NH3 is a compound of great importance. Its toxicity can cause environmental pollution, but the high hydrogen storage capacity (17.7wt%) and energy density (3000 Wh/kg) make it to be used as an excellent and COx-free hydrogen provider [1-3]. Due to the drive for better environmental protection and energy conversion efficiency, the catalytic performance and surface behavior of NH3 have received considerable attention [4-6]. A fundamental understanding of catalysts and decomposition mechanism of NH3 has become very important. Different types of catalysts, including transition metals, alloys, compound of noble metals, oxide and carbon supported metals, have been tested for NH3 decomposition [4-19]. The sequences of NH3 decomposition activities, Ru>Ni>Rh>Co>Ir>Fe>>Pt>Cr>Pd>Cu>>Te and Ru>Ir>Rh>Ni>Fe, were reported in literature [4, 9]. In general, the Ru-based catalysts are believed to be the most active for NH3 decomposition. However, Ru is very expensive and has a limited availability, which prohibits its wide applications in industry . In the past two decades, great efforts have been made to develop some cheap alternative catalysts . The Ni-based catalysts are regarded as the most attractive candidates for NH3 decomposition . Experimental studies of NH3 decomposition have been performed on Ni (110) [15, 16], Ni (111) , Ni films , and various nono-sized Ni particles . The results suggest that NH3 decomposition over Ni-based catalysts is a structure-sensitive reaction. Theoretical calculations indicate that the first dehydrogenation step is easy on the stepped Ni (211) surface [19, 20], but the N recombination is rather difficult thermodynamically owing to the high energy barrier . On Ni (110) surface, the desorption is rather competitive with the decomposition of NH3 since the desorption energy is calculated to be the same as the reaction barrier of first N-H bond scission in NH3 . The close-packed Ni (111) surface is less active than Ni (110), the energy barrier to cleave the first N-H bond is 0.23-0.26 eV higher than the binding energy of NH3, implying that the NH3 molecule would rather desorb than dissociate on this surface, but the N recombination barrier is evidently lower than on Ni (211) surface [19, 22]. To increase the binding energy of NH3 as well as to decrease the energy barriers for the first dehydrogenation step and N recombination reaction is the important question to be solved. Recently, a series of monolayer bimetallic catalysts, consisting of a monolayer of an admetal in the top layers of a host metal, have been proposed and tested for NH3 decompositions , of which the Ni/Pt (111) and Fe/Pt (111), a Ni or Fe monolayer on top of the Pt (111) surface, were predicted theoretically and verified experimentally to be active for NH3 decomposition, but the Pt (111) tuning effect to the Ni or Fe monolayer and the decomposition mechanism on these surface are not reported. In addition, a following studies of Fe/Pt (111) system revealed that the inhibition of NH3 decomposition reaction due to the strong bonding between Fe and N may still be a challenge .
Since Ni is inexpensive and WC has similar properties to Pt-group metals [24, 25], one can expect that adding a monolayer of Ni on top of WC substrate may result in a catalyst with activity similar to the Ni/Pt (111) surface. In addition, acting as a diffusion barrier for the Ni adatoms, the WC substrate can prevent the thermally-induced diffusion of Ni . Moreover, an active monolayer Ni catalyst supported on WC instead of Pt or Ru would lead to considerable cost savings. However, when a Ni monolayer was supported on Pt and WC substrate, how the electronic states are modified by the supporters and the adsorption and decomposition behavior of NH3 on these surfaces remain to be uncovered. In this work, we first discuss the electronic structure of the Ni monolayer on Pt (111) and WC (001) and then report the adsorption and decomposition mechanism of NH3 on Ni monolayer covered surfaces.Ⅱ. MODELS AND COMPUTATIONAL METHODS
Density functional theory (DFT) calculations in this work are performed using the periodic supercell plane wave basis method, as implemented in the VASP code (ver. 4.6) [27, 28]. Atomic cores are described with the projector augmented wave (PAW) method , the electron states are expanded in a plane wave basis set and plane waves are included to an energy cutoff of 400 eV. Electronic energies are calculated with the PW91 implementation of the generalized gradient approximation (GGA) . A Gaussian smearing scheme with a smearing parameter of 0.15 eV is imposed at the Fermi level, the energies are extrapolated to zero smearing. The calculated lattice parameters of Ni and Pt are 3.52 and 3.98 Å, compared well to the experimental values of 3.52 and 3.92 Å respectively  and the calculated values of 3.53  and 3.99 Å  respectively. For the hexagonal close packed structure of WC, the optimized lattice constants are a=b=2.92 Å, c=2.85 Å, which are in good agreement with the experiments a=b=2.91 Å, c=2.84 Å . To compare the tuning effects of substrate to the top Ni monolayer, three surface models, Ni/Ni (111), Ni/Pt (111) and Ni/WC (001), were constructed. For Ni/Ni (111) and Ni/Pt (111), six atomic layer surfaces were truncated from the optimized structures of bulk Ni and Pt respectively and then optimized with the bottom two layers frozen, six Ni layer surface was used to mimic Ni monolayer on a five layer Ni substrate, i.e. Ni/Ni (111), the top atomic layer of the six layer Pt (111) surface was replaced by Ni atoms to create the bimetallic surface Ni/Pt (111). For Ni/WC (001), calculations were performed using a W terminated (001) surface (six layers of alternating W and C atoms) with Ni atoms on the hcp sites which were tested to be the most stable structure (the mean adsorption energies of Ni on WC (001) were -1.82, -2.53, and -2.69 eV on top, fcc, and hcp sites respectively, the bridge site was unstable and transformed into the hcp structure when optimized). All the calculations were performed within a 2×2 supercell with the vacuum thickness of 15 Å. For the adsorption and decomposition of NH3 on Ni/Pt (111) and Ni/WC (001), one molecule adsorbed on one side, yielding a 1/4 ML coverage. The numerical integration over the Brillouin zone was calculated using the Monkhorst-Pack method and a 5×5×1 k-point mesh , which is tested to be accurate enough in our calculations (see Table S1 in supplementary materials). Transition states were identified using the Lanczos method . Vibration frequency under the harmonic approximation is calculated upon perturbing the atoms by±0.03 Å to verify the energy minimum or transition states. Zero-point energy corrections are included in the energy calculations. No spin polarization considered in this work since its influence is very small for binding and activation energies (see Table S2 in supplementary materials).Ⅲ. RESULTS AND DISCUSSION A. Geometry and Ni binding energy
The bulk of metal Ni and Pt has a face-centered cubic structure, the atoms are in closely packed in the (111) surfaces. WC is known to crystallize in a hexagonal structure with the W and C layers alternatively piled along . When a monolayer Ni atoms bind to Pt (111) and WC (001) surfaces, the distance between Ni atoms in the monolayer is different due to the lattice mismatch, this will result in the property variations of Ni atoms. In the Ni monolayer covered structures relaxed (see Fig.S1 in supplementary materials), the Ni-Ni distances (dNi-Ni) are 2.82 and 2.92 Å in Ni/Pt (111) and Ni/WC (001), 0.38, and 0.43 Å longer than that of Ni/Ni (111) respectively, which varies in the same order of r3 moments (rcm) of Ni atoms in the monolayer (the values are 77.17 and 78.43 Å3 respectively and for Ni/Ni (111) it is 75.24 Å3). This distance variation alters the Ni-Ni interaction in the monolayer and the binding of the monolayer to the substrate, more importantly it will invoke the variation of the electronic structure and thus the catalytic activity.
We calculated the binding energy using
For Ni/Ni (111), Ni/Pt (111), and Ni/WC (001) systems, we calculate the total bond order (TBO) of Ni atom in the top monolayer using the DDEC program , the TBO values are 2.86, 2.45, and 2.66 respectively. Small TBO signifies strong residual bonding ability. In this respect, Ni/Pt (111) and Ni/WC (001) are more able to bind adsorbate than Ni/Ni (111), which is important for NH3 adsorption and decomposition on these surfaces. The d-band center referenced to the Fermi level has been calculated as the first moment of the projected d-band density of states (PDOS) corresponding to the Ni atoms in the monolayer. The results are -2.03, -1.56, and -1.56 eV for Ni/Ni (111), Ni/Pt (111), and Ni/WC (001) respectively. We can find the similarity between the Ni atoms in the monolayers of Ni/Pt (111) and Ni/WC (001) respectively since WC has properties resemblance to Pt [24, 25].
To better understand the bonding effects between the Ni monolayer and the substrate, we characterize the electron redistribution around the surface atoms by ∆ρs(z)=ρ(z)-ρmono(z)-ρsub(z), where ρ(z), ρmono(z) and ρsub(z) correspond to the plane averaged electron density of the whole slab, the top monolayer, and the substrate (the slab with the top monolayer removed), respectively. Figure 1 shows the results for Ni/Ni (111), Ni/Pt (111), and Ni/WC (001), the inset figures are charge density differences calculated by ∆ρ=ρ(z)-ρmono(z)-ρsub(z), where ρ(z), ρmono(z), and ρsub(z) are electron density of the whole slab, the top Ni monolayer and the substrate respectively. We can see ∆ρs(z) in different surfaces is significantly different. For Ni/Ni (111), the negative peaks of ∆ρs(z) at 0.77, 0.00 Å and -1.64, -2.55 Å correspond to the charge depletion on the dz2 orbitals of Ni atoms (this phenomena is also observed from the ELF, see Fig.S2 in supplementary materials) in the top monolayer and the subsurface (the top layer of the substrate) respectively, the electrons are transformed mainly to three regions, including the dxz and dyz orbitals of Ni in the top and the subsurface layers as well as the regions between top Ni monolayer and the substrate, as indicated by the arrow in Fig. 1(a). If the substrate is replaced by Pt (111) (Fig. 1(b)), the evident difference is observed at 0.06 Å where the electron accumulates obviously instead of the depletion in Ni/Ni (111), and the shift-up of the peak can be explained by the mixing between dxy/dx2-y2 and dxz/dyz, which can be found in the projected density of states onto the Ni atom in monolyer (Fig.S3 in supplementary materials). When the Ni monolayer was supported on WC (001), remarkable charge accumulations can be seen in the range from -1.12 Å to 0.39 Å, the peak at 0.15 Å arises in the same way as the case of Ni/Pt (111), the charge accumulation between the top Ni monolayer and the substrate surface reaches maximum at -0.72 Å due to dxy/dx2-y2 mixing with dxz/dyz, and the charge perturbation is rapidly dropped below the substrate surface. The accumulated electrons at the regions between Ni monolayer and the substrate surface are responsible for the binding of Ni atom, the peak of the charge accumulation in this area is more and more close to the Ni monolayer from Ni/Ni (111) to Ni/WC (001). The area of the peak can be used to measure the charge transferred, it can be seen that more and more electrons are shifted away from the dz2 orbital of Ni atom in the monolayer when the substrate changes from Ni (111) to Pt (111) and to WC (001), this phenomena coincides with the changes of dz2 band center which are -1.97, -1.55, and -1.50 eV for the Ni atoms in the monolayer of Ni/Ni (111), Ni/Pt (111) and Ni/WC (001) respectively. Charge depletion atop the Ni atom in the monolayer is significant to the adsorption of NH3 because NH3 is an electron donor adsorbate .C. The adsorption and decomposition of NH3
The adsorption and decomposition of NH3 on Ni (111) surface (which can be viewed as Ni/Ni (111)) has been reported in Ref., we focus our calculations on the behavior of NH3 on Ni/Pt (111) and Ni/WC (001) and compare the results with that of NH3/Ni (111) reported in Ref.. The binding energy (EbindA) for an adsorbate (A) on the surface is defined as EbindA=Eslab+EA-EA/slab, where EA/slab and Eslab are the total energy of the slab with or without the adsorbate, EA is the energy of the adsorbate in the gas phase. According to this definition, positive values of EbindA means the stable adsorption. Calculations on different adsorption sites, including top, bridge, fcc and hcp positions, have been performed for the related species, the binding energies at the most stable adsorption site are presented in Table Ⅰ.
NH3 and NH2 prefer the top and bridge sites on Ni/Pt (111) and Ni/WC (001) respectively, the same as that on Ni (111). The C3 of NH3 and C2 of NH2 axes are perpendicular to the surface respectively. The binding energies of NH3 are 0.83 and 0.74 eV respectively, 0.18 and 0.09 eV larger than that on Ni (111) surface , the NH3 binding energies on different surfaces are found to be correlate very well with the TBO of Ni atoms: Ebind(NH3)=1.89-0.43TBO (R2=1.00), indicating that TBO can be used as an indicator to measure the stability of NH3 on the surfaces. The binding energies of NH2 are 3.39 and 3.37 eV respectively which are 1.79 and 1.77 eV higher compared to that on Ni (111) surface. NH favors the fcc position with the N-H bond along the surface normal on all the surfaces and again it binds more stable on Ni/Pt (111) and Ni/WC (001) than on Ni (111). N absorbs at the fcc site both on Ni (111) and Ni/Pt (111) but the hcp position on Ni/WC (001). The most stable position for H is fcc site on Ni/Pt (111) but the hcp site on Ni (111) and Ni/WC (001). In general, modification to the surface by loading a Ni monolayer onto Pt (111) and WC (001) improved the surface ability to bind NH3 and the related species.
To understand more clearly the reaction behavior of NH3, a stepwise dehydrogenation mechanism is considered , which includes four steps: NH3→NH2+H, NH2→NH+H, NH→N+H and N+N→N2. For each of dehydrogenation steps, we used the structures with the most stable adsorption configurations of NHx (x=3, 2, 1) and the most stable co-adsorbed states of NHx+H (x=2, 1, 0) as the initial and final states respectively, and for the N-N recombination step the co-adsorbed N+N (N atoms binding on the fcc positions on Ni/Pt (111) and hcp sites on Ni (111) and Ni/WC (001)) is the initial state, N2 adsorbed on a hcp site with the N-N bond nearly parallel to the surface used as the final state on Ni/WC (001), but a desorbed state of N2 on Ni/Pt (111) as the final state since it is plausible for N2 formation.
Reaction NH3→NH2+H begins with the most stable configuration of NH3 at the top site (Fig. 2, aI), followed by one of the N-H bonds gradually becoming longer and arrived the transition state with the N-H bond length of 1.61 Å both on Ni/Pt (111) and Ni/WC (001) respectively (Fig. 2, aT), and finally the NH2 and H move to a bridge and hcp sites respectively. The energy barriers are 0.67 eV on Ni/Pt (111) and 0.49 eV on Ni/WC (001), 0.44 and 0.62 eV lower than on Ni (111) respectively . The reaction barriers of this step on different surfaces are found to correlate well with the rcm of Ni atom (r3 moments) in monolayer as well as dNi-Ni respectively: Ea=15.97-0.20 rcm (R2=0.97), Ea=4.45-1.34dNi-Ni (R2=0.94), suggesting that Ni r3 moments and the distance between Ni atoms in monolayer can be used as a descriptor to predict the reaction barrier of the first step of dehydrogenation reactions. The reaction is exothermic by -0.87 eV on Ni/Pt (111) and -0.54 eV on Ni/WC (001) respectively. In the second reaction step, NH2→NH+H, NH2 adsorbed at a bridge site in the initial state (Fig. 2, bI), the N-H bond over the hcp position is lengthened with the NH2 plane tilted towards the hcp position, when the N-H bond lengths reach 1.37 and 1.52 Å on Ni/Pt (111) and Ni/WC (001) respectively, transition states are observed (Fig. 2, bT), in the end both NH and H adsorbed at the fcc sites respectively ((Fig. 2, bF). The energy barriers of this step are 0.31 and 0.73 eV on Ni/Pt (111) and Ni/WC (001) respectively. This step is exothermic (-1.03 eV) evidently on Ni/Pt (111), but the reaction heat is very small on Ni/WC (001). The third step, NH→N+H, begins with the NH adsorbed at the fcc site (Fig. 2, cI), the transition states occur when the N-H bond lengths are 1.53 and 2.28 Å on Ni/Pt (111) and Ni/WC (001) respectively (Fig. 2, cT), after that N and H shifted gradually to a hcp and a fcc position. The reaction barriers are 1.09 and 1.21 eV on Ni/Pt (111) and Ni/WC (001) respectively, very close to the barrier of 1.11 eV on Ni (111) . For the final reaction step, N+N→N2, initially both of the N atoms adsorbed at the nearest fcc positions on Ni/Pt (111) and hcp sites on Ni/WC (001) (Fig. 2, dI), they approach each other, and in the transition states, the distances between the N atoms are 1.65 and 1.97 Å on Ni/Pt (111) and Ni/WC (001) respectively (Fig. 2, dT), in the final states the N2 (N-N bond length is 1.11 Å) desorbed from Ni/Pt (111) but adsorbed on the hcp position on Ni/WC (001) with the N-N bond nearly parallel to the surface. This is a rate-limiting step for all the surfaces, the reaction barrier is 1.73 eV on Ni/Pt (111), similar to that on Ni (111) (1.86 eV) , but the barrier on Ni/WC (001) is 0.91 eV higher than on Ni/Pt (111), signifying that the N2 is formed easily on Ni/Pt (111) and hardly on Ni/WC (001) surface, more effort should be paid to improve the Ni/WC (001) surface in the future. Recently, Guo et al. studied the NH3 decomposition on Ni loaded Pt (111) surface, they showed that the edge sites formed by the patched Ni atoms are active for the nitrogen association . This provides a possible way to improve the Ni/WC (001) system.
The reaction energy path is presented in Fig. 3. For each step, a NH3-x species (x=0, 1, 2) plus x adsorbed H atoms without lateral interaction is taken as the initial state, co-adsorbed NH3-x-1+H in their most stable configuration and x infinitely separated and adsorbed H atoms is considered as the final state. It is evident that the energy barriers of the first N-H bond scission both on Ni/Pt (111) and Ni/WC (001) are lower than their binding energies, indicating that NH3 would decompose to NH2 and H rather than desorb from the surfaces, this is different from the case of NH3 on Ni (111) where the breaking of N-H bond is difficult since the reaction energy barrier (1.11 eV) is higher than the binding energy (0.65 eV) . The second N-H bond is the most feasible to be broken in all the reaction steps both on Ni/Pt (111) and Ni/WC (001) surfaces, especially the reaction barrier on Ni/Pt (111) is 0.31 eV, lower than the 0.59 eV on Ni (111) surface. The energy barrier of the third N-H bond scission is close to each other on Ni/Pt (111) and Ni/WC (001) and comparable to that on Ni (111). The N recombination is the hardest step, the barrier on Ni/Pt (111) is 0.13 eV lower than on Ni (111), but the barrier is 0.78 eV higher on Ni/WC (001) than on Ni (111). However, the instability of Ni/Pt (111) surface is still a problem since it has been found that the Ni monolayer begins to diffuse into the second layer at temperatures as low as 450 K and formed a Ni sandwiched between a Pt top layer and Pt bulk (Pt/Ni/Pt (111)) at 600 K, resulting in the debasement of the catalytic activity .Ⅳ. CONCLUSION
The geometry and electronic structures of Ni/Pt (111) and Ni/WC (001) are computed based on the density functional theory, detailed reaction steps of NH3 are presented, discussed and compared with each other. These results revealed that the Ni monolayer covered surfaces are rather different from the Ni (111) surface, the substrate Pt (111) and WC (001) move more dz2 electrons of Ni atoms in the monolayer to other areas compared with Ni (111), the depletion of charge density on this orbital is favorable to the adsorption of NH3 which is verified to bind at top site through the long pair . NH3 binds stronger on Ni/Pt (111) and Ni/WC (001) than on Ni (111), the reaction barriers of the first dehydrogenation step on Ni/Pt (111) and Ni/WC (001) are evidently lowered as opposed to that on Ni (111). These are significantly important to the decomposition of NH3 since it favors to decompose to NH2 and H instead of desorbing from the surface like that on Ni (111). The substrate also changes catalytic activity for other dehydrogenation steps, but N recombination barrier is the highest of all the reaction steps, indicating that it is still the rate-limiting step for NH3 decomposition. In addition, the relatively high reaction barrier for N2 generation suggests that N2 is produced only at high temperatures, this is in agreement with the experimental reports . WC is similar to Pt in properties, but the differences in electronic structures and catalytic activities are identified for Ni/Pt (111) and Ni/WC (001), particularly the energy barrier for the rate-determined step increases on Ni/WC (001) instead of decreasing on Ni/Pt (111) when compared to Ni (111). To get cheap and active catalyst, Ni/WC (001) should be improved further, a Ni alloy monolayer supported on WC (001) deserves to be tested in the future work.
Supplementary materials: Table S1 and S2 show the k-point mesh and spin polarization tests, respectively. Figure S1 shows the Ni monolayer structures on Ni (111), Pt (111), and WC (001), respectively. Figure S2 shows the electronic localization function. Figure S3 shows the projected density of states on the Ni atom in monolayer of Ni/Pt (111).Ⅴ. ACKNOWLEDGMENTS
This work was supported by the Natural Science Foundation of Henan Province (No.532221) and computation support by the High Performance Computing Center of Henan Normal University.
|||A. Klerke, C. H. Christensen, J. K. Norskov, and T. Vegge, J. Mater. Chem. 18 , 2304 (2008). DOI:10.1039/b720020j|
|||M. R. Rahimpour, and A. Asgari, Int. J. Hydrogen Energy 34 , 5795 (2009). DOI:10.1016/j.ijhydene.2009.05.013|
|||S. Appari, V. M. Janardhanan, S. Jayanti, L. Maier, S. Tischer, and O. Deutschmann, Chem. Eng. Sci. 66 , 5184 (2011). DOI:10.1016/j.ces.2011.07.007|
|||S. F. Yin, B. Q. Xu, X. P. Zhou, and C. T. Au, App. Catal. A 277 , 1 (2004). DOI:10.1016/j.apcata.2004.09.020|
|||A. Boisen, S. Dahl, J. K. Norskov, and C. H. Christensen, J. Catal. 230 , 309 (2005). DOI:10.1016/j.jcat.2004.12.013|
|||T. V. Choudhary, C. Sivadinarayana, and D. W. Goodman, Catal. Lett. 72 , 197 (2001). DOI:10.1023/A:1009023825549|
|||C. Egawa, T. Nishida, S. Naito, and K. Tamaru, J. Chem. Soc., Faraday Trans. 80 , 1595 (1984). DOI:10.1039/f19848001595|
|||F. Hayashi, Y. Toda, Y. Kanie, M. Kitano, Y. Inoue, T. Yokoyama, M. Hara, and H. Hosono, Chem. Sci. 4 , 3124 (2013). DOI:10.1039/c3sc50794g|
|||J. C. Ganley, F. S. Thomas, E. G. Seebauer, and R. I. Masel, Catal. Lett. 96 , 117 (2004). DOI:10.1023/B:CATL.0000030108.50691.d4|
|||J. Zhang, H. Y. Xu, X. L. Jin, Q. J. Ge, and W. Z. Li, Appl. Catal. A 290 , 87 (2005). DOI:10.1016/j.apcata.2005.05.020|
|||H. C. Liu, H. Wang, J. H. Shen, Y. Sun, and Z. M. Liu, Appl. Catal. A 337 , 138 (2008). DOI:10.1016/j.apcata.2007.12.006|
|||Y. M. Zhang, X. Z. Xiao, Y. L. Cao, Y. Y. Cai, and J. J. Wang, Int. J. Hydrogen Energy 38 , 2965 (2013). DOI:10.1016/j.ijhydene.2012.12.080|
|||D. A. Hansgen, D. G. Vlachos, and J. G. Chen, Nat. Chem. 2 , 484 (2010). DOI:10.1038/nchem.626|
|||J. Zhang, H. Y. Xu, Q. J. Ge, and W. Z. Li, Catal. Commun. 7 , 148 (2006). DOI:10.1016/j.catcom.2005.10.002|
|||M. Grunze, M. Golze, R. K. Driscoll, and P. A. Dowben, J. Vac. Sci. Tech. 18 , 611 (1981). DOI:10.1116/1.570833|
|||D. Chrysostomou, J. Flowers, and F. Zaera, Surf. Sci. 439 , 34 (1999). DOI:10.1016/S0039-6028(99)00458-6|
|||C. W. Seabury, T. N. Rhodin, R. J. Purtell, and R. P. Merrill, Surf. Sci. 93 , 117 (1980). DOI:10.1016/0039-6028(80)90050-3|
|||P. M. Gundry, J. Haber, and F. C. Tompkins, J. Catal. 1 , 363 (1962). DOI:10.1016/0021-9517(62)90065-9|
|||S. Stolbov, and T. S. Rahman, J. Chem. Phys. 123 , 204716 (2005). DOI:10.1063/1.2121467|
|||X. Duan, G. Qian, Y. Liu, J. Ji, X. Zhou, D. Chen, and W. Yuan, Fuel Proc. Tech. 108 , 112 (2013). DOI:10.1016/j.fuproc.2012.05.030|
|||X. Duan, G. Qian, C. Fan, Y. Zhu, X. Zhou, D. Chen, and W. Yuan, Surf. Sci. 606 , 549 (2012). DOI:10.1016/j.susc.2011.11.030|
|||X. Duan, J. Ji, G. Qian, C. Fan, Y. Zhu, X. Zhou, D. Chen, and W. Yuan, J. Mol. Catal. A 357 , 81 (2012). DOI:10.1016/j.molcata.2012.01.023|
|||L. Wang, Y. Zhao, C. Y. Liu, W. M. Gong, and H. C. Guo, Chem. Commun. 49 , 3787 (2013). DOI:10.1039/c3cc41301b|
|||R. B. Levy, and M. Boudart, Science 18 , 1547 (1973).|
|||H. H. Hwu, and J. G. Chen, Chem. Rev. 105 , 185 (2005). DOI:10.1021/cr0204606|
|||M. P. Humbert, C. A. Menning, and J. G. Chen, J. Catal. 271 , 132 (2010). DOI:10.1016/j.jcat.2010.02.016|
|||G. Kresse, and J. Hafner, J. Phys.:Condens. Matter 6 , 8245 (1994). DOI:10.1088/0953-8984/6/40/015|
|||G. Kresse, and J. Furthmuller, Phys. Rev. B 54 , 11169 (1996). DOI:10.1103/PhysRevB.54.11169|
|||P. E. Bl, and ö chl, Phys. Rev. B 50 , 17953 (1994). DOI:10.1103/PhysRevB.50.17953|
|||J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77 , 3865 (1996). DOI:10.1103/PhysRevLett.77.3865|
|||C. Kittel, Introduction to Solid State Physics. 7th Edn New York: John Willy and Sons (2005).|
|||D. A. Hansgen, D. G. Vlachos, and J. G. Chen, Surf. Sci. 605 , 2055 (2011). DOI:10.1016/j.susc.2011.08.004|
|||L. E. Toth, Transition Metal Carbides and Nitrides. New York: Academic press (1971).|
|||H. J. Monkhorst, and J. D. Pack, Phys. Rev. B 13 , 5188 (1976). DOI:10.1103/PhysRevB.13.5188|
|||R. A. Olsen, G. J. Kroes, G. Henkelman, A. Arnaldsson, and H. Jonsson, J. Chem. Phys. 121 , 9776 (2004). DOI:10.1063/1.1809574|
|||T. A. Manz and N. G. Limas, DDEC6:A Method for Computing Even-Tempered Net Atomic Charges in Periodic and Nonperiodic Materials, arXiv:1512.08270.|
|||W. Guo, and D. G. Vlachos, Nat. Commun. 6 , 8619 (2015). DOI:10.1038/ncomms9619|
|||J. R. Kitchin, N. A. Khan, M. A. Barteau, J. G. Chen, B. Yakshinksiy, and T. E. Madey, Surf. Sci. 544 , 295 (2003). DOI:10.1016/j.susc.2003.09.007|