English

• With global warming and the depletion of crude oil reserves, the development of alternative resources attracted more attention over the past decades^[1]. Methane has been regarded as an important clean energy and it can be converted to various commodity chemicals^[2]. The activation of methane to form CH_x through C−H bond breaking is the key ^[3-11]. Hence, many efforts have been carried out to develop and design efficient catalyst for the activation of CH₄.

  Transition metals such as Rh^[3], La^[4] and Ni^[5-11] possess a remarkable catalytic activity for methane dissociation. Typically, supported Ni-based catalysts are of much interest, because of their high activity and low costs. For methane decomposition, the activity and dispersion of Ni are crucial. In other words, the more exposed sites in Ni-based catalyst, the higher reactivity.

  Firstly, the activation of C−H bond in methane needs additional electrons. Due to the abundant d orbitals, metal oxide support exhibits better electron donation ability that enhances the reactivity of Ni. Secondly, the support with higher specific surface area is extremely benefit to disperse and anchor the fine Ni particles. This has been confirmed by previous reported literatures^[12-16]. Therefore, loading Ni onto a proper support can provide additional electronic property and improve the dispersion of Ni, thereby promoting the dissociation of CH₄.

  In particular, ZrO₂ is known to have a superior electronic donor ability to enhance the Ni catalytic activity^[12], although ZrO₂ itself has no activity for CH₄ dissociation^[17,18]. Wang et al.^[12] concluded that the Ni/ZrO₂ catalyst can stabilize the original Ni state due to its small size; the strong electronic donor ability of ZrO₂ was benefit to the formation of Ni active particles in carbon dioxide reforming of methane. Besides, the introduction of Zr ensured an excellent dispersion of Ni/Zr alloy and promoted the formation of active center, both of which facilitated the activation of the C–H bond in CH₄^[19], and thus, decreasing the E_a value in dry reforming of methane. Similarly, Han et al.^[13] pointed out that in addition to facilitating the Ni dispersion, support can also alter the electronic property of the catalysts that influences the adsorption characteristics, the activation energy and even the reaction pathways.

  In fact, the influence of strong interaction between Ni and ZrO₂ on the activity and dispersion of Ni has been confirmed by the recent reports^[19-23]. Thanks to the strong interaction between the support ZrO₂ and Ni catalyst, the dispersion of Ni active components is considerably enhanced^{[13,17,19-23]}. Besides, the interaction between nickel and support might maintain the initial state of Ni^[12]. Meanwhile, the moderate interaction, generated from the partial electron transfer between Ni and Zr, might promote the adsorptions of CH_x^[12]. Li et al.^[24] believed that La-modified Ni/Al₂O₃ is responsible for improving the stability and reactivity of Ni catalyst via modulating the interaction between Ni and Al₂O₃.

  Since the support has significant influence on the activity of Ni-based catalyst in CH₄ activation, it is necessary to investigate the interaction of nickel and support and the electron transfer between them. It is shown that the catalytic activity of small cluster Ni₁₃ supported on ZrO₂(111) surface differs from that of large Ni(111) in the CO₂ hydrogenation reaction due to their different surface atomic arrangement and electronic characteristics^[25]. Ni₁₃ exhibits higher catalytic activity and selectivity, as it has larger number of exposed surface atoms and more active sites with different coordination numbers^[26]. Ni₁₃ has stable icosahedron configurations that contains 42 Ni–Ni bonds^[27,28]. This makes Ni₁₃ can well maintain the structure during catalysis process^[29]. Ni atom in the center of Ni₁₃ shows the highest coordination number, while each Vertex Ni atom of Ni₁₃, possessing the significantly coordinatively unsaturated site, is the predominant active center for Ni catalyst. Yilmazer’s^[30] stated that ethylene adsorption energy gradually increases with the decrease of Ni coordination number from 9 to 6 on Ni(111), Ni(100), Ni(110) and Ni₁₃. Therefore, the icosahedral Ni₁₃ with I_h symmetry shows higher the structural stability and reactivity^[31,32] among different Ni_n^[33].

  Hence, the reaction mechanism for CH₄ dehydrogenation on pure Ni₁₃ and Ni₁₃ supported ZrO₂(111) catalysts was investigated by using DFT calculations. The effect of support on the adsorption and activation of CH_x (x=0−3) was analyzed. The results suggested that the interaction between Ni and ZrO₂ can improve the electron delocalization of Ni and make the adsorbed CH_x (x=0−3) species become more electron-rich in reaction.

  1.   Computational details

  DFT calculations were performed using the Vienna Ab Initio Simulation Package (VASP), where the exchange-correlation energy functional is described with Perdew-Burke-Ernzerhof (PBE) of the generalized gradient approximation (GGA)^[34]. The configurations of Ni₁₃ and Ni₁₃-ZrO₂(111) are shown in Figure 1. Ni₁₃ is obtained on the basis of the magic number cluster structure^[30], the average Ni–Ni distance in Vertex-Vertex (2.444 Å) and in Center-Vertex (2.325 Å) are in line with the experimental results (2.389 and 2.274 Å, respectively)^[35] and theoretical calculation^[26]. The p (3×3) slabs ZrO₂(111) has nine layers. A vacuum of 15 Å is added, and a lattice parameter of 5.13 Å is used^[36-38]. The top five layers are fully relaxed, while the bottom four layers are fixed at their bulk positions. The energy convergence for electronic relaxation is set to 10⁻⁵ eV. All atoms are relaxed until the atomic force is less than 0.02 eV/Å with a kinetic energy cutoff of 400 eV^[39]. The Monkhorst-Pack 2×2×1 k-point mesh is used to Brillouin zones of sample surface^[40]. The transition state is searched by using the nudged elastic band method , as described by our previous work^[41].

  Figure 1

  

  Figure 1.  Top view correspond to Ni₁₃ and Ni₁₃-ZrO₂(111) morphologies, respectively

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  For the adsorptions and reactions on Ni₁₃ and Ni₁₃-ZrO₂(111), the adsorption energies (E_ads), the activation energy (E_a) and reaction energy (ΔE) with the zero-point-energy (ZPE) are defined according to equations (1), (2) and (3)^[41,42], where E_cluster, E_adsorbate and E_{adsorbate/cluster} are the total energies of the bare cluster, the isolated adsorbate, and the optimized structures of the adsorption configuration, respectively. ΔZPE_ads, ΔZPE_barrier and ΔZPE_reaction refer to ZPE corrections for E_ads, E_a and ΔE, respectively, which are determined according to equations (4), (5) and (6)^[41,42]; h is Planck's constant, υ_i refers to the vibrational frequencies. The d-band center ($ {\varepsilon _{\rm{d}}} $) of Ni₁₃ and Ni₁₃-ZrO₂(111) is calculated by equation (7)^[7], where ${\rho _{\rm{d}}}$ represents the density of states projected onto the Ni atoms' d-band; E is the energy of d-band.

  $ E_{{\rm{ads}}}=E_{{\rm{adsorbate/cluster}}}－(E_{{\rm{cluster}}}+E_{{\rm{adsorbate}}})+△ZPE_{{\rm{ads}}} $

  (1)

  $ {E_{\rm{a}}} = ({E_{{\rm{TS}}}} - {E_{{\rm{IS}}}}) + \Delta ZP{E_{{\rm{barrier}}}} $

  (2)

  $ \Delta E = ({E_{{\rm{FS}}}} - {E_{{\rm{IS}}}}) + \Delta ZP{E_{{\rm{reaction}}}} $

  (3)

  $ \Delta ZP{E_{{\rm{ads}}}} = {\left( {\sum\limits_{i = 1}^{{\rm{vibration}}} {\frac{{h{v_{i}}}}{2}} } \right)_{{\rm{adsorbed}}}} - {\left( {\sum\limits_{i = 1}^{{\rm{vibrations}}} {\frac{{h{v_{i}}}}{2}} } \right)_{{\rm{gas}}}} $

  (4)

  $ \Delta ZP{E_{{\rm{barrier}}}} = {\left( {\sum\limits_{i = 1}^{{\rm{vibration}}} {\frac{{h{v_{i}}}}{2}} } \right)_{{\rm{TS}}}} - {\left( {\sum\limits_{i = 1}^{{\rm{vibrations}}} {\frac{{h{v_{i}}}}{2}} } \right)_{{\rm{IS}}}} $

  (5)

  $ \Delta ZP{E_{{\rm{reaction}}}} = {\left( {\sum\limits_{i = 1}^{{\rm{vibration}}} {\frac{{h{v_{i}}}}{2}} } \right)_{{\rm{FS}}}} - {\left( {\sum\limits_{i = 1}^{{\rm{vibrations}}} {\frac{{h{v_{i}}}}{2}} } \right)_{{\rm{IS}}}} $

  (6)

  $ {\varepsilon _{\rm{d}}} = \frac{{\int_{ - \infty }^{{E_{\rm{f}}}} {E{\rho _{\rm{d}}}\left( E \right){\rm{d}}E} }}{{\int_{ - \infty }^{{E_{\rm{f}}}} {{\rho _{\rm{d}}}\left( E \right){\rm{d}}E} }} $

  (7)

  2.   Results and discussion

  2.1   Adsorption of all species

  The optimization structure in DFT calculation and corresponding energy of all adsorbed species involving in CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111) are presented in Figure 2 and Table 1. For comparison, previous calculated results on Ni(100) and Ni₄ are also given in Table 1. The partial density of states (pDOS) and the differential charge density for CH adsorbed on Ni₁₃ and Ni₁₃-ZrO₂(111) are shown in Figure 3.

  Figure 2

  

  Figure 2.  Most stable configurations of adsorbed species involved in CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111), respectivelyThe blue, gray, red, white and turquoise balls represent Ni, C, O, H and Zr atoms, respectively Bond length are in Å

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  Table 1

  

  Table 1.  Adsorption sites and adsorption energies (E_ads) of the stable configurations for the adsorbed species involved in CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111), respectively

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  Species	Ni13		Previous results Ni4[6], Ni(100)[7]		Ni13-ZrO2(111)
  	site	Eads/eV	Eads/eV		site	Eads/eV
  CH4	Ni-top	0.04	−0.41[6]		Ni-top	−0.02
  CH3	Ni-bridge	−2.22	−2.37[6]		Ni-bridge	−2.46
  CH2	Ni-fold	−4.36	−4.85[6], −3.76[7]		Ni-fold	−4.76
  CH	Ni-fold	−6.40	−6.71[6], −6.43[7]		Ni-fold	−7.00
  C	Ni-fold	−7.21	−8.94 [6], −7.27[7]		Ni-fold	−7.96
  H	Ni-fold	−2.78	−2.41[6], −2.36[7]		Ni-fold	−3.02
  DFT methods: Gaussian 09W code, GGA-PBE[6]; ADF-BAND code, GGA-RPBE[7]

  Figure 3

  

  Figure 3.  (a) Differential charge density, and (b) projected density of states (pDOS) for CH on Ni₁₃ and Ni₁₃-ZrO₂(111)

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  2.1.1   Structures and energies of all adsorbed species

  As shown in Figure 2 and Table 1, CH₄ is weakly adsorbed at Ni-top of Ni₁₃ and Ni₁₃-ZrO₂(111) with similar adsorption energies of 0.04 and −0.02 eV, respectively. The physisorption nature of CH₄ arises from the van der Waals interaction between CH₄ and catalyst. The calculated CH₄ adsorption energy is in agreement with the results of An et al. (−0.01 eV) ^[43], despite that Roy and co-workers gave a more negative value (−0.41 eV)^[6].

  The configurations for CH₃, CH₂, CH, C and H adsorption on Ni₁₃-ZrO₂(111) are quite similar to those on Ni₁₃. CH₃ adsorbed at the Ni-bridge site of Ni₁₃-ZrO₂(111) is more stable than at Ni₁₃; notably, the calculated CH₃ adsorption energy (−2.46 eV) in this work is similar to previous results (−2.37 eV), proving the credibility of current calculations^[6]. CH₂, CH, C and H prefer to adsorb at Ni-fold sites (Table 1), and they give higher adsorption energy on Ni₁₃-ZrO₂(111) than on Ni₁₃. Moreover, the calculated adsorption energies of CH₂ and CH (−4.76 and −7.00 eV) on Ni₁₃-ZrO₂(111) are also consistent with the reported values (−4.85 and −6.71 eV) on Ni₄ by Roy et al. (Table 1)^[6]. But the C is strongly adsorbed in four-fold hollow site with adsorption energy of −8.94 eV ^[6] than in three-fold hollow site on Ni₁₃-ZrO₂(111) (−7.96 eV), thus signifying that C atom tends to satisfy its valence. It should be noticed that the adsorption energies of CH₂ (−3.76 eV), CH (−6.43 eV), C (−7.27 eV) and H (−2.36 eV) on Ni(100) obtained by Li et al.^[7] are different to our results (−4.76, −7.00, −7.96 and −3.02 eV) on Ni₁₃-ZrO₂(111). This may be due to the use of different functional.^[7]

  2.1.2   Stabilizing effect of ZrO₂ support on all adsorbed species

  Despite the similarity in adsorption configuration and site, the adsorption strength of all these species are stronger on Ni₁₃-ZrO₂(111) than on Ni₁₃, possibly due to the existence of ZrO₂ support that modifies the electronic environment of Ni₁₃. For example, for CH adsorption, as shown in Figure 3(a), the electron accepting behavior of C and charge loss behavior of Ni occur in the yellow areas and in the scattered blue areas, respectively. An accumulation of electron density is observed on the C atom, whereas for Ni atoms bonding to C atom, the electron density is decreased. Thus, the electron transfer between Ni→C turns the chemisorbed state of free CH_x^[44].

  As shown in Figure 3(b), with the addition of ZrO₂ support, C 1s and C 2p orbitals are shifted to higher value, while the Ni 3d orbital gives an opposite result. This leads to a larger overlap between C 2p and Ni 3d as well as a stronger interaction between Ni and C atoms. Therefore, a strong adsorption of CH on Ni₁₃-ZrO₂(111) is observed. Similar result was also observed by Li et al.^[7]: the adsorption strength of C on various Ni surfaces dependents on the mixing between C 2p and Ni 3d orbitals. Furthermore, the more downshift the Ni 3d orbital is, the more stable adsorption of CH_x is^[34].

  In addition, as shown in Figure 2, C−H bond distance for CH₄ (1.104 Å), CH₃ (1.143 Å), CH₂ (1.189 Å) and CH (1.108 Å) are significantly enlarged on Ni₁₃-ZrO₂(111), compared to that on Ni₁₃ (1.089, 1.107, 1.107 and 1.107 Å, respectively). This means that the cleavage of C−H bonds in CH_x is easier on Ni₁₃-ZrO₂(111).

  2.2   CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111)

  The corresponding energies of various elementary steps for CH₄ dissociation are listed in Table 2. Previously reported results on Ni(100) and Ni₄ are also given in Table 2 for comparison. The energy profile and the main configurations for the initial state (ISs), transition state (TSs) and final states (FSs) on Ni₁₃ and Ni₁₃-ZrO₂(111) are displayed in Figure 4(a) and 4(b), respectively. The values for C₂ formation and C elimination are calculated in Figure 5.

  Table 2

  

  Table 2.  Activation energies the reaction energies the C−H bonds length of ISs and TSs (d_C–H/Å) and H displacements (Å) involved in CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111)

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  Reaction		Our results							Previous results
  		Ea/eV	ΔE/eV	v/cm−1	dC–H ISs/Å	dC–H TSs/Å	H displacements/Å		Ea/eV	ΔE/eV
  		Ni13							Ni4[6]	Ni(100)[7]
  CH4→CH3+H	R1-1	0.61	−0.50	932 i	1.089	1.561	0.472		1.23[7]
  CH3→CH2+H	R1-2	0.46	−0.15	416 i	1.107	2.337	1.230		0.84[6], 0.62[7]	−1.41[6]
  CH2→CH+H	R1-3	0.48	−0.22	625 i	1.107	1.795	0.688		0.33[6], 0.22[7]	−4.40[6]
  CH→C+H	R1-4	0.70	−0.07	747 i	1.107	1.479	0.372		1.37[6], 0.64[7]	−5.96[6]
  C+C→C2	R1-5	3.80	0.62	524 i
  	Ni13-ZrO2(111)
  CH4→CH3+H	R2-1	0.14	−0.66	59 i	1.104	1.122	0.018
  CH3→CH2+H	R2-2	0.35	−0.47	760 i	1.143	1.662	0.519
  CH2→CH+H	R2-3	0.14	−0.53	488 i	1.189	1.782	0.593
  CH→C+H	R2-4	0.40	−0.30	657 i	1.108	1.389	0.281
  C+C→C2	R2-5	1.90	1.87	170 i

  Figure 4

  

  Figure 4.  Structures of the ISs, TSs and FSs relevant to CH₄ dissociation on (a) Ni₁₃ and (b) Ni₁₃-ZrO₂(111) Bond lengths are in Å see Figure 2 for color coding

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  Figure 5

  

  Figure 5.  Potential energy profile of C₂ formations and C eliminations on (a) Ni₁₃ and (b) Ni₁₃-ZrO₂(111) together with the corresponding structures

  Bond lengths are in Å see Figure 2 for color coding

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  2.2.1   Effect of ZrO₂ support on activating the C−H bonds

  We mainly focus on the E_a , ΔE and the C−H bonds length of ISs and TSs. The activation energies for the dehydrogenation of CH_x (x=4−1) on Ni₁₃-ZrO₂(111) are lower than on Ni₁₃, indicating that the dehydrogenation of CH_x is kinetically more favorable on the former than on the latter.

  As shown in Table 2, the calculated activation energy ( E_a , 0.61 eV) on Ni₁₃ is lower than the reported result (1.23 eV) by Li et al.^[7] on Ni(100), whereas that for CH₃ (0.46 eV) and CH₂ (0.48 eV) dehydrogenations are similar to the obtained values by Li et al. (0.62 and 0.22 eV)^[7] and Roy et al. (0.84 and 0.33 eV)^[6]. For CH dehydrogenation, the activation energy on Ni₁₃ (0.70 eV) and on Ni(100) (0.64 eV) are similar, but both of them are much lower than on Ni₄ cluster (1.37 eV). It should be noticed that the dissociations of CH_x (x=4−1) on Ni₁₃-ZrO₂(111) are all exothermic, with more negative ΔE than Ni₁₃.

  For CH₄→CH₃+H on Ni₁₃-ZrO₂(111), it shows a low E_a of 0.14 eV, with exothermic by −0.66 eV; the C–H bond is increased from 1.104 Å in CH₄ to 1.122 Å in TS2-1 . After a rearrangement between H and CH₃ fragments, the structure of TS2-1 is obtained. Similar procedure is used for TS1-1 , despite that the E_a is increased to 0.61 eV, with a weak exothermic by −0.50 eV on Ni₁₃. The C–H distance of TS1-1 is enlarged from 1.089 Å to 1.561 Å. Since the dissociation of C−H bond is more exothermic on Ni₁₃-ZrO₂(111) (TS2-1), it leads to the reduction of E_a^[45]. Accordingly, the ZrO₂ support facilitates CH₄→CH₃+H, due to the strong interaction between Ni and ZrO₂, being line with previous investigation^[17].

  Similar to CH₄→CH₃+H, stepwise dehydrogenations of CH₃ to CH₂, CH and C show low E_a values of 0.35, 0.14 and 0.40 eV for TS2-2 , TS2-3 and TS2-4 , with exothermic by −0.47, −0.53 and −0.30 eV, respectively, on Ni₁₃-ZrO₂(111). The displacements between the detaching H and the remaining fragment are 0.519, 0.593 and 0.281 Å, respectively, as shown in Table 2. However, without ZrO₂, the activation energy of TS1-2 , TS1-3 and TS1-4 is elevated to 0.46, 0.48 and 0.70 eV, along with the reduction of exothermic energy to −0.15, −0.22 and −0.07 eV, respectively. Meanwhile, the displacements between H and remaining fragments are also increased to 1.230, 0.688 and 0.372 Å, respectively (Table 2). Thus, the ZrO₂ support has a significant influence on CH₄ dissociation. This observation is consistent with the previous study^[12] where the ZrO₂ support can modulate the electronic environment of Ni and promote the dissociation of C−H bond.

  2.2.2   Effect of ZrO₂ support on the activity of CH₄ dissociation

  Based on E_a and ΔE of CH₄ stepwise dehydrogenations to C, the overall activation energies of CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111) are calculated to be 0.61 and 0.14 eV, respectively, as plotted in Figure 4(a) and 4(b). This gives additional evidence that ZrO₂ support effectively promotes CH₄ dissociation. Similar situation is also observed in previous reports^[12,19]. As stated by Han et al.^[13], this is because the support can tune the adsorption behaviors, decrease the activation barrier and even adjust pathways of dry reforming of methane by modifying the Ni catalyst.

  2.2.3   C nucleation and C elimination

  Once C is formed, C nucleation may lead to coke deposition. Interestingly, as shown in Figure 5, C+H→CH, as the reverse steps of CH scission, is preferred to C+C→C₂ on Ni₁₃ and Ni₁₃-ZrO₂(111), suggesting that carbon deposition is unlikely to occur on both catalyst surfaces. Furthermore, the activation energy ( E_a ) of 1.90 eV for C+C→C₂ on Ni₁₃-ZrO₂(111) is similar to that of C₂ dimmer formation (1.89 eV)^[46]. Therefore, the undesired coke deposition may be observed only when the residual C can not be timely removed from the catalyst surface^[47]. Thus, both the highly dispersed Ni₁₃ and the superior electronic donor ability of ZrO₂ support suppress the coke deposition. This is because C nucleation is inferior to C elimination.

  2.3   Role of ZrO₂ support in stabilizing Ni–C bond and activating C−H bond

  The most important steps in CH₄ dissociation are adsorption and dissociation, which leads to the formation of Ni–C bond and the dissociation of C−H bond, respectively. To further explore the effect of ZrO₂ support on CH₄ decomposition, the pDOS of CH₃ on Ni₁₃ and Ni₁₃-ZrO₂(111), as an example, is calculated in Figure 6. Accordingly, the role of ZrO₂ support in CH₄ dissociation is obtained.

  The result of electronic analysis indicates that the presence of ZrO₂ support broadens the d-band electrons at C of CH₃ bonding on Ni (Figure 6(a)). This causes a larger overlap between C 2p and Ni 3d, i.e. and a stronger interaction between Ni and C (Figure 6(b)), thereby leading to more stable adsorptions of CH_x (x=3−1) and higher exothermic energy for CH₄ dehydrogenation. As stated by Boukelkoul et al.^[48], CH₄ dehydrogenation on W-Cu(100) is exothermic because W-doping stabilizes better for all species. Ou et al.^[44] also proved that the adsorption state becomes highly stable, when more electrons are transferred from Ni to C of CH_x .

  Besides, the charge distribution on C and H is influenced due to the enhancement of electron transfer Ni→C on Ni₁₃-ZrO₂(111), whereas that of H→C is reduced. This causes a weaker C 2p −H 1s hybridization than the situation on Ni₁₃, as seen in Figure 6(c), thereby decreasing the E_a for C−H bond breaking. Similar results^[44] are observed on Co/Ni, where the low activation energy for C−H bond dissociation in CH₄ dehydrogenation resulted from the abundant d-band electrons on Co/Ni catalyst.

  As a result, the overall activation energy for CH₄ dissociation drastically decreases with the addition of ZrO₂ support. This is because ZrO₂ support can act as the d-band electron reservoir at Ni₁₃ that promotes the activation of C−H bond in CH₄ dehydrogenation reactions. As stated by Ou et al.^[44], introduction of Co into Ni leaded to the downshift of d-band center of Co/Ni that increased the E_ads of the CH_x , but decreased the E_a of C−H bond breakage. These results are further supported by the work Li et al.^[8]; the strong C−Ni chemical bonding can electronically adjust the ability of Ni atoms in adsorbing and dissociating CH_x (x=4−1) species.

  Figure 6

  

  Figure 6.  Partial density of states for CH₃ adsorbed on Ni₁₃ and Ni₁₃-ZrO₂(111) for the role of the support ZrO₂: (a) broadening d-band, (b) stabilizing Ni−C bond and (c) activating C−H bond

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  3.   Conclusions

  DFT calculations are used to investigate the dehydrogenation mechanism of CH₄ on Ni₁₃ and Ni₁₃-ZrO₂(111). The results show that ZrO₂ support has a significant influence on promoting CH₄ dissociation.

  The E_ads, E_a, ΔE and the displacements of the detaching H are obtained. Although the configuration and adsorption site are similar, the adsorptions of all species involving in CH₄ dissociation are stronger on Ni₁₃-ZrO₂(111) than on Ni₁₃. This is because the ZrO₂ support remarkably modifies the electronic environment of Ni₁₃. Besides, introduction of the ZrO₂ support can obviously decrease E_a and simultaneously increase ΔE for all the elementary steps in CH₄ dissociation. In particular, the E_a for conversion of CH₄ to CH₃ is reduced from 0.61 eV on Ni₁₃ to 0.14 eV on Ni₁₃-ZrO₂(111). This results in the decrease of overall activation energy for CH₄ dissociation on Ni₁₃-ZrO₂(111) than on Ni₁₃. Thus, the ZrO₂ modified Ni₁₃ can improve the activity towards CH₄ dissociation, compared with the pure Ni₁₃.

  Moreover, the C−H bonds distance in the ISs of CH_x (x=4−1) dissociation is significantly enlarged when the ZrO₂ support is added. This implies that the cleavage of C−H bonds of CH_x (x=4−1) becomes easier. Based on TSs , the stepwise detachment of H from CH₄ to CH₃, CH₂, CH and C needs to shift smaller distances to reach the final state. This also benefits to decrease the activation energy ( E_a ) of C−H bond dissociation.

  In viewpoint of the electronic environment, the ZrO₂ support can broaden d-band electrons at C atom bonding to Ni that enhances the electron transfer Ni→C, but reduces that of H→C. This causes a stronger interaction between Ni and C, along with the weakness of C−H polar bonds, thereby leading to a strong adsorption of CH_x (x=3−1) and a low E_a for C−H bond dissociation. Hence, the presence of ZrO₂ support can stabilize the Ni–C bond and activate the C−H bond. The mechanistic investigation of CH₄ dehydrogenation over Ni₁₃ and Ni₁₃-ZrO₂(111) may provide an approach to reveal the role of ZrO₂ support and design new Ni-based catalysts for CH₄ dissociation.

  
  
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  Figure FIG. 1528. 

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  Figure 1  Top view correspond to Ni₁₃ and Ni₁₃-ZrO₂(111) morphologies, respectively

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  Figure 2  Most stable configurations of adsorbed species involved in CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111), respectivelyThe blue, gray, red, white and turquoise balls represent Ni, C, O, H and Zr atoms, respectively Bond length are in Å

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  Figure 3  (a) Differential charge density, and (b) projected density of states (pDOS) for CH on Ni₁₃ and Ni₁₃-ZrO₂(111)

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  Figure 4  Structures of the ISs, TSs and FSs relevant to CH₄ dissociation on (a) Ni₁₃ and (b) Ni₁₃-ZrO₂(111) Bond lengths are in Å see Figure 2 for color coding

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  Figure 5  Potential energy profile of C₂ formations and C eliminations on (a) Ni₁₃ and (b) Ni₁₃-ZrO₂(111) together with the corresponding structures

  Bond lengths are in Å see Figure 2 for color coding

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  Figure 6  Partial density of states for CH₃ adsorbed on Ni₁₃ and Ni₁₃-ZrO₂(111) for the role of the support ZrO₂: (a) broadening d-band, (b) stabilizing Ni−C bond and (c) activating C−H bond

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  Table 1.  Adsorption sites and adsorption energies (E_ads) of the stable configurations for the adsorbed species involved in CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111), respectively

  Species	Ni13		Previous results Ni4[6], Ni(100)[7]		Ni13-ZrO2(111)
  	site	Eads/eV	Eads/eV		site	Eads/eV
  CH4	Ni-top	0.04	−0.41[6]		Ni-top	−0.02
  CH3	Ni-bridge	−2.22	−2.37[6]		Ni-bridge	−2.46
  CH2	Ni-fold	−4.36	−4.85[6], −3.76[7]		Ni-fold	−4.76
  CH	Ni-fold	−6.40	−6.71[6], −6.43[7]		Ni-fold	−7.00
  C	Ni-fold	−7.21	−8.94 [6], −7.27[7]		Ni-fold	−7.96
  H	Ni-fold	−2.78	−2.41[6], −2.36[7]		Ni-fold	−3.02
  DFT methods: Gaussian 09W code, GGA-PBE[6]; ADF-BAND code, GGA-RPBE[7]

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  Table 2.  Activation energies the reaction energies the C−H bonds length of ISs and TSs (d_C–H/Å) and H displacements (Å) involved in CH₄ dissociation on Ni₁₃ and Ni₁₃-ZrO₂(111)

  Reaction		Our results							Previous results
  		Ea/eV	ΔE/eV	v/cm−1	dC–H ISs/Å	dC–H TSs/Å	H displacements/Å		Ea/eV	ΔE/eV
  		Ni13							Ni4[6]	Ni(100)[7]
  CH4→CH3+H	R1-1	0.61	−0.50	932 i	1.089	1.561	0.472		1.23[7]
  CH3→CH2+H	R1-2	0.46	−0.15	416 i	1.107	2.337	1.230		0.84[6], 0.62[7]	−1.41[6]
  CH2→CH+H	R1-3	0.48	−0.22	625 i	1.107	1.795	0.688		0.33[6], 0.22[7]	−4.40[6]
  CH→C+H	R1-4	0.70	−0.07	747 i	1.107	1.479	0.372		1.37[6], 0.64[7]	−5.96[6]
  C+C→C2	R1-5	3.80	0.62	524 i
  	Ni13-ZrO2(111)
  CH4→CH3+H	R2-1	0.14	−0.66	59 i	1.104	1.122	0.018
  CH3→CH2+H	R2-2	0.35	−0.47	760 i	1.143	1.662	0.519
  CH2→CH+H	R2-3	0.14	−0.53	488 i	1.189	1.782	0.593
  CH→C+H	R2-4	0.40	−0.30	657 i	1.108	1.389	0.281
  C+C→C2	R2-5	1.90	1.87	170 i

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