E_{slab+n×BBOHs} (2)

ΔE_{H2_desorption} = E_H2 + E_{slab+(n−2)×BBOHs} − E_{slab+n×BBOHs} (3)

where E_{fin state} and E_{init state} refer to the final state energy and initial state energy, respectively; E_{slab+n×BBOHs} or E_{slab+(n−2)×BBOHs} are the total energy of the six-layer slab with n or (n−2) BBOHs on the surface, respectively; E_{slab+Ov+(n−2)BBOHs} is the total energy of the six-layer slab with (n−2) BBOHs on the surface with an O_v; and E_H2O or E_H2 is the total energy of the isolated H₂O or H₂ species.

Results

The mechanism of H₂ and H₂O recombinative desorption from a stoichiometric TiO₂(110) surface

As mentioned above, the direct coupling of the two BBOHs to produce H₂ (pathway H₂_A) is rather hard, and we will search for alternative mechanisms. On a stoichiometric TiO₂(110) surface, only Ti_5c is unsaturated and able to form a Ti_5c–H intermediate. We then consider a mechanism that starts with BBOH migration to Ti_5c to obtain Ti_5c–H. Then this negatively charged hydrogen atom couples with the positively charged BBOH to form H₂. In this mechanism, the key transition state for H₂ desorption is BBO–H^δ+⋯H^δ−–Ti_5c. We denote this pathway as pathway H₂_B. Since 1 ML BBOHs are not available experimentally, we have investigated the H₂ desorption on 1/4 and 1/2 ML BBOHs models using a 4 × 2 unit cell of TiO₂(110).

The reaction coordinates of pathway H₂_B for the 1/4 ML BBOHs model are shown in Fig. 1. The H transfers from the BBO site (1-a) to the sub-surface oxygen (O_s) site (1-b) are endothermic by 0.48 eV, with a barrier of 0.82 eV (TS1-1). The H transfers from the O_s site (1-b) to the Ti_5c site (1-c) are highly endothermic (0.62 eV), and the barrier is also much higher (1.72 eV, TS1-2). The barrier for the coupling of BBO–H and Ti_5c–H to produce H₂ (TS1-3) is 0.20 eV. The H₂ desorption energy is 0.62 eV, and the rate-determining step is the H transfers from O_s to Ti_5c with an overall barrier of 2.20 eV. BBOH can also transfer to Ti_5c directly (pathway H₂_C). We have tried very hard to locate its transition state using the force reversed method, but we are not successful. Therefore, we calculated the barrier using the CI-NEB method, and the barrier we obtained is 2.19 eV (see Fig. S1†) which is almost the same as pathway H₂_B.

We have also considered the pathway where H₂ has been formed by the coupling of sub-surface hydroxyls (O_s–H) and Ti_5c–H (pathway H₂_D). However, the intermediate ready for dehydrogenation is already higher in energy than TS1-3 by 0.45 eV (see Fig. S2†), and therefore this is not the preferred pathway.

Based on these results, we propose that pathway H₂_B is the most facile pathway for dehydrogenation of BBOHs to form H₂ on a stoichiometric TiO₂(110) surface. Its overall barrier is lower than that of pathway H₂_A by more than 0.4 eV.

The optimized structures are also shown in Fig. 1. The optimized bond lengths for BBO–H, O_s–H, and Ti_5c–H are 0.97, 0.98 and 1.72 Å, respectively. In Ts1-1, r(BBO–H) is 1.37 Å, and r(H–O_s) is 1.12 Å. In TS1-2, r(O_s–H) is 1.32 Å and r(H–Ti_5c) is 1.81 Å. In Ts1-3, r(BBO–H), r(H–H), and r(H–Ti_5c) are 1.21 Å, 1.03 Å and 1.91 Å, respectively.

To better compare the H₂ and H₂O desorption reactions, we have re-evaluated the H₂O desorption pathway with our theoretical model. The results are shown in Fig. 2. The H transfers from one BBO to another BBO to produce H₂O is endothermic by 0.40 eV, with a barrier of 0.82 eV (TS2-1). The H₂O desorption energy is 1.09 eV. We denote this pathway as pathway H₂O_A, and the results are pretty similar to those in ref. 14 and 18. In TS2-1, r(BBO–H) and r(H–BBOH) are 1.21 Å and 1.27 Å, respectively.

Fig. 2 Reaction profiles for H₂O desorption on 1/4 ML BBOHs on a stoichiometric TiO₂(110) surface. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

We have also investigated another pathway, denoted as pathway H₂O_B, for H₂O desorption. Firstly, H transfers from BBO to O_s to form O_s–H and then transfers from O_s to another BBO to form H₂O. The first transition state is TS1-1 in pathway H₂_B, and the second transition state is TS2-2 as shown in Fig. 2. In TS2-2, r(O_s–H) is 1.16 Å, and r(H–BBOH) is 1.30 Å. The overall barrier is 1.09 eV.

Furthermore, we have considered other relative positions of two BBOHs. If the two BBOHs are on the same BBO row (but not adjacent), they can easily migrate to adjacent sites (1-a) firstly and then follow the H₂ and H₂O desorption pathways as discussed above. The calculated barrier of H migration between BBO sites is 0.93 eV, which is pretty similar to that in ref. 20. The energy differences of the isomers with different relative BBOH positions are less than 0.15 eV. It suggests that no matter where the BBOH starting positions were, for H₂ desorption, the rate-determining step is always the H transfers from O_s to Ti_5c (TS1-2); for H₂O desorption, the rate-determining step is always the H₂O desorbed from the stoichiometric surface.

Meanwhile, when two H atoms are adsorbed on different BBO rows, one H atom should transfer to the Ti_5c for H₂ desorption, and two H atoms should transfer to the same row for H₂O desorption. In both cases, the rate-determining steps are the H transfers from O_s to Ti_5c, and the barriers are comparable to that for pathway H₂_B. As shown above, the barrier is pretty high; therefore in the following studies, we didn't consider the cases where two H atoms are adsorbed on different BBO rows.

We have also calculated the reaction profiles of H₂ and H₂O desorption for the 1/2 ML BBOHs model (as shown in Fig. 3 and 4). For pathway H₂_B, the H transfers from the BBO site (3-a) to the O_s site (3-b) are endothermic by 0.56 eV, with a barrier of 0.76 eV (TS3-1). The H transfers from the O_s site (3-b) to the Ti_5c site (3-c) are also endothermic (0.16 eV), and the barrier is much higher (1.28 eV, TS3-2). The barrier for the coupling of BBO–H and Ti_5c–H to produce H₂ (TS3-3) is 0.09 eV. The H₂ desorption energy is 0.08 eV, and the rate-determining step is the H transfers from O_s to Ti_5c with an overall barrier of 1.84 eV. The desorption energy of H₂O is 1.00 eV. For pathway H₂O_A, the coupling of two BBOHs to produce H₂O is endothermic by 0.49 eV, with a barrier of 0.90 eV (TS4-1). By pathway H₂O_B, the coupling of O_s–H and BBO–H to produce H₂O has a barrier of 0.23 eV (TS4-2). Therefore, with the 1/2 ML BBOHs model, the H₂ desorption barrier (1.84 eV) is also much higher than the H₂O desorption barrier (1.00 eV), which is the same as in the case of the 1/4 ML BBOHs model (see Fig. 1 and 2 and 3 and 4, respectively). In addition, with an increase in BBOHs, the H₂ desorption barrier decreases, and the H₂O desorption barrier does not change obviously. Therefore, the barrier difference between H₂ and H₂O desorption becomes smaller.

Fig. 3 Reaction profiles for H₂ desorption on 1/2 ML BBOHs on a stoichiometric TiO₂(110) surface. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Fig. 4 Reaction profiles for H₂O desorption on 1/2 ML BBOHs on a stoichiometric TiO₂(110) surface. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Therefore, although we proposed new mechanisms, we also predict that the H₂ desorption is much harder than the H₂O desorption on the stoichiometric TiO₂(110) surface. Thus, the H₂O desorption is dominant at the beginning of desorption, which is in good agreement with the experimental observations.¹⁵ Since H₂O desorption leaves O_vs on the surface, later on we will investigate how do these O_vs affect the H₂ and H₂O desorption.

The mechanism of H₂ and H₂O recombinative desorption from the TiO₂(110) model of an O_v

The H₂ desorption barrier is higher than the H₂O desorption barrier by 0.84–1.11 eV on a stoichiometric TiO₂(110) surface, and the desorption of H₂O leaves O_vs on the TiO₂(110) surface. Each O_v results in two adjacent Ti_5c-Ovs (the five coordinated Ti at the O_v) which can be used to form bridging Ti_5c-Ov−H−Ti_5c-Ov species. These titanium hydride species can also couple with BBOH to form new mechanisms for H₂ desorption.

With these ideas, we have investigated the mechanism of H₂O and H₂ desorption on the 1/4 ML BBOHs model with an O_v. We have considered the following three cases: 1) an O_v and two BBOHs are on different BBO rows; 2) two BBOHs are on different sides of an O_v; 3) two BBOHs are on the same side of an O_v.

For the first case where an O_v and two BBOHs are on different BBO rows, H₂ can be formed via pathway H₂_B (as shown in Fig. 5). The H transfers from the BBO site (5-a) to the O_s site (5-b) are endothermic by 0.56 eV, with a barrier of 0.77 eV (TS5-1). The H transfers from the O_s site (5-b) to the Ti_5c site (5-c) is also endothermic (0.44 eV), and the barrier is much higher (1.56 eV, TS5-2). The barrier for the coupling of BBO–H and Ti_5c–H to produce H₂ (TS5-3) is 0.19 eV. Finally, the H₂ desorption energy is 0.51 eV. The H₂O desorption energy is 1.10 eV. For pathway H₂O_A, the coupling of two BBO–Hs to produce H₂O is endothermic by 0.42 eV, with a barrier of 0.82 eV (TS6-1). For pathway H₂O_B, the coupling of O_s–H and BBO–H to produce H₂O has a barrier of 0.25 eV (TS6-2). The H₂ desorption barrier (2.12 eV) and H₂O desorption barrier (1.10 eV) were found to be almost the same as the 1/4 ML BBOHs model on a stoichiometric surface (see Fig. 1 and 2). Therefore, we came into a conclusion that if the O_v is far from BBOHs, it will have minor effects on H₂ desorption and H₂O desorption.

Fig. 5 Reaction profiles for H₂ desorption of the model where an O_v and two BBOHs are on different BBO rows. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

In the case of two BBOHs on different sides of an O_v, the Ti_5c-Ov may be involved in the reaction. We have considered three pathways for H₂ desorption. The first one is pathway H₂_B as discussed above. In the second pathway (denoted as pathway H₂_E), one H migrates from BBO to O_s and then migrates to Ti_5c-Ov. The H₂ is therefore formed through a transition state featured by BBO–H^δ+⋯H^δ−–Ti_5c-Ov. The third pathway (denoted as pathway H₂_F) is pretty similar to pathway H₂_E, except that H migrates from BBO to Ti_5c-Ov directly but not through O_s.

For pathway H₂_B (as shown in Fig. 7), the migration of H from the BBO site (7-Ba) to the O_s site (7-Bb) is endothermic by 0.47 eV, with a barrier of 0.68 eV (TS7-B1). The H transfers from the O_s site (7-Bb) to the Ti_5c site (7-Bc) are also endothermic (0.38 eV), and the barrier is much higher (1.57 eV, TS7-B2). Then, the migration of H from the Ti_5c site (7-Bc) to the O_s site (7-Bd) is exothermic by −0.16 eV, with a barrier of 1.15 eV (TS7-B3). The H transfers from the O_s site (7-Bd) to the Ti_5c site (7-Be) are endothermic by 0.06 eV, with a barrier of 1.16 eV (TS7-B4). The barrier for BBO–H and Ti_5c–H to produce H₂ (TS7-B5) is 0.15 eV. Finally, the H₂ desorption energy is 0.20 eV. For pathway H₂_E, the migration of H from the BBO site to the O_s site is the same as that in pathway H₂_B; the migration of H from the O_s site (7-Bb) to the O_v site (7-Ec) is exothermic by −0.22 eV, with a barrier of 1.43 eV (TS7-E2). The barrier for the coupling of BBO–H and Ti_5c-Ov–H to produce H₂ (TS7-E3) is 0.76 eV. For pathway H₂_F, the migration of H directly from the BBO site (7-Ba) to the O_v site (7-Ec) is endothermic by 0.25 eV, with a barrier of 1.90 eV (TS7-F1). Then, the H₂ is formed as that in pathway H₂_E. The overall barriers for the three pathways are 2.04 eV, 1.90 eV and 1.90 eV, respectively, and it has the trend B > E ≈ F. They are all lower than those for the 1/4 ML BBOHs model on a stoichiometric surface (see Fig. 1), as well as for the case of an O_v and two BBOHs on different BBO rows (see Fig. 5), but a little higher than that for the 1/2 ML BBOHs model on a stoichiometric surface (see Fig. 3).

The optimized structures are also shown in Fig. 7. In Ts7-E2, r(O_s–H) is 1.29 Å, and r(H–Ti_5c-Ov) is 1.84 Å. In Ts7-E3, r(BBO–H), r(H–H), and r(H–Ti_5c-Ov) are 1.21 Å, 1.04 Å and 1.91 Å, respectively. In TS7-F1, r(BBO–H) is 1.40 Å and r(H–Ti_5c-Ov) is 1.75 Å.

We have calculated the H₂O desorption profile for the model where two BBOHs are on different sides of an O_v. For the H₂O desorption, H could be initially transferred to the O_v site, and then H₂O is produced by the BBO–H and Ti_5c-Ov–H. The H₂O desorption energy is 1.47 eV. The rate-determining step is the H transfers from O_s to Ti_5c-Ov (TS7-E2) with an overall barrier of 1.90 eV, which is the same as H₂ desorption. But the H₂O desorption energy is much higher than the barrier of BBO–H and Ti_5c–H to produce H₂ (TS7-B5, 0.15 eV). Therefore, under these conditions, H₂ desorption is more competitive than H₂O desorption.

In the case of the BBOHs that are on the same side of an O_v (8-a), we have also considered three pathways for H₂ desorption. For pathway H₂_B, the rate-determining step is the H transfers from O_s to Ti_5c with an overall barrier of 1.89 eV. For pathway H₂_E, the rate-determining step is the H transfers from O_s to Ti_5c-Ov with an overall barrier of 1.87 eV. For pathway H₂_F, the rate-determining step is the H transfers from BBO to Ti_5c-Ov with an overall barrier of 1.87 eV. These results are similar to the case of two BBOHs that on different sides of an O_v (see Fig. 7), which suggests that the relative positions of BBOHs and O_vs have mirror effects on H₂ desorption.

We have also calculated the H₂O desorption profile for the model where two BBOHs are on the same side of an O_v. For pathway H₂O_A, the H transfers from the BBO site (8-a) to the adjacent BBO site (8-b) costs 0.15 eV, with a barrier of 1.26 eV (TS8-1). The coupling of two BBOHs to produce H₂O is endothermic by 0.44 eV, with a barrier of 0.96 eV (TS8-2). For pathway H₂O_B, the H transfers from the BBO site (8-a) to the O_s site (8-d) are endothermic by 0.48 eV, with a barrier of 0.89 eV (TS8-3); the H transfers from the O_s site (8-d) to the BBO site (8-b) are exothermic by −0.33 eV, with a barrier of 0.45 eV (TS8-4); then the H transfers from the BBO site (8-b) to the O_s site (8-e) are endothermic by 0.32 eV, with a barrier of 0.72 eV (TS8-5); the coupling of O_s–H and BBO–H to produce H₂O has a barrier of 0.43 eV (TS8-6). Finally, the H₂O desorption energy is 1.47 eV (as shown in Fig. 8). Therefore in this case, the H₂O desorption barrier (1.47 eV) is higher than those on 1/4 or 1/2 ML BBOHs on a stoichiometric surface (see Fig. 2 and 4, respectively) or on the model with an O_v and two BBOHs that are on different BBO rows (see Fig. 6), but it is less than the model with two BBOHs that are on different sides of an O_v (TS7-E2). We propose that this is because in this model the H₂O desorption will create two adjacent O_v sites, exposing a highly unsaturated Ti_4c (four-coordinated titanium) site, and the location of BBOHs and O_vs has played a decisive role in the H₂O desorption pathway with an O_v model.

Fig. 6 Reaction profiles for H₂O desorption of the model where an O_v and two BBOHs are on different BBO rows. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

We have only considered limited relative positions of the O_v sites and the BBOHs. However, given the fact that the H migration between BBO sites is facile (with a barrier of 1.26 eV) under the conditions of H₂ desorption, our proposed pathways are expected to be also valid for other relative positions of O_v sites and the BBOHs if they are in the same BBO row.

The mechanism of H₂ and H₂O recombinative desorption from the TiO₂(110) model of two O_vs

Our calculations show that the H₂ desorption barrier is much higher than the H₂O desorption barrier on stoichiometric TiO₂(110) models. However, the barriers become closer when an O_v is introduced on the surface. Thus it is very interesting to know how the competition changes if we introduce more O_vs. Is it possible that at the end the H₂ desorption can be more facile than the H₂O desorption? Although our 4 × 2 slab with an O_v reflects 1/8 ML of O_vs, which is already not small in reality, we know that the O_vs are not perfectly distributed equally on the TiO₂(110) surface, and there are O_vs which are more closer to each other, which is in line with a local region with a higher O_v concentration.

Thus we have investigated the mechanism H₂ desorption and H₂O desorption on 1/4 ML BBOHs TiO₂(110) surface model with two O_vs. We have considered four cases concerning the relative positions of the two O_vs: two BBOHs are on different sides of two adjacent O_vs; two BBOHs are on the same side of two adjacent O_vs; two alternate O_vs are near the BBOHs; one O_v is near the BBOHs, and the other O_v is on the different BBO row of the BBOH case.

Firstly, in the case of two BBOHs that are on different sides of two adjacent O_vs, we have evaluated four possible pathways for H₂ desorption. The first three pathways are pathway H₂_B, pathway H₂_E and pathway H₂_F as shown above. In the fourth pathway, each BBOH migrates to an O_v site, and then the two Ti_5c-Ov–H couple with each other to give H₂ (pathway H₂_G).

For pathway H₂_B, the H transfers from the BBO site (9-Ba) to the O_s site (9-Bb) are endothermic by 0.72 eV, with a barrier of 0.87 eV (TS9-B1). The H transfers from the O_s site (9-Bb) to the Ti_5c site (9-Bc) are also endothermic (0.03 eV), and its barrier is also much higher (1.20 eV, TS9-B2). The barrier for the coupling of BBO–H and Ti_5c–H to produce H₂ (TS9-B3) is 0.03 eV. The H₂ desorption energy is −0.01 eV. For pathway H₂_E, the H transfers from the BBO site (9-Ba) to the O_s site (9-Eb) are endothermic by 0.65, with a barrier of 0.84 eV (TS9-E1); the H transfers from the O_s site (9-Eb) to the O_v site (9-Ec) are exothermic by −0.96 eV, with a barrier of 0.92 eV (TS9-E2); the H transfers from the O_v site (9-Ec) to the adjacent O_v site (9-Ed) are endothermic by 0.17 eV, with a barrier of 0.53 eV (TS9-E3). The barrier for BBO–H and Ti_5c-Ov–H to produce H₂ (TS9-E4) is 0.99 eV. Meanwhile, we have also studied the formation of H₂ from Ti_5c-Ov–H and O_s–H (pathway H₂_H, see Fig. S3†), and we found that it is similar to those from BBO–H and Ti_5c-Ov–H in pathway H₂_E. For pathway H₂_F, the migration of H directly from the BBO site (9-Ba) to the O_v site (9-Ec) is exothermic, with a barrier of 1.66 eV (TS9-F1). The coupling of BBO–H and Ti_5c-Ov–H to produce H₂ is the same as that in pathway H₂_E. For pathway H₂_G, the migration of other H from the BBO site (9-Ec) to the O_v site (9-Ge) is endothermic by 0.26 eV, with a barrier of 1.97 eV (TS9-G1). The coupling of the two adjacent Ti_4c-Ov–Hs to produce H₂ has a barrier of 0.43 eV (TS9-G2). The overall barriers of the four pathways are 1.92 eV, 1.57 eV, 1.66 eV and 1.97 eV, respectively, and it has the trend G ≈ B > E ≈ F. The barriers of pathways H₂_E and H₂_F are all smaller than those on the stoichiometric surface models (see Fig. 1 and 3) and the models with an O_v (see Fig. 5 and 7). Because the barrier of H₂_B and H₂_G are much higher than those of other pathways, we will not calculate it anymore for other surface models with two O_vs. Besides, if the BBOHs are on the same side of two adjacent O_vs, the rate-determining step is also the H transfers from O_s to the O_v site (TS9-E2). It is similar to the case where two BBOHs are on different sides of two adjacent O_vs, and we didn't show the details any more.

Fig. 7 Reaction profiles for H₂ desorption of the model where two BBOHs are on different sides of an O_v. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

As mentioned above, the locations of BBOHs and O_vs are both crucial for the H₂O desorption. Thus, we have studied the mechanism of H₂O desorption on two BBOHs that are on the same side of two adjacent O_vs, firstly. For pathway H₂O_A, the coupling of two BBO–Hs to produce H₂O is endothermic by 0.91 eV, with a barrier of 1.25 eV (TS10-1); for pathway H₂O_B, the O_s–H and BBO–H produce H₂O with a barrier of 0.43 eV (TS10-2). The H₂O desorption energy in this model is found to be 1.81 eV (as shown in Fig. 10), which is much higher than that on the stoichiometric model and the models with an O_v. We think that this is because, with this two O_vs model, the H₂O desorption will create three adjacent O_v sites, exposing two highly unsaturated Ti_4c sites. If two BBOHs are on different sides of two adjacent O_vs, the H atom could initially be transferred to the O_v site (9-Ec), and then H₂O is produced by the BBO–H and Ti_5c-Ov–H. The H₂O desorption energy is also 1.81 eV which is much higher than the barrier of H₂ formation (TS9-E4, 0.99 eV). Therefore, if two BBOHs are on different sides of O_vs, H₂ desorption is more competitive than H₂O desorption.

We are curious if the results discussed above highly depend on the relative position of the two O_vs. Therefore we also calculated the reaction profile of H₂ desorption and H₂O desorption on the 1/4 ML BBOHs TiO₂(110) surface model with two alternative O_vs. For H₂ desorption, we have considered pathways H₂_E and H₂_F. For pathway H₂_E, the migration of H from the BBO site (11-Ea) to the O_s site (11-Eb) is endothermic by 0.58 eV, with a barrier of 0.72 eV (TS11-E1); the H migration from the O_s site (11-Eb) to the O_v site (11-Ec) is highly exothermic by −1.19 eV, with a barrier of 0.69 eV (TS11-E2). The barrier for BBO–H and Ti_5c-Ov–H to produce H₂ (TS11-E3) is 1.23 eV. Finally, the H₂ desorption energy is 0.25 eV. By pathway H₂_F, the barrier of H directly migrating from the BBO site to the O_v site is 1.41 eV (TS11-F1). For the H₂O desorption pathway, we considered that the H would be initially transferred to the O_v site, and then H₂O is produced by the BBO–H and Ti_5c-Ov–H. The formation of H₂O is endothermic by 1.27 eV, with a barrier of 1.96 eV (TS12-1), and the H₂O desorption energy is 1.94 eV (as shown in Fig. 12). The overall barrier is 2.55 eV. Therefore, for this model, we also found that H₂ desorption is easier than H₂O desorption. The barrier for H₂ desorption is even lower than that in the model with two adjacent O_vs (see Fig. 9 and 11), which suggest that the relative positions of the O_vs are important for H₂ desorption. The rate-determining barriers of the two alternative O_v models, 1.27–1.41 eV, fit with the H₂ desorption temperature in the TPD experiments.¹⁵

In order to further understand the role of the relative position of O_vs in the H₂ desorption, we calculated the case where one O_v is near the BBOHs, while the other O_v is on the different BBO row of BBOHs. In this case, for pathway H₂_E, the migration of H from the BBO site (13-Ea) to the O_s site (13-Eb) is endothermic by 0.44 eV, with a barrier of 0.63 eV (TS13-E1); the H transfers from the O_s site (13-Eb) to the O_v site (13-Ec) are exothermic by 0.26 eV, with a barrier of 1.37 eV (TS13-E2). The barrier for the coupling of BBO–H and Ti_5c-Ov–H to produce H₂ (TS13-E3) is 0.75 eV. Finally, the H₂ desorption energy is 0.12 eV. By pathway H₂_F, the barrier of the H that directly transfers from the BBO site (13-Ea) to the O_v site (13-Ec) is 1.84 eV (TS13-F1, as shown in Fig. 13). The results are similar to those for the case of two BBOHs that are on different sides of an O_v (see Fig. 7). These results suggest that if the O_v is not on the same row of BBO–H, it has a minor effect on H₂ desorption.

Furthermore, the barrier of H migration between BBO sites is 1.25 eV, which is pretty similar to those for the stoichiometric surface models and one O_v models_. Thus our proposed pathways are expected to be also valid for other relative positions of O_vs sites and the BBOHs.

Discussion

The effect of two BBOHs versus an O_v in H₂ and H₂O desorption

From the above discussion, we know that the concentration of O_vs play an important role in the H₂ and H₂O desorption. It has been suggested that the two adjacent BBOHs and an O_v made equal contributions to the band-gap states.^46–48 Based on our results, we are able to discuss whether BBOHs and an O_v also have similar effects on chemical reactions such as H₂ and H₂O desorption. We have made comparisons for two different models, which have similar electronic properties. The first is 1/2 ML BBOHs on a stoichiometric surface versus 1/4 ML BBOHs on the same side of an O_v. We found that the H₂ desorption is slightly preferred for the first case (rate-determining barrier, 1.84 eV versus 1.87 eV), while the H₂O desorption is highly preferred for the first case (rate-determining barrier, 1.00 eV versus 1.47 eV, see Fig. 4versusFig. 8, respectively). Concerning the different pathways for H₂ desorption, we found that pathway H₂_B which involves Ti_5c–H is more sensitive to the concentration of BBOHs, while H₂_E or H₂_F which involves Ti_5c-Ov is more sensitive to the concentration of O_vs. In the second comparison, we start with an O_v near the BBOHs, and then we compare the effect of an O_v or two BBOHs that are on different BBO row of BBOHs. The calculated H₂ desorption barriers for the two cases are 1.81 eV (as discussed above, see Fig. 13) and 1.82 eV (as shown in Fig. 14), respectively.

Fig. 8 Reaction profiles for H₂O desorption of the model where two BBOHs are on the same side of an O_v. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Fig. 9 Reaction profiles for H₂ desorption of the model where two BBOHs are on different sides of two adjacent O_vs. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Fig. 10 Reaction profiles for H₂O desorption of the model where two BBOHs are on the same side of two adjacent O_vs. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Fig. 11 Reaction profiles for H₂ desorption of the model where two alternative O_vs are near the BBOHs. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Fig. 12 Reaction profiles for H₂O desorption of the model where two alternate O_vs are near the BBOHs. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Fig. 13 Reaction profiles for H₂ desorption of the model where one O_v is near the BBOHs, while the other O_v is on the different BBO row of BBOHs. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Fig. 14 Reaction profiles for H₂ desorption of the model where an O_v is near BBOHs, while two BBOHs are on the different BBO row of BBOHs. The side views of selected intermediates and transition states are shown in the figure with simplified schematic diagrams.

Therefore, we predict that if two BBOHs or an O_v is far from BBOHs, they have similar but very small effects for H₂ desorption. Otherwise, if they are near the BBOHs, they have very different effects for H₂O desorption, and mirror effects for H₂ desorption. H₂O desorption is more influenced by the surface structure, and desorption near the O_v is much more difficult, while H₂ desorption is more controlled by the electronic properties on the surface where BBOHs and O_vs contributed similarly. This is reasonable since in the H₂ desorption the surface is oxidized, while in the H₂O desorption it is not.

The competition of H₂ and H₂O desorption on a TiO₂(110) surface

As shown by the experiments, H₂ desorption and H₂O desorption are competing reactions on a TiO₂(110) surface.¹⁵ The H₂O yield increases pretty faster at the beginning and then reaches a plateau; after that, the H₂ yield was increasing faster than that of H₂O. Based on our theoretical results, we can also compare the competition of H₂ and H₂O desorption. At the beginning of the reaction, there are BBOHs on the surface, while O_vs are rare. According to our calculations on the stoichiometric model, the H₂O desorption barrier is 1.09 eV, which is much lower that the H₂ desorption barrier; therefore, H₂O desorption is dominated at this stage. However, H₂O desorption creates O_vs, which means that there are more and more O_vs on the surface along with the H₂O desorption. As shown in Fig. 15, the calculated H₂O desorption barriers increases from 1.00 to 1.09 eV for stoichiometric models to 1.1–1.90 eV for the O_v models and to 1.81–2.55 eV for two O_vs models. It suggests that although the H₂O desorption is the dominating reaction at the beginning, however, as the reaction goes, the H₂O desorption becomes harder and harder. Certainly, because in reality the surface is not extremely reduced, there are always local regions which have similar structures as the O_v models and are better for H₂O desorption than the two O_vs structures. Therefore even at the late stage of the reaction, the actual barrier for H₂O desorption is estimated to be close to that in the O_v models but not the two O_vs models.

Fig. 15 The comparison of H₂ and H₂O desorption on models with different O_vs coverage.

As a comparison, the H₂ desorption is pretty hard for a stoichiometric surface. However, as shown in Fig. 15, the calculated H₂ desorption barrier decreases slightly from 1.84 to 2.20 eV for stoichiometric models to 1.82–2.12 eV for the O_v models, and then decreases dramatically to 1.27–1.81 eV for two O_vs models. It suggests that the H₂ desorption is pretty hard at the beginning; however, as the H₂O desorption goes, the H₂ desorption becomes easier and easier. For the two O_vs models, we actually predicted that H₂ desorption becomes easier than H₂O desorption. These predictions perfectly fit with the experimental observations in ref. 15.

We have discussed above that the H₂ desorption is mostly controlled by the electronic effect, more specifically, the reducing power of the TiO₂ surface. Then another question is how to understand that H₂O desorption makes the H₂ desorption easier since H₂O desorption does not provide additional electrons to the surface. We think that there are two reasons. Firstly, H₂O desorption creates O_vs which enable pathways H₂_E and H₂_F. These two pathways are the most preferred pathways for H₂ desorption, especially when the concentration of O_v on the surface is large. Secondly, as shown in ref. 48, the Ti 3d electrons induced by BBOH and O_v are distributed in a local region, rather than on the whole surface. Under the H₂ desorption conditions, BBOH can diffuse easily along the BBO row, while O_v cannot. Therefore, there are chances that desorption already creates a significant amount of O_vs. Then we have two O_vs close to each other, which result in local regions with more Ti 3d electrons and stronger reducing power. As suggested by our two O_vs models, H₂ is ready to be formed on such local regions.

Besides, M. A. Henderson and coworkers have found that BBOHs can diffuse to the rutile bulk.⁴⁹ Y. Du et al. have shown that the diffusion of BBOH to the bulk has a barrier of about 1.1 eV,¹⁴ which is lower than the H₂ desorption barrier. The energy changes for the H diffusion are quite small, suggesting that the H diffusion between the surface and bulk is reversible. H₂ and H₂O desorption happens at a relatively high temperature, and under these conditions the desorption has a significant entropic drive. Therefore, we expect the BBOHs in the bulk can also diffuse to the surface, followed by desorption as H₂O or H₂.

Beside the O_vs, as shown above, BBOHs also have strong effects on the H₂ desorption. On the stoichiometric surface model, the H₂ desorption barriers of our proposed mechanism for 1/4 ML and 1/2 ML BBOHs are 2.20 eV and 1.84 eV, respectively, while the H₂ desorption barriers of the direct coupling of two BBOHs for 1/4 ML and 1/2 ML BBOHs are 2.66 eV, 2.00 eV, respectively. In each case, our mechanism has a smaller barrier. As a comparison, the H₂O desorption barrier is similar for 1/4 ML and 1/2 ML BBOHs. As discussed above, this is because when there are more BBOHs or O_vs on the TiO₂(110) surface, the surface has stronger reducibility.

The locations of BBOHs and O_vs are also relevant. When the BBOHs are on the same side of the O_v, for H₂ desorption, the rate-determining steps are always the H transfers from the O_s site to the O_v site; for H₂O desorption, the rate-determining steps are always the H₂O desorbed from the surface. In both cases, the desorption barrier does not change obviously with the locations of BBOHs and O_vs. When the BBOHs are on different sides of the O_v, for H₂ desorption, the rate-determining step is still the H transfers from the O_s site to the O_v site, but for H₂O desorption, the H would be initially transferred to the O_v site, and then H₂O is produced by the BBO–H and Ti_5c-Ov–H. In these cases, H₂ desorption is more competitive than H₂O desorption.

Although we did not exhaust all possible relative positions of BBOHs and O_vs, the general picture for H₂O desorption and H₂ desorption should be valid since BBOHs can easily diffuse along the BBO rows. When the initial coverage of BBOHs is small, there is much less chance for the surface to build up local regions with high O_v concentration, and H₂O desorption will be the only available process. Perhaps this is the reason why for a long time H₂ desorption on a TiO₂(110) surface has not been observed.

The Ti–H species

We propose that the Ti–H species is the key intermediate for H₂ desorption, and its stability is crucial for the rate-determining barrier. There are two types of Ti–H species, the Ti_5c–H and Ti_5c-Ov–H. The Ti_5c–H has also been assumed to respond to H₂ desorption under other conditions.^14,21 Here for the first time we have proposed the complete reaction profiles involving Ti–H species for H₂ desorption on a TiO₂(110) surface. The Ti_5c-Ov–H is more stable than the Ti_5c–H species. However, for all stoichiometric and O_v models, the formation of Ti–H species is endothermic, suggesting that the Ti–H species are pretty unstable. The stability of the Ti–H species increases with an increase in the O_v, which is the key reason for the decrease in the H₂ desorption barrier. In our two O_vs models, the formation of Ti_5c-Ov–H could even be exothermic.

Nevertheless, to our knowledge, Ti–H species on a TiO₂(110) surface has never been observed experimentally. Can we actually observe it? Our answer is that it will be pretty hard in the current H₂ desorption experiments. Although we predict that the formation of Ti_5c-Ov–H species can be exothermic for the local regions with high O_v concentration, in each case the formation of Ti_5c-Ov–H is the rate-determining step, and the reaction between Ti_5c-Ov–H and BBOH to form H₂ is very fast. We think that it is possible to observe these Ti_5c-Ov–H species by sputtering H atoms to a surface with a very high O_v concentration.

Conclusions

In summary, we have investigated the mechanism of H₂ and H₂O desorption from BBOH of a TiO₂(110) surface. Our results suggest that it is unlikely for two BBOHs to couple directly to form H₂, and we propose that the reaction undergoes a Ti–H key intermediate, which then forms an O–H^δ+⋯H^δ−–Ti type dehydrogenation transition state. The H₂ desorption is pretty hard on a stoichiometric surface. However, it becomes easier with an increase in O_vs which is generated by H₂O desorption. As a comparison, the H₂O desorption is pretty easy on a stoichiometric surface but becomes harder and harder. In the case of close O_vs that are generated by H₂O desorption, H₂ desorption could be easier than H₂O desorption on these local regions. Therefore, our theoretical results suggest that H₂O desorption is the major product at the beginning of the reaction. If the initial BBOH concentration is high enough, at the late stage of the reaction the H₂ desorption becomes a competitive reaction. These results fit with the experimental observations very well.

The H₂ production is a key process for photocatalytic H₂O splitting. Currently, the H₂ yield is pretty low and the desorption temperature is pretty high on the TiO₂(110) surface. Based on our results, possible ways to improve the current reaction system include the following: a) use the surface with a high O_vs concentration; b) specifically design close O_vs on the surface; c) other surface modifications to increase the reducing power of the surface; d) introduce other metals which have more stable M–H species. With these strategies, if the H₂ desorption temperature can be reduced to lower than that for H₂O desorption at Ti_5c, we expect that the H₂ desorption from the H₂O/TiO₂ system could be available.

Acknowledgements

This work was supported by the National Science Foundation of China (21210004, 21673224) and the Strategic pilot science and technology project of the Chinese Academy of Sciences (XDB17010200).

References

1. M. R. Hoffmann, S. T. Martin, W. Y. Choi and D. W. Bahnemann, Chem. Rev., 1995, 95, 69–96.
2. T. L. Thompson and J. T. Yates, Chem. Rev., 2006, 106, 4428–4453.
3. M. A. Henderson, S. Otero-Tapia and M. E. Castro, Faraday Discuss., 1999, 114, 313–319.
4. X. Q. Gong, A. Selloni, O. Dulub, P. Jacobson and U. Diebold, J. Am. Chem. Soc., 2008, 130, 370–381.
5. M. A. Henderson, Surf. Sci. Rep., 2011, 66, 185–297.
6. C. L. Pang, R. Lindsay and G. Thornton, Chem. Soc. Rev., 2008, 37, 2328–2353.
7. A. Fujishima, X. Zhang and D. Tryk, Surf. Sci. Rep., 2008, 63, 515–582.
8. A. Fujishima and K. Honda, Nature, 1972, 238, 37–38.
9. W. S. Epling, C. H. F. Peden, M. A. Henderson and U. Diebold, Surf. Sci., 1998, 412, 333–343.
10. S. Suzuki, K. Fukui, H. Onishi and Y. Iwasawa, Phys. Rev. Lett., 2000, 84, 2156–2159.
11. M. Kunat, U. Burghaus and C. Wöll, Phys. Chem. Chem. Phys., 2004, 6, 4203–4207.
12. X. L. Yin, M. Calatayud, H. Qiu, Y. Wang, A. Birkner, C. Minot and C. Wöll, ChemPhysChem, 2008, 9, 253–256.
13. N. G. Petrik and G. A. Kimmel, J. Phys. Chem. C, 2009, 113, 4451–4460.
14. Y. Du, N. G. Petrik, N. A. Deskins, Z. Wang, M. A. Henderson, G. A. Kimmel and I. Lyubinetsky, Phys. Chem. Chem. Phys., 2012, 14, 3066–3074.
15. C. B. Xu, W. S. Yang, Q. Guo, D. X. Dai, M. D. Chen and X. M. Yang, J. Am. Chem. Soc., 2013, 135, 10206–10209.
16. M. A. Henderson, Surf. Sci., 1996, 355, 151–166.
17. G. H. Enevoldsen, H. P. Pinto, A. S. Foster, M. C. R. Jensen, W. A. Hofer, B. Hammer, J. V. Lauritsen and F. Besenbacher, Phys. Rev. Lett., 2009, 102, 136103.
18. P. M. Kowalski, B. Meyer and D. Marx, Phys. Rev. B, 2009, 79, 115410.
19. C. B. Xu, W. S. Yang, Q. Guo, D. X. Dai, M. D. Chen and X. M. Yang, J. Am. Chem. Soc., 2014, 136, 602–605.
20. S. C. Li, Z. Zhang, D. Sheppard, B. D. Kay, J. M. White, Y. Du, I. Lyubinetsky, G. Henkelman and Z. Dohnalek, J. Am. Chem. Soc., 2008, 130, 9080–9088.
21. Z. F. Wu, W. H. Zhang, F. Xiong, Q. Yuan, Y. K. Jin, J. L. Yang and W. X. Huang, Phys. Chem. Chem. Phys., 2014, 16, 7051–7057.
22. P. Chen, Z. T. Xiong, J. Z. Luo, J. Y. Lin and K. L. Tan, J. Phys. Chem. B, 2003, 107, 10967–10970.
23. Z. T. Xiong, G. T. Wu, H. J. Hu and P. Chen, Adv. Mater., 2004, 16, 1522–1525.
24. W. Luo, J. Alloys Compd., 2004, 381, 284–287.
25. J. Lu and Z. G. Z. Fang, J. Phys. Chem. B, 2005, 109, 20830–20834.
26. W. L. Xu, G. T. Wu, W. Yao, H. J. Fan, J. S. Wu and P. Chen, Chem. – Eur. J., 2012, 18, 13885–13892.
27. T. A. Rokob, A. Hamza, A. Stirling, T. Soos and I. Papai, Angew. Chem., Int. Ed., 2008, 47, 2435–2438.
28. A. Comas-Vives and G. Ujaque, J. Am. Chem. Soc., 2013, 135, 1295–1305.
29. Y. Duan, L. Li, M. W. Chen, C. B. Yu, H. J. Fan and Y. G. Zhou, J. Am. Chem. Soc., 2014, 136, 7688–7700.
30. A. Paul and C. B. Musgrave, Angew. Chem., Int. Ed., 2007, 46, 8153–8156.
31. K. J. Sun, Y. H. Zhao, H. Y. Su and W. X. Li, Theor. Chem. Acc., 2012, 131, 1–10.
32. R. M. Wang and H. J. Fan, Sci. China., Chem., 2015, 58, 614–619.
33. Q. Guo, C. B. Xu, Z. F. Ren, W. S. Yang, Z. B. Ma, D. X. Dai, H. J. Fan, T. K. Minton and X. M. Yang, J. Am. Chem. Soc., 2012, 134, 13366–13373.
34. G. Kresse and J. Hafner, Phys. Rev. B, 1993, 47, 558–561.
35. G. Kresse and J. Furthmuller, Phys. Rev. B, 1996, 54, 11169–11186.
36. P. E. Blöchl, Phys. Rev. B, 1994, 50, 17953–17979.
37. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868.
38. G. Henkelman, B. P. Uberuaga and H. Jonsson, J. Chem. Phys., 2000, 113, 9901–9904.
39. G. Henkelman and H. Jonsson, J. Chem. Phys., 2000, 113, 9978–9985.
40. J. Perdew, M. Ernzerhof and K. Burke, J. Chem. Phys., 1996, 105, 9982–9985.
41. J. Zhao, J. Yang and H. Petek, Phys. Rev. B, 2009, 80, 235416.
42. J. Paier, R. Hirsch, M. Marsman and G. Kresse, J. Chem. Phys., 2005, 122, 234102.
43. R. Sanchez de Armas, J. Oviedo, M. A. San Miguel and J. F. Sanz, J. Phys. Chem. C, 2007, 111, 10023–10028.
44. E. V. Stefanovich and T. N. Truong, Chem. Phys. Lett., 1999, 299, 623–629.
45. H. J. Monkhorst and J. D. Pack, Phys. Rev. B, 1976, 13, 5188–5192.
46. R. L. Kurtz, R. Stockbauer, T. E. Madey, E. Roman and J. L. Desegovia, Surf. Sci., 1989, 218, 178–200.
47. M. A. Henderson, W. S. Epling, C. H. F. Peden and C. L. Perkins, J. Phys. Chem. B, 2003, 107, 534–545.
48. C. Di Valentin, G. Pacchioni and A. Selloni, Phys. Rev. Lett., 2006, 97, 166803–166806.
49. M. I. Nandasiri, V. Shutthanandan, S. Manandhar, A. M. Schwarz, L. Oxenford, J. V. Kennedy, S. Thevuthasan and M. A. Henderson, J. Phys. Chem. Lett., 2015, 6, 4627–4632.

---

Footnote

† Electronic supplementary information (ESI) available: Reaction profiles for pathways H₂_C, H₂_D and H₂_H are shown. The optimized individual structures of the Cartesian coordinates from theory. See DOI: 10.1039/c6cy02007k

---