DFT  +  U study of H2O adsorption and dissociation on stoichiometric and nonstoichiometric CuO(1 1 1) surfaces

Surface interaction through adsorption and dissociation between H2O and metal oxides plays an important role in many industrial as well as fundamental processes. To gain further insights on the interaction, this study performs dispersion-corrected Hubbard-corrected density functional theory calculations in H2O adsorption and dissociation on stoichiometric and nonstoichiometric CuO(1 1 1) surfaces. The nonstoichiometric surfaces consist of oxygen vacancy defect and oxygen-preadsorbed surfaces. This study finds that H2O is chemically adsorbed on the top of Cusub and Cusub–Cusub bridge due to the interaction of its p  orbital with d orbital of Cu. The adsorption is found to be the strongest on the surface with the oxygen vacancy defect, followed by the stoichiometric surface, and the oxygen-preadsorbed surface. The oxygen vacancy increases the reactivity for H2O adsorption and reduces the reaction energy required for H2O dissociation on the surface. However, the surface modification by the oxygen-preadsorbed significantly reduces the barrier energy for H2O dissociation when compared with the other surfaces.


Introduction
Disclosing the physicochemical phenomena of adsorption and dissociation of H 2 O on metal oxide is of great importance for both industrial applications as well as fundamental studies. From industrial point of view, there are many catalytic processes involving H 2 O with metal oxides as a catalyst [1][2][3] in which H 2 O could be a reactant as well as a product [4][5][6][7]. From fundamental perspectives, over the past decade, many theoretical studies have been conducted to investigate adsorption and dissociation of H 2 O on catalyst surfaces such as TiO 2 [8], Cu 2 O [9], CeO 2 [10], SrTiO 3 [11], goethite [12], and CoO [13]. In general, the studies focussed on the adsorption and dissociation of H 2 O on stoichiometric and modified surfaces. The interaction of water and solid surface including the influence of oxygen vacancy and oxygen-preadsorbed surfaces have been extensively explored [14]. It was found that the crystal defects usually affect the reactivity of water on the surface of the catalyst, whereas the oxygen-preadsorbed (O pre ) can show different effects depending on the catalyst materials. On one hand, the oxygen-preadsorbed promotes the separation of water on several solid surfaces, but on the other hand, it inhibits water dissociation on several other surfaces.
Copper oxide is one of metal oxide that can potentially be used as the H 2 O dissociation catalyst. It comprises copper (I) oxide (Cu 2 O) and copper (II) oxide (CuO). CuO is generally synthesized through Cu oxidation at a high temperature, which is easier than the synthesis of Cu 2 O because of the stability [15]. The activity of Cu 2 O catalysts in reactions involving H 2 O has been widely reported [9,[16][17][18]. When used in aqueous solutions, Cu 2 O tends to be easily oxidized to CuO [19,20]. Meanwhile, when interacting with hydrogen, CuO tends to be reduced to Cu more easily than Cu 2 O [21].
Density functional theory (DFT) studies on the adsorption and dissociation of molecules on CuO surfaces have been conducted by previous researchers that included adsorption of O 2 , H 2 , H 2 O, CO 2 , C 2 H 5 OH, NO 2 and H 2 S molecules [22][23][24][25][26][27][28][29][30][31]. Hu et al [22] reported the effect of H 2 O adsorption on the CuO conductivity. Fronzi and Nolan [29] examined the stability of H 2 O adsorption on reduced and oxidized CuO surfaces. They observed that the calculation of adsorption energy is strongly influenced by the Hubbard potential (U). Yu et al [30] reported adsorption of H 2 O on CuO(1 1 1) with high coverage and found that H 2 O molecular adsorption was preferred at a lower coverage, whereas molecular adsorption and dissociative mixtures were preferred at a higher coverage. Zhang et al [31] investigated the H 2 O dissociation on the stoichiometric and nonstoichiometric CuO(1 1 1) using DFT approach but without considering the strong correlation effect or dispersion effect.
It is now established that the standard DFT fails to obtain the correct electronic structure of CuO due to the strong electron correlation and antiferromagnetic behavior [32][33][34]. The two modified DFT methods that can be used to solve this problem are Heyd-Scuseria-Ernzerhof hybrid functional (HSE) and Hubbard-corrected DFT (DFT + U). The HSE method requires a relatively high computational cost compared to DFT + U. However, although HSE can solve the band gap problem of some materials, in the case of CuO, the HSE approach with reasonable alpha parameters that can reproduce an appropriate local magnetic moment still results in an overestimation bandgap [33]. A dispersion correction may be crucial for long Van der Waals interactions to improve the binding strength in chemisorption [35,36]. Therefore this report presents the effect of Hubbard parameter on H 2 O adsorption and dissociation on the stoichiometric and nonstoichiometric (oxygen vacancy defect and oxygen-preadsorbed) CuO(1 1 1) surfaces by using dispersion corrected DFT + U and considering antiferromagnetic spin ordering. The results, in turn, will further uncover the physical phenomena responsible for the catalytic capabilities of CuO(1 1 1). Hence this paper would unravel the following questions: (a) how the Hubbard U parameter is determined, (b) how the stoichiometric and nonstoichiometric surfaces are constructed, (c) what processes are involved in H 2 O adsorption and dissociation on the stoichiometric and nonstoichiometric CuO(1 1 1) surfaces.

Computational methods
All calculations are carried out using spin-polarized Kohn-Sham DFT [37,38] with Hubbard [39] and Van der Waals dispersion corrections of Grimme [40] using Quantum ESPRESSO package [41]. Exchange and correlation functions are expressed by GGA (generalized gradient approx imation) based on functional PBE (Perdew-Burke-Ernzerhoff) [42]. Core ions are represented by using projector augmented wave (PAW) [43]. Integration of the Brillouin zone is done on a 4 × 4 × 1 k-points grid sampled by Monkhorst-Pack scheme [44]. A cut-off energy of 500 eV is used to limit the plane wave basis set. The appropriate U value is selected for the localized 3d electrons correction of Cu.
The surface U parameter can be determined using at least two different empirical approaches, first by reproducing bulk properties and second by reproducing surface experimental data. Mishra et al [25] and Maimaiti et al [26] employed the first approach and found that U of 7 eV could reproduce bulk properties such as the local magnetic moment of Cu atoms and the bandgap of CuO. Trinh et al [45] and Bhola et al [46], who applied the second approach by comparing the x-ray photoelectron spectroscopy and enthalpy data for the H 2 adsorption on CuO surfaces with DFT + U calculations, suggested low U values (4.0-4.5 eV). Maimaiti et al also showed that the variation of U did not change the energetic preferences of different oxygen vacancies on CuO(1 1 1). Hence, they concluded that for CuO(1 1 1), the U value of 7 eV was adequate to describe the appropriate electronic structure and reaction energetics.
In this study, the effective U value (U eff ) is determined using the first approach, i.e. by calculating the U depend ence of the bandgap and atomic magnetic moment (μ).Based on the calculation results (see figure 1 in the electronic supplementary information (ESI) available online at stacks.iop.org/ JPhysCM/32/045001/mmedia), the values of bandgap and μ Cu increase as the value of U increases. Conversely however the value of μ O decreases as the value of U increases. By comparing the results with the experimental data of bandgap and μ Cu that are 1.34 (at 300 K)-1.67 eV (at 0 K) [47] and 0.64-0.74 μ B [48], respectively, we obtain that U eff = 7 eV is the appropriate value for U. Although our U is derived for the bulk CuO however the fact that Cu 3d orbitals are quite localized, this study also adopts this U for the surface too. Moreover, this approach have been used successfully by previous researchers as well [22,25,26]. To convince further on the correctness of U, at the end of this report, we discuss the effect of different U values by applying U = 0 eV (plain DFT), U = 4.5 eV, and U = 7 eV on H 2 O dissociation on the stoichiometric and nonstoichiometric CuO(1 1 1) surface.    [22,49]. CuO(1 1 1) is nonpolar which means it has no net dipole perpendicular to the surface. In this study, CuO(1 1 1) surfaces are built based on the bulk structure of CuO with the experimental lattice parameters are given by a = 4.68 Å, b = 3.42 Å, c = 5.13 Å and β = 99.54° [50]. The experimental lattice parameters are preferred to be used to avoid spurious effects [33]. The magnetic unit cell of bulk CuO is represented in a unit cell consisting of eight formula units of CuO [51] generated based on lattice vector transformations by a = a − c, b = b, and c = a + c (see figure 1(a)) [33,52]. The CuO(1 1 1) surface is modeled by a slab comprising of three layers with (1 × 2) supercell size and a vacuum (see figure 1(d)). The sufficiency for the number of layers is confirmed by the density of states profile (see figure 2 in ESI). The vacuum space between slabs is about 15 Å which is large enough to eliminate spurious effect due to periodic boundary condition [22,25]. Magnetic spin ordering for the surface follows a bulk-like model [22] (see figure 1(b)). Further, surface optimization is achieved by relaxing the two top layers and fixing the bottom layer in bulk condition.
In the top layer, there are two types of Cu and O atoms, including coordinatively unsaturated and fully coordinated atoms. The first ones are Cu 3c (Cu sub ) and O 3c (O suf ), both coordinate with three neighbor atoms. The second ones consist of Cu 4c (Cu suf ) and O 4c (O sub ), coordinate with four neighbor atoms. The subscript 'sub' and 'suf' are used to label subsurface and outer-most atoms, respectively. We define six adsorption sites namely Cu sub -Cu sub bridge, Cu sub , Cu suf -Cu suf bridge, Cu suf , O sub -O sub bridge, and O suf -O suf bridge, which are denoted by A, B, C, D, E, and F, respectively (figure 1(c)). (1 1 1) surface. The oxygen vacancy defect CuO(1 1 1) surface is modeled by removing an oxygen atom from the stoichiometric surface. This study chooses to remove O suf (O 3c ) from the outer most layer because it is under-coordinated and, thus, weakly bonded to its surrounding. The removal also leaves Cu 2c with more dangling bonds (see figure 1(e)). The stability of this slab model is confirmed by the previous work of Maimati et al [26]. Physically, the structure can be formed through surface reduction by hydrogen [26]. (1 1 1) surface. The oxygen-preadsorbed CuO(1 1 1) surface is modeled by placing an oxygen adatom on the site A of the stoichiometric surface (see figure 1(f)). Physically, the structure can be formed through adsorption of oxygen molecule over CuO(1 1 1) with an oxygen vacancy defect. Our preliminary work found that such mechanism could proceed with low activation energy of 0.12 eV and exothermic by −1.21 eV (see Figure 3 in ESI). (1 1 1) surfaces. H 2 O adsorption is modeled by placing one H 2 O molecule as an adsorbate on the above mentioned (1 × 2) super-cell which corresponds to 1/2 ML adsorption coverage. The molecule is allowed to relax in all degrees of freedom along with the two atomic layers of the surface during the optimization.

H 2 O adsorption on CuO
H 2 O adsorbate is placed on the previously defined sites on the respective surface. These sites are chosen due to the presence of unstable dangling bonds that tend to interact with the adsorbates and are expected to play an important role in the process of adsorption, activation, or dissociation [53].
The interaction strength of H 2 O and CuO(1 1 1) surface is described by the magnitude of adsorption energy (E ads ) that is calculated by the following equation (1).
where E sub/sorb , E sub , and E sorb denote the total energies of surface and adsorbed molecule system, the energy of clean surface, and energy of a free adsorbed molecule in a vacuum, respectively. Based on this definition, negative value of E ads indicates a stable adsorption.   (1 1 1) [54]; this calculation provides the activation energy (E act ) and the reaction energy (ΔE) as the potential barrier between IS and TS and the total energy difference between IS and FS, respectively. They are expressed as follows:

H 2 O dissociation on CuO
with E act is the activation energy, E TS is the energy of the TS, E R is the energy of the IS and E P is the energy of the FS. In addition, a vibrational frequency analysis is performed [55] to validate the transition state (TS) where it shall have only one imaginary frequency.

Results and discussions
Initially, we study the energetic and electronic structure of H 2 O adsorption on the stoichiometric and nonstoichiometric CuO (1 1 1)      the calcul ation without incorporating dispersion correction.
Clearly that the dispersion correction provides better adsorption energies than that without the correction for the same configuration. It is also obvious that the strongest adsorption is on site A. The weakening of the O-H bond is further confirmed by the vibrational analysis. Table 2 shows the comparison between the calculated vibrational frequencies H2O molecule in the isolated and adsorbed phase. It is easy to see a significant redshift of stretching vibration frequencies related to the modes with notable OH H2O bond length elongation.
Charge redistribution due to the interaction can be studied from charge density difference (∆ρ) obtained from the following formula: where ρ CuO (1 1 1) figure 3. Obviously there are some charge depletions in the oxygen lone-pair orbital along with charge accumulation in the bonding region between O H2O and Cu sub . There is also a strong charge accumulation in between H H2O atom and O suf . This is the origin of the O-H bond elongation upon the adsorption. The position of the electronic orbitals of Cu sub atoms and H 2 O before and after adsorption is shown in orbital energy diagram [56] (see figure 5). It appears that Cu 3d(up) states  shift towards higher energy and H 2 O orbitals shift toward lower energy. Hybridization of H 2 O molecular orbitals with the surface is shown by splitting 1b 1 and 3a 1 orbitals until its energy levels match to that of Cu 3d. These become an important interface of charge transfer between surface and H 2 O molecule. The charge transfer from 1b 1 orbitals of H 2 O to Cu 3d states is shown by the emergence of unoccupied 1b 1 splitted orbitals on the conduction band with energy levels equal to that of Cu 3d states.
The bonding and anti-bonding states can be seen from overlapping orbital in crystal orbital overlap population (COOP) plot [57] as shown in figure 6. The positive sign of COOP of H H2O -O suf and O H2O -Cu sub pairs shows bonding state formation between them and this in turn indicating their bonds are strengthen and negative sign of COOP of H H2O -O H2O shows anti-bonding state formation that indicates its bonds are weakened. Table 3 lists the values of adsorption energy along with some structural parameters of H 2 O adsorption on sites A, B and C of the CuO(1 1 1) surface with oxygen vacancy. We found that H 2 O is strongly adsorbed on the surface with adsorption energy −1.06 eV on site C. The trend of the adsorption strength is C > B > A with their structural geometry are shown in figure 7. The bond length O H2O -Cu sub and the shortest distance between O H2O -O suf are 2.06 Å and 1.99 Å, respectively (see figure 8(a)). Based on charge density difference as depicted in figure 8(b), it is found that O H2O loses its electrons to the surface.

Adsorption on the oxygen vacancy defect surface.
The origin of the strong bonding can be traced from the electronic structure. The presence of an oxygen vacancy defect on CuO(1 1 1) surface leads to electron deficiencies on the surface. It increases the local radical characteristic of the dangling bond on the surface. We could see it from LDOS plot of the system as given in figure 9. The LDOS are projected to O H2O p orbital, surface Cu d orbital and O suf p orbital. Unlike the case of adsorption on stoichiometric surface, the H 2 O molecular orbitals are largely shifted down albeit remain localized in energy. There is only a small amount of mixing with d-states that can be found on higher energy, close to the Fermi-level, as well as mixing on lower and higher energy that can be found with O suf p orbital. It suggests that the interaction is a radical type. The shifting down of H 2 O molecular orbitals corresponds to the stabilization interactions due to coupling with surface oxygen p orbital which is responsible for the strong adsorption. However, this type of stabilizing interaction usually results in a stronger adsorption molecular structural integrity. Indeed, considerably higher vibrational frequency of symmetric O-H stretching mode (table 4) as compared to the  adsorption on stoichiometric surface (table 3) figure 11(b), it is found that O H2O loses its electron to the surface.
LDOS plot of the adsorption system is given in figure 12. The LDOS are projected on the p orbitals of O H2O and O pre atoms, and d orbital of Cu sub . The LDOS profiles share some similarities with the adsorption on stoichiometric surface such as the broadening of peak of H 2 O HOMO toward Fermi level and the splitting of the orbital into unoccupied state. It indicates that H 2 O molecule is adsorbed strongly enough and its O-H bond is weakened. The similarity can also be found in the magnitudes of vibrational frequencies of H 2 O shown in table 4 that comparably close to the ones for the case of adsorption in stoichiometric surface.
However, the presence of preadsorbed oxygen induced a new unoccupied state above the Fermi level, which will attract an electron donor, in this case, the H atom of the H 2 O adsorbate. Thus, it may interact with O pre , as indicated by the charge density difference profile shown in figure 11(b). This feature is found to be important in the H 2 O dissociation process described later. Based on COOP analysis, it appears that there is no bonding overlap between H H2O and O pre . This in turn indicates hydrogen bond or Coulombic interaction between them is dominant (see figure 4 in ESI). Table 6 compares the results of this study with previous reports [14,21,22]. The discrepancies are mainly due to the We proceed to study the dissociation reactions on the stoichiometric and nonstoichiometric surfaces similar to the case of adsorption. The structures for the initial (IS), transition (TS) and final state (FS) are shown in figure 13. The FS structure for reaction on the stoichiometric surface is obtained from relaxed co-adsorption of O and OH on O suf and Cu sub -Cu sub bridge, respectively. In case of the oxygen vacancy defects, because the OH-dissociated product is assumed to fill the vacancy, its structure is obtained by relaxing two H atoms on top of two O suf sites of a stoichiometric surface. Finally, for the oxygen-preadsorbed case, the FS structure is obtained by relaxing two co-adsorbed OH on each Cu sub site, assuming that the dissociated H atom was attracted by the preadsorbed O atom to form OH. The comparison for energetic of the reactions is shown in the energy diagram in figure 14. Dissociation on the stoichiometric and oxygen vacancy defects surface results in almost similar amount of activation energies of 0.18 eV and 0.17 eV. However, dissociation on the oxygen vacancy defect surface   is much more exothermic (−0.74 eV) as compared to the stoichiometric surface (−0.29 eV). The more exothermic reaction can be attributed to the larger stabilization of the FS due to the filling of the vacancy by the dissociated OH.
The smallest activation energy is observed for the oxygenpreadsorbed surface case; the barrier was only 0.04 eV, and the reaction was exothermic by −0.30 eV. The presence of O atom on the surface is thus important in water dissociation on CuO(1 1 1) as also suggested by the interaction between O and H H2O in the adsorption phase. Nevertheless, if we include the activation energy for the formation of the oxygen-preadsorbed surface mentioned previously (0.12 eV), the total activation energy is 0.17 eV. This is very close with the activation energy for dissociation on the stoichiometric and oxygen vacancy defect surfaces.
Finally, the CuO(1 1 1) surface exhibits a strong catalytic activity for H 2 O dissociation, with a considerably small activation barrier (<0.2 eV). The surface modification enhances the H 2 O binding and improves the H 2 O dissociation activity. Thermodynamically, the oxygen vacancy defect CuO (1 1 1) is the most favorable surface which will attract H 2 O reactants effectively, thus ensuring the availability of reactants on the surface. Kinetically, the oxygen-preadsorbed CuO(1 1 1) act  [22]. c Zhang et al [31]. d Fronzi and Nolan [29].    ). Furthermore, the different U also lead the different thermodynamics and kinetics of the reactions. In H 2 O dissociation on the stoichiometric surface, the addition of U potential lowers activation barrier and changes thermodynamic of the reaction from endothermic at U = 0 eV (as obtained by Zhang et al [23]) to exothermic at U = 4.5 eV and U = 7.0 eV, whereas, on the nonstoichiometric surfaces the addition of U causes decrease in both activation and reaction energies, except for U = 7.0 eV on the oxygen vacancy defect surface due to significant difference of its IS geometric. If we compare between U = 4.5 eV and U = 7.0 eV, U = 4.5 eV is more effective in reducing activation barrier in the nonstoichiometric surface than U = 7.0 but vice versa on the stoichiometric surface. This result is slightly different from that obtained by Miamiati et al [27] which reported that Hubbard variation does not change energetic preferences in case of oxygen vacancy formation.

Conclusions
The dispersion-corrected Hubbard-corrected density functional theory is performed on H 2 O adsorption and dissociation on the stoichiometric and nonstoichiometric CuO (1 1 1) surface. H 2 O is favorably adsorbed on the top Cu sub -Cu sub bridge in the stoichiometric and oxygen-preadsorbed surface and on the top of Cu sub (Cu 2c ) in the oxygen vacancy surface. Based on changes in OH bond length and angle distortion, we conclude that the adsorption of H 2 O on the oxygen-preadsorbed CuO(1 1 1) surface leads to the weakening of OH bond more significantly as compared to H 2 O adsorption on the stoichiometric and oxygen vacancy defect CuO (1 1 1). The H 2 O molecule is strongly adsorbed on the oxygen vacancy defect surface with the adsorption energy of −1.06 eV, followed by the stoichiometric surface (−0.87 eV) and the oxygen-preadsorbed surface (−0.83 eV). Charge transfer occurs through electron transfer from the H 2 O molecule to the CuO(1 1 1) surfaces. The dissociation of H 2 O into OH and H species on CuO(1 1 1) surfaces are exothermic with the lowest reaction energy (−0.74 eV) is observed on the oxygen vacancy defect surface, followed by cases of the oxygen-preadsorbed surface (−0.31 eV) and stoichiometric surface (−0.29 eV). Surface modification of CuO(1 1 1) with the oxygen-preadsorbed significantly reduces the barrier energy of H 2 O dissociation up to 0.04 eV as compared to the stoichiometric surface of 0.18 eV and the oxygen vacancy defect surface of 0.17 eV. These results indicate that CuO(1 1 1) surface exhibits a strong catalytic activity for H 2 O dissociation and the surface modification of CuO(1 1 1) with the oxygen-preadsorbed significantly reduces the barrier energy of H 2 O dissociation and with the oxygen vacancy defect can increase the reactivity of surface in H 2 O adsorption.