The hydroxyl group (OH) is perhaps one of the most common species in heterogeneous catalysis as it can play an important role as both a reductant and an oxidant. There are many types of industrial reactions involving the OH group, such as Fischer-Tropsch synthesis [1-3], methane reformation [4, 5], ammonia oxidation [6], as well as the ethanol synthesis reaction [7]. In the process of carbon dioxide hydrogenation, a moderate amount of OH groups and some adsorbed O^* are generated when water is used [8-11] that may cover the Cu surface, which block the active sites and affect the reaction rate to some extent. Traditionally, the hydroxyl groups and adsorbed O are removed from catalyst surfaces by reduction with H adsorbed on the surfaces both experimentally and theoretically, which results in the formation of water via the so-called classic Horiuti-Polanyi (HP) mechanism [12-14]. This involves a three-step process, namely, H₂ adsorption, followed by dissociation, and hydrogenation by H. In the reduction reaction, H₂ is generally over a large quantity to increase the turn over frequency, and theoretical simulations are desirable for understanding the nature of the catalytic process.

Hydrogenation by adsorbed H, which is the HP mechanism, was generally acknowledged, and other possibilities were virtually neglected, until two interesting results were reported. The first result was that the non-Horiuti-Polanyi (non-HP) mechanism is favorable for the hydrogenation of acrolein when the catalyst used is Ag or Au, as revealed through our previous theoretical work [15], and the other one was that the reductant reacts with H through a H₂ molecule over supported Ag nanoparticles [16]. As for the catalyst, transition metals are widely used for hydrogenation reactions [17-20], especially, late transition metals are utilized for the oxycarbide redox reaction.

In addition to the two metals mentioned above, Cu is the active component in methanol synthesis [21, 22], and Ni-based catalysts are used in the steam reforming of natural gas [23-25] (C_xH_y + xH₂O → xCO₂ + (x + y/2)H₂) and in methanation [26, 27] (CO + 3H₂ → CH₄ + H₂O); Pt metal is often utilized as a catalyst in water-gas shift reactions [28], in which the coupling of OH^* with H^* is generally accepted [29]. It is well known that transition metals with different activities are widely used to catalyze hydrogenation reactions [17-19, 30], but the hydrogenation mechanism may be sensitive to the surface type [15]. The following important questions remain to be answered. Are all the adsorbed OH^* or O^* hydrogenated via the HP mechanism? Are there any possibilities that OH^* or O^* are attacked by molecular H₂? If the answer is yes, when is the non-HP mechanism favored? To obtain a good understanding, systematic exploration of the reaction mechanism was carried out for representative transition metals, such as Ni, Pt, Cu, Ag, and Au, based on density functional theory (DFT) calculations in this work. Two surfaces with different Miller indices were investigated, including the stepped (211) surfaces and the flat (111) surfaces.

In this work, the adsorption and dissociation of H₂ were first studied. All the hydrogenation pathways were investigated and detailed comparisons are made. A structural descriptor has been introduced to analyze the structures based on the reaction mechanisms.

First-principles energy calculations were performed within the density functional theoretical [31, 32] framework by using Vienna ab initio simulation package [33-35]; Perdew-Burke-Ernzerhof functional with generalized gradient approximation [36] was employed to describe the exchange correlation between electrons [37]. PAW method [38, 39] was used to describe the core-electron interactions, and the cut-off energy of the plane-wave basis set was set as 400 eV. For Ni, the calculations were carried out with spin-polarized. The geometry was relaxed using Broyden method, which stopped only when the force of the ions became less than 0.05 eV/Å. The lattice constants of the unit cells were optimized first and then periodic four-layer slabs were modeled as metal surfaces. The vacuum region between the slabs was in excess of 15 Å. 4 × 4 × 1 k-point sampling of Monkhorst Pack scheme was used for the p(1 × 4) supercell of fcc(211) and the p(3 × 3) supercell of fcc(111) surfaces. The bottom two layers of the slab were fixed at the bulk truncated position, with the top two layers fully relaxed during the structural optimization. All the adsorption geometries were optimized using a force-based conjugate gradient algorithm, while the transition states (TSs) of reactions were searched using a constrained minimization scheme [40-42]. The adsorption energy of surface-absorbed species X was defined as follows:

(1)

where E_{X +surface}, E_surface, and E_X are the optimized energies of the total adsorption system, the adsorbate in the gas phase, and the clean surface, respectively. A more negative value of E_ads suggests stronger binding on the surface.

A series of metal surfaces was investigated for OH/O hydrogenation, including Ni, Pt, Cu, Au, and Ag. The mechanistic study of water formation from OH hydrogenation, as well as that of O^* hydrogenation, was extended from the flat (111) surfaces to the stepped (211) surfaces.

First, we examined the adsorption and dissociation of H₂ on the abovementioned metal surfaces. Fig. 1(c) shows that in the TS, two adsorbed H atoms occupy the fcc and top sites on the (111) surface, whereas they are located at the bridge and top sites along the stepped edge of the (211) surface, respectively. The corresponding energy values are listed in Table 1. Accordingly, the relationships between the dissociative energy barrier and the adsorption energy as well as the reaction energy could be mapped out, as illustrated in Fig. 1(a, b). The adsorption of H₂ on Cu, Ag, and Au surfaces is very weak, whereas a strong bonding is observed between H₂ and the catalytically active Ni surface. Particularly, at the stepped edge sites of Ni(211), the adsorption energy of H₂ (E_ads(H₂^*)) could reach -0.48 eV.

Pt catalysts find wide applications in redox reactions leading to water formation [43-46], as the dissociative adsorption of H₂ on Pt is very facile. It is found that the adsorption of H₂ on both Pt(211) and Pt(111) is very weak, but that the dissociative adsorption is reasonably strong [47, 48]. The barriers for H₂ dissociation E_a (H_{2, dis}^*) on Ni and Pt surfaces are very low (less than 0.2 eV), and the H-H bond can be easily broken. The strong driving force for H₂ dissociation renders the reaction strongly exothermic. Their energies are reduced by 0.65 and 0.87 eV over Ni(211) and Ni(111) surfaces and by 1.22 and 1.00 eV over Pt(211) and Pt(111) surfaces, respectively. The calculated results are in good agreement with those of Zhu et al. [46] on the reforming of methane on Ni(111).

Au and Ag surfaces display low activities toward H₂ adsorption and the barriers for H₂ dissociation are very high. The E_a (H_{2, dis}^*) values exceed 1 eV on Ag(111), Au (111), and Ag(211). On the other hand, E_a (H_{2, dis}^*) is 0.57 eV on Au(211) surface, which indicates that the activities of Au are distinct over different crystal surfaces. The H₂ dissociation reaction is endothermic on Au and Ag surfaces, which suggests that the forward reaction is unfavorable. On the two Cu surfaces, although the dissociative chemisorption energy ∆E (H_{2, dis}^*) is ~ -0.5 eV, the dissociation barrier E_a (H_{2, dis}^*) requires an energy of ~0.5 eV.

Subsequently, we studied the relations of E_a with E_ads and ∆E. Some correlations were identified, as shown in Fig. 1(a, b). It is found that there is no linear relationship between E_a and E_ads, but the data points are located at two different regions: the data points of inactive metals, which exhibit higher dissociation barriers and lower adsorption energies, can be found in the upper right corner, whereas those of active metals are observed in the bottom left area (Fig. 1(a)).

On the other hand, a linear correlation between E_a and ∆E can be observed, as revealed in Fig. 1(b). These results demonstrate that H₂ dissociation on these metals is strongly related to the adsorption of H^*. It is clear that the data in the bottom left region represent the catalytically active metals for H₂ dissociation, whereas those at the upper right corner correspond to the catalytically inert metals for H₂ dissociation, though they may be possible catalysts for H₂ to hydrogenate OH^*/O^*. The bondings of H^* with Pt and Ni surface atoms lower the energies Ev by 0.3-0.6 eV. Moreover, the H₂ dissociation barriers are no more than 0.3 eV. These results are consistent with those of Phatak et al. [49]. On Ag(111), Au(111), and Ag(211), E_a are rather high, and the formed H^* is also not stable on these surfaces. The H₂ dissociation may not proceed. Hence, the reaction equilibrium shifts to H₂ in the gas phase, which results in the attack of OH^*/O^* by H₂ becoming more probable. The H₂ dissociation performance on Cu surfaces is in the middle of the corresponding performances on the metal surfaces. Therefore, it is not easy to energetically assess whether H₂ can be activated. This will be further discussed in section 3.2.

Both the classic HP hydrogenation and the non-HP hydrogenation mechanisms of OH^*/O^* reduction on metal surfaces were investigated. The energy profiles over three typical surfaces, which include inactive Ag(211), active Pt(211), and the moderately active Cu(211), are shown in Fig. 2.

As illustrated by the solid line in Fig. 2, the two mechanisms of OH^* hydrogenation were compared. H₂ dissociation was also considered, which is essential to understand the hydrogenation by H₂. It can be seen from Fig. 2(a) that, on Pt(211), the H₂ dissociation is easier to occur than coupling with OH^* species, although the latter displays a lower energy barrier than the direct hydrogenation of OH^* by atomic H^* (0.25 eV vs. 0.90 eV); the data are listed in Table 2. This result suggests that the classic HP mechanism is more favorable than non-HP mechanism on active surfaces. Similar reaction characteristics are found on the Pt(111), Ni(211), as well as Ni(111), surfaces. Fig. 2(b) elucidates the difference between the two hydrogenation mechanisms on Ag(211), which is a representative inactive metal. H₂ dissociation exhibits the highest barrier (1.14 eV; Table 1), and the barrier for direct OH^* hydrogenation by H^* is 0.6 eV; the hydrogenation of OH^* by H₂ reveals a barrier that is as low as 0.3 eV. Hence, the reduction of OH^* by H₂ catalyzed by inactive metals offers an advantage over the mechanism of direct addition of atomic H^*. The other inactive surfaces, such as Ag(111), Au(211), Au(111), and Cu(111), also exhibit this tendency, as observed in Table 2.

The difference in mechanism between OH^* hydrogenation on active metals (Pt, Ni) and that on inactive metals (Ag, Au) is obvious. However, Cu(211) is a special case: it displays a moderate activity, which results in a dependence of the mechanism on the specific reaction condition. The H₂ dissociation and the hydrogenations by atomic and molecular hydrogens on Cu(211) are compared in Fig. 2(c). The hydrogenation of OH^* by H₂^* reveals a barrier that is comparable to that of H₂ dissociation (0.47 eV vs. 0.48 eV). Although the hydrogenation of OH^* by H^* exhibits a higher barrier than that by H₂, the adsorption of H^* on Cu(211) is stronger than that of H₂^*. As a result, the balance between the adsorption energy of H^* and the H₂ dissociation barrier would determine which pathway is favored, and can be affected by the experimental reaction temperature and the partial pressure. Our results show that the non-HP mechanism dominates at low temperatures, whereas the classic HP mechanism is more favored when the temperature is significantly increased.

Considering the importance of adsorbed O^* in heterogeneous catalysis, the hydrogenation of O^* via the two different pathways was researched and the results on three representative surfaces are shown in the form of dotted lines in Fig. 2. On Pt(211) surface, H₂ dissociation is easier to occur than coupling with O^* species, although the latter displays a much lower energy barrier than that for direct hydrogenation of O^* by atomic H^* (0.30 eV vs. 0.80 eV). Therefore, the classic HP mechanism is preferred. Similar results are obtained on the other three active surfaces, namely, Pt(111), Ni(211), and Ni(111).

On Ag(211), the hydrogenation of O^* by H₂^* reveals the lowest barrier (0.42 eV), in comparison with 0.58 and 1.14 eV for hydrogenation by atomic H^* and H₂ dissociation, respectively. On Ag(111), Au(211), Au(111), Cu(211), and Cu(111), the barriers for hydrogenation by H₂ are found to be 0.38, 0.17, 0.51, 0.22, and 0.41 eV, respectively, whereas the H₂ dissociation barriers are 1.21, 0.57, 1.00, 0.48, and 0.56 eV, respectively. The energy barrier for the non-HP hydrogenation mechanism is lower than that for the classic HP mechanism on every surface except Au(111). On Au(111), the two barriers are nearly equal and the H₂ dissociative adsorption energy (E_ads (H^*)) is positive (0.23 eV); E_ads (H₂^*) almost equals zero. Therefore, the effective barrier for O^* hydrogenation by H^* is 0.73 eV, which is higher than that for O^* hydrogenation by H₂ (0.51 eV). In other words, the O^* hydrogenation is similar to the OH^* hydrogenation.

A descriptor, E_ads(O^*) was utilized to fit the energy barriers of both OH^* and O^* hydrogenations as well as those of H₂ dissociation on these surfaces, considering that the adsorption energy of O^* may be of importance. The value of E_ads(O^*) may be a key measure of catalytic activity. The results are displayed in Fig. 3.

We can observe the following features in the figure. First, E_a (H_{2, dis}^*) changes linearly as a function of E_ads(O^*). The more negative the E_ads(O^*) value, the lower is the dissociation barrier, which indicates that there are some correlations between O^* adsorption and H₂ reactivity, as reported by Wang et al. [50-52]. Secondly E_a, linearly increases with E_ads(O^*) for both the hydrogenation pathways. The strong bonding between OH^* and the surface atoms inhibits the reactivity and enhances the hydrogenation barrier. Thirdly, the fact that nearly all the red square points (corresponding to the hydrogenation by H₂) lie below the blue circles (which represent the HP mechanism) shows that the energy barriers of the non-HP mechanism are lower than those of the HP mechanism. However, the mechanism changes when the green line crosses the red line; the lines beyond the point of intersection are displayed in yellow in Fig. 3. Starting from the left hand side, the HP mechanism is preferred and, after the intersection point, the non-HP mechanism is favored. Of course, this is only a qualitative description of the trend.

It is obvious that the geometric effect should be of importance in determining which of the two mechanisms is preferred [53]. Fig. 4 shows the TS structures of OH^*/O^* hydrogenation on both (211) and (111) surfaces. For the pathway of hydrogenation by H₂, the TS structure of HO-HH/O-HH is parallel to the surface, with a relatively flat configuration, which results in a better orbital overlap. On the contrary, for the pathway of hydrogenation by H, the TS structure of HO-H/O-H is inclined to the surface, especially at the step edge site on (211). This agrees well with reports that metal (211) surfaces exhibit higher activities for bond breaking than metallic (111) surfaces [43, 54, 55].

It is worth pointing out that whether the mechanism of hydrogenation by H₂ or the classic HP mechanism is favored depends on the nature of the TS structure, in particular, the distance between two H atoms is of importance. Our DFT calculations revealed the bond lengths between two H atoms in the TSs of hydrogenation by H₂ on all the metal surfaces (Table 3).

To characterize the TS structures of non-HP hydrogenation, the distance between H atoms is inadequate. Therefore, a parameter η was introduced, which is defined as follows:

where D_i is the distance between two H in the TS of molecular hydrogenation of OH^* or O^*. D_H2 is the bond length of optimized H₂, which is calculated to be 0.75 Å in our work. D_dis is the distance between two H in the TS of H₂ dissociation.

The parameter η is a measure of the H-H separation in the TS of hydrogenation, and its value is 0 < η < 1, by definition. The lower and upper boundaries represent the structure of the H₂ molecule in the gas phase and the H₂ dissociation structure in the TS, respectively. The higher the η value, the more similar is the structure of H-H in the TS of OH^* or O^* hydrogenation to that of H₂ dissociation. Fig. 5 shows the η values of all the steps of hydrogenation by H₂ on both (211) and (111) surfaces as functions of the metal d-band centers [56, 57]. The η values for the Pt and Ni surfaces are not less than 0.4, being 0.65 (Pt(211)), 0.57 (Ni(211)) for OH^* hydrogenation and 0.53 (Pt(211)), 0.55 (Ni(211)) for O^* hydrogenation on the stepped surfaces vs. 0.64 (Pt(111)), 0.68 (Ni(111)) and 0.49 (Pt(111)), 0.63 (Ni(111)) on the flat surfaces. On the other hand, the η values of Au and Ag are less than 0.4, being 0.27 (Au(211)), 0.25 (Ag(211)), 0.18 (Au(111)), 0.31 (Ag(111)) and 0.16 (Au(211)), 0.12 (Ag(211)), 0.14 (Au(111)), 0.18 (Ag(111)), which correspond to the hydrogenation of OH^* and O^* by H₂. Likewise, on Cu surfaces, the η values are found to be 0.19 (Cu(211)), 0.34 (Cu(111)) and 0.23 (Cu(211)), 0.25 (Cu(111)) for OH^* and O^* for the non-HP mechanism.

It is clear that Ni and Pt are active catalysts, whereas Au and Ag are inactive. Therefore, the upper boundary is approximately determined by the η value of 0.49 for Ni and Pt, and the lower one by the η value of 0.31 for Au and Ag, which are displayed as brown and yellow triangles, respectively, in Fig. 5. The center for this region is determined to be η = 0.41 by calculating the geometric average of the η values. The boundary zone divides the data into two regions. On the left hand side of Fig. 5, i.e., η values below 0.41, the H-H distances in the TSs of non-HP mechanism are similar to the H-H distance in the gas phase, which is observed on inactive metal surfaces with highly negative values of d-band centers. On the right hand side of Fig. 5, the data points of η for the active metals are characterized by the d-band center located in the region beyond η = 0.41, which suggests that the H-H bond length is close to that of H-H dissociation distance and, thus, the HP mechanism can be distinguished from the non-HP mechanism.

Having presented the results above, it is worth discussing the results of Fig. 1 further. The boundary marked by E_a = 0.4 eV is found to realize the goal of dividing all the data points into two parts, as illustrated in Fig. 1(a, b). The region below 0.4 eV is the area in which H₂ can readily dissociate, namely, the catalytically active region for H₂ dissociation. The region above 0.4 eV is the area in which H₂ dissociation is not active. Interestingly, the energy of 0.4 eV is the entropy of H₂ in the gas phase at room temperature. In summary, H₂ dissociation occurs most likely in the region below 0.4 eV, whereas, in the region above 0.4 eV, the mechanism of hydrogenation by H₂ is preferred.

The non-HP mechanism of OH^* and O^* hydrogenation reactions over a series of metals has been systematically investigated by DFT calculations and comprehensively compared with the classic HP hydrogenation mechanism. Some insights have been obtained. The H₂ dissociation activity over a catalyst decides whether the HP mechanism or the non-HP mechanism is preferred. It is found that the energy barriers of OH^*/O^* hydrogenation by H₂ are generally lower than those of direct hydrogenation of OH^*/O^* by H^*. On active catalysts such as Ni and Pt, H₂ molecules prefer to dissociate, with strong adsorption energies of H^*, which leads to the classic HP mechanism being favored. On inactive surfaces, e.g., Au and Ag catalysts, the H^* adsorption is weak and, therefore, the existence of H₂ molecules is thermodynamically preferred, which results in the non-HP mechanism being favored. Based on these interesting results, future research can be extended to surface alloys [58] to verify the universality of the conclusions. The parameter η was introduced to evaluate the hydrogenation mechanisms. When the η value is higher than 0.41, it signifies that the H-H structure in the TS of the hydrogenation reaction is similar to the H₂^* dissociation structure; the HP mechanism will then be favored. In contrast, the non-HP mechanism is favored if η < 0.41 and E_a of H₂^* dissociation is relatively high.