DFT studies of Ni cluster on graphene surface: effect of CO₂ activation

Abstract

CO₂ capture, storage, sequestration (CCS), and utilization (CCU) are regarded as the most effective way to slow the pace of global warming. In our present work, the structural stability and catalytic properties for adsorbing CO₂ on the surface of isolated Ni clusters and 5–8–5 monovacancy graphene (MGr) supported Ni clusters have been investigated using density functional theory. The results show that, with the increasing of atomic number, the structure of isolated Ni clusters tended to be stable and the structural parameters approached to that of metal crystal. In addition, when Ni clusters deposited on the MGr surface, the Ni–Ni bond generally elongated, indicating activation of the isolated metal clusters by graphene. Adsorption energies of CO₂ onto Ni₄ cluster and MGr were −1.80 and −1.35 eV, respectively, while the value reached −2.72 eV when CO₂ adsorbed on Ni₄ cluster modified with MGr (Ni_x/MGr). The phenomenon indicates that the adsorption capacity of CO₂ were significantly improved by depositing Ni clusters onto MGr surface and the system tended to be more stable. According to the analyses of Mulliken charge, electrostatic potential (EP) and partial density of states (PDOS), more electrons transferred from Ni_x cluster to the region of CO₂ and MGr when CO₂ adsorbed on Ni_x/MGr. The mechanism was proposed for CO₂ adsorption on Ni_x/MGr at the molecular level. It is of great significance to devise high activity catalyst of CO₂ storage and hydrocarbon production from CO₂.

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I Introduction

Due to large number of burning fossil fuels such as oil, coal, etc., or deforestation, large amounts of carbon dioxide have been produced, causing a global greenhouse effect. Carbon capture, storage, sequestration and utilization are regarded as the most effective measure to reduce CO₂ in atmosphere, or at least to control greenhouse effect.^1–5 Among them, adsorption technologies using metal oxide, zeolite, or carbon materials like carbon nanotubes (CNTs) and graphene as a candidate of adsorbent beds have been experimentally and theoretically investigated.⁶

Additionally, other studies involve using carbon dioxide in a certain reaction,^7–10 for example, hydrocarbon production from CO₂. Hydrocarbons can be used as fuel components and this approach will help relieve energy crisis. The dominating mechanism for this process is the Sabatier reaction:¹¹ CO₂ + 4H = CH₄ + 2H₂O (−252 kJ mol⁻¹). The first step of this reaction is to adsorb and activate CO₂. However, as a linear molecule, CO₂ has no polarity and is hard to activate due to its high thermodynamic stability. If the linear structure of CO₂ transfers into a bent structure, the activation energy barrier will be significantly reduced.¹² It is a generally accepted fact that CO₂ activation on transition metal surfaces is structure sensitive, that is, different surface structures have different activity capacities.^13–15 The catalytic activities of CO₂ on the surface of Co, Ni,⁸ Cu,¹⁶ Pt,¹⁷ Pd,¹⁸ Fe,¹⁹ CeO₂,¹² Ni₄/γ-Al₂O₃ (ref. 20) and Pd/DOH zeolite²¹ have been explored in recent years, and the results show that the CO₂ activation energy can be greatly decreased by lengthening the C–O bond, and increasing the bending degree of molecules, owing to a large number of electron transfer from CO₂ molecular to the metal atom.^22,23 It has been verified that the reaction of CO₂ on Ni also involves the formation of the bent intermediate CO₂^δ−, which can greatly reduce the reaction energy barrier.²⁴ So metal Ni is the most widely used in the study of CO₂ activation mechanism.

Recently, metal-decorated carbon materials have attracted more attention as they exhibit excellent stability and durability under harsh conditions.^25–27 Johll²⁸ explored Fe, Co, and Ni adatoms and dimers adsorbed on graphene and the results showed adatoms bonding weakly to graphene with binding energies ranging from 0.2 to 1.4 eV. At the same time, the computational insight into the activity of transition metal clusters has been hotly investigated. Deshpande⁹ carried out a stable seven-atom pentagonal bipyramidal Cu cluster acting as a biomimetic CO₂ hydration catalyst and the result exhibited the metal clusters as a good catalyst for CO₂ capture. Pacchioni²⁹ investigated electronic interactions and charge transfer of metal atoms and clusters on oxide surfaces. Additionally, Sun⁸ carried out experimental and theoretical investigations on the interaction between palladium nanoparticles/clusters and functionalized carbon nanotubes for Heck synthesis. The results reveal the defects on carbon material promoted the redistribution of electrons, enhanced the metal–C interaction, and further decreased the size of metal nanoparticle. Hahn³⁰ considered the effects of CO₂ adsorption on CeO₂ (111) surface by depositing Ni cluster.

However, up to now the investigation of CO₂ adsorption on MGr surface deposited with Ni clusters for carbon utilization application has been few. In our work, monolayer monovacancy grapheme was selected mainly because that defect on graphene could reallocate electrons between the metal and the C atom of CO₂, thereby promoting interaction of metal and graphene. And grapheme is comprised of benzene rings, a characteristic beneficial for electron transfer on the surface. First, the activities and stabilities of isolated Ni_x (x = 1, 2, 3, 4, 5, 6, 7, 9, 10) cluster in the gas phase were taken into account and identified. Then, the adsorption behavior of Ni clusters on MGr surface and CO₂ on the surfaces of Ni₄ cluster, MGr, and Ni₄/MGr were simulated and analyzed in terms of energetic (binding energy), structural (Ni–Ni bond length and gyration radius), and electronic properties (Mulliken charge, EP and PDOS). Finally, the adsorption mechanism of CO₂ activated on Ni₄/MGr was proposed and a systematic comparison of CO₂ activation capacity on isolated Ni clusters, pristine MGr, and Ni₄/MGr were listed, which aimed to illuminate the influence of CO₂ adsorption capacity over supported metal Ni clusters on the surface of monolayer graphene at the molecule level based on the density functional theory (DFT). Consequently, the work provides fundamental insight for CO₂ utilization by depositing Ni clusters onto MGr, and potentially provides the synthesis of new carbon-based materials.

II Theoretical methods

All the calculations were carried out in DMol³ package of Materials Studio^31,32 based on density functional theory (DFT). Generalized gradient approximation (GGA)³³ with Perdew–Burke–Ernzerhof (PBE) functional was used to model the electron exchange and correlation interaction. All electron double numerical atomic orbitals augmented by p- and d-polarization functions (DNP)^34,35 were set as the basis set in the simulation of isolate Ni clusters, and orbital cutoff quality was set at fine. The thermal smearing level was set at 0.005 to improve the convergence, and basis set superposition error (BSSE) was not taken into account, as the numerical basis sets implemented in DMol³ minimized or even eliminated basis set superposition error.³⁶ Spin-polarization was considered in all calculations, the ground state of Ni cluster structures was obtained from the minimum in the total energy and preferred spin multiplicity, and the atomic positions of all models were allowed to relax in all calculations.

Simulation of isolate Ni clusters in the gas phase consisting of one to ten atoms was investigated first. The energy of formation E_form of that Ni clusters was calculated according to eqn (1):

E_form = (E_cluster − n_NiE_Ni,g)/n_Ni (1)

where E_cluster and E_Ni,g correspond to the total energy of the Ni cluster and the Ni atom in the gas phase (triplet), n_Ni defines the number of Ni atoms in the cluster, respectively. The process is an exothermic reaction if E_form is negative, and a higher negative value of E_form corresponds to a more stable structure.

The binding energy E_B of Ni clusters adsorbed on MGr has been calculated in analogy to the formation energy according to eqn (2):

E_B = [E_slab+Nix − (n_NiE_Ni,g + E_slab)]/n_Ni (2)

where E_slab and E_slab+Nix refer to the total energy of the clean MGr surface and the total energy of the MGr slab decorated with Ni_x clusters, respectively.

Simulation of MGr was implemented in a periodically repeated box of 12.3 × 12.3 × 20 Å. One layer of 5 × 5 × 1 periodic super unit cell was employed to avoid interaction between periodic unit cells. Monovacancy graphene is defined as MGr in this paper, which is a vacancy structure of one C-atom missing in the perfect grapheme and leaving each of three neighboring C-atoms with sp² dangling bonds. Plane-wave electronic density functional theory with long range dispersion interaction corrections DFT-D^37–39 was considered to balance computational efficiency and accuracy, and the lattice parameter of graphene was optimized to be 4.12 Å, which was in well agreement with a previous report⁴⁰ and theoretical calculations.⁴¹ All calculations consisting of graphene was performed with periodic boundary conditions, and a vacuum region of 20 Å between periodic basal planes was introduced along the [111] direction for avoiding interactions with adjacent plane.

The adsorption behavior of CO₂ onto the surface of respective substrate was simulated, and the adsorption energy of CO₂ (E_ads) was calculated according to eqn (3):

E_ads = E_slab*+CO2 − E_slab* − E_CO2 (3)

where, E_slab* corresponds to respective slab, namely Ni_x clusters, stoichiometric MGr, and Ni_x/MGr.

III Results discussion

A. Isolated Ni_x clusters

Isolated Ni_x clusters were optimized (Fig. 1) firstly from two atoms to ten atoms in gas phase. The three-dimensional (3D) structure of Ni cluster is more stable than the flat structure,⁴² thus 3D models as small metal clusters were chosen for the following research. Total energy (E_total), d_Ni–Ni, atomization energies (E_A) and formation energies (E_form) were calculated, data shown in Table 1.

Fig. 1 The optimization structures of Ni_x clusters.

Table 1 Calculated total energies (E_total), atomization energies (E_A), formation energies (E_form), vibrational frequencies and intensities of Ni_x cluster modes^a,b

Molecule	m	Etotal/(a.u.)	dNi–Ni/nm	EA/(eV)	Eform/(eV)
a m is the number of Ni atom in the cluster modes.b EA = [E(Nix) − xE(Ni)], Eform = EA/x.
CO2	—	−188.48	—	—	—
Ni1	—	−1508.08	—	—	—
Ni2	1	−3016.26	2.12	−2.70	−1.35
Ni3	3	−4524.42	2.24	−5.08	−1.69
Ni4	4	−6032.60	2.31	−7.87	−1.97
Ni5	5	−7540.80	2.34	−10.58	−2.12
Ni6	6	−9049.00	2.35	−13.80	−2.30
Ni7	7	−10 557.21	2.38	−17.23	−2.46
Ni9	9	−13 573.64	2.37	−24.52	−2.72
Ni10	10	−15 081.82	2.38	−27.66	−2.77

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The results indicate that total energies E_total and atomization energies E_A decreased with the increasing number of Ni atoms. The formation energies E_form ranged from −1.35 eV to −2.72 eV with Ni clusters getting larger, which agreed with the previous result^43,44 that metal clusters became more stable with increasing Ni atoms, while their structural parameters approaching that of metal crystals. The d_Ni–Ni increased and E_form decreased with increasing Ni atom numbers, as described in Fig. 2. For the Ni₃ cluster, the equilateral triangle with bond length of 2.24 Å was the most stable configuration, with atomization energy E_A = −5.08 eV and formation energy E_form = −1.69 eV. Our results are in agreement with that of Park's experimental results that the Ni₃ cluster preferred to choose triangle as the ground state structure.⁴⁵ These results are also consistent with ref. 42 and 46–48 where the atomization energy ranged from −3.4 eV to −5.4 eV, but slightly different from those references in an allowable deviation that generating different functions and parameters. For Ni₅, a nearly perfect trigonal bipyramid was found, and the E_form = 2.12 eV agreed with the previous report of 2.40 eV.⁴⁹ Additionally, the approximate value of formation energy for Ni₉ and Ni₁₀ showed the tendency of formation energy slowing down and stabilizing gradually, indicating the structure parameters of Ni clusters turning to that of metal crystal.

Fig. 2 Average Ni–Ni bond length d_Ni–Ni (solid symbols) and formation energy E_form (empty symbols) of isolated Ni clusters (gas phase).

A similar trend for the formation energy was observed for the average Ni–Ni bond length (d_Ni–Ni). It increased from 2.12 Å in the Ni dimer to 2.38 Å for Ni₁₀, which was consistent with the previously calculation studies by using DFT^30,42,48 where the Ni–Ni bond elongated from 2.06 to 2.10 Å in the Ni dimer to more than 2.40 Å in a Ni cluster with 15 atoms. The amplification of d_Ni–Ni curve became smooth and steady up to seven Ni atoms, and the variation tendency of bond length was in good agreement with experimental measurement of 2.15 Å.⁵⁰

B. Ni_x cluster adsorbed on MGr: geometry and stability

Geometry and stable configurations of Ni_x clusters (x = 1–7, 9, 10) on MGr are showed in Fig. 3. It is found that the Ni clusters are out of shape and Ni–C bond formed in the interface of Ni cluster and MGr. For the system of one Ni atom deposited on MGr surface, the elevation (h) out of the graphene sheet is 1.50 Å, and the binding energy is 0.73 eV, whose structure is given in ESI (Fig. S1†) and those results are well in agreement with the previous report.⁵¹

Fig. 3 Geometry and stable configurations of Ni_x cluster (x = 2–7, 9, 10) adsorbed on MGr.

The structure of Ni cluster with no more than ten atoms deposited on MGr surface was optimized, and every Ni atom in the triplet state for all configurations, the curve of binding energy is shown in Fig. 4. A lower binding energy corresponds to a more stable system. The trend of stability for Ni clusters deposited on MGr is similar to isolated Ni clusters, in which the binding energy decreases with the number of Ni atoms. E_B increases quickly when the value of n is no more than 4 and then it becomes stable gradually, which indicates the system of Ni_x/MGr tended to be stable. The binding energies E_B changed from −0.73 eV to −3.59 eV, referring to chemisorption.

Fig. 4 Binding energy E_B (eV) of Ni cluster adsorb on MGr as a function of the number of Ni atoms in the cluster for 3D configuration.

Structural changes. The interaction of Ni clusters with the surface of MGr leads to small loosing of the cluster structure. Fig. 5 shows average Ni–Ni bond length d_Ni–Ni of 3D isolated Ni cluster and Ni cluster adsorbed on MGr. It can be seen that the average bond length of Ni–Ni in Ni clusters supported on MGr was slightly longer than that of isolated Ni clusters. The bond length of Ni–Ni in isolated Ni clusters increased with the number of Ni atoms, while bond length of Ni–Ni reduced firstly and then increased when Ni clusters supported on MGr. For a Ni₂ cluster adsorbed on MGr, the Ni–Ni bond length was significantly extended, and the relative change value was the greatest compared with the isolated Ni cluster in the gas phase. For the number of Ni atoms from 2 to 3, the relative variable quantity of d_Ni–Ni was becoming smaller, indicating the influence of MGr grows gradually weak. When the number of Ni atoms was more than 3, the relative variable quantity of d_Ni–Ni was smaller and the bond length of Ni cluster on MGr slightly elongated compared with isolated Ni cluster, indicating there was a little influence of MGr on Ni clusters. These show that the binding capacity of Ni clusters accessibility was facilitated by MGr compared with isolated Ni clusters, which possibly has a positive impact of activated CO₂ molecule on grapheme in the hydrogen production reaction.

Fig. 5 Average Ni–Ni bond length d_Ni–Ni of isolated Ni cluster (solid circle symbols) and Ni cluster adsorbed on MGr (empty circle symbols).

A frequently used parameter to classify shapes is the radius of gyration (R_g), and the morphology of a particular Ni cluster at a given time can be defined as the equation:³⁰

where r_k was the position of atom Ni_k, and r̄ was the mean position of the Ni cluster, N was the number of Ni atoms.

Radius of gyration refers to the distribution of the components of an object around an axis. In terms of mass moment of inertia, it is the perpendicular distance from the axis of rotation to a point mass that gives an equivalent inertia to the original object(s). The gyration radius were calculated and tabulated in Table 2, using linear regression (QSAR) procedures based on the linear combination of atomic orbital and molecular orbital method. A smaller radius of gyration indicates a more compact structure of the cluster. The linear relationship of their normalized radius of gyration ³⁰ and binding energy (E_B) both as pristine Ni_x and adsorbed on MGr is displayed in Fig. 6.

Table 2 Formation energy E_form of isolated Ni cluster, binding energy E_B of Ni cluster adsorbed on monovacancy graphene, average Ni–Ni bond length d_Ni–Ni and radius of gyration R_g of Ni cluster with varying number of atoms

Configuration	EF (ev)	EB (ev)	dNi–Ni (Å)		Rg (Å)
			Gas phase	On MGr	Gas phase	On MGr
1Ni	—	−0.73	—	—	—	—
2Ni	−1.35	−1.52	2.12	2.34	1.06	1.17
3Ni	−1.69	−1.73	2.24	2.33	1.29	1.34
4Ni	−1.97	−2.68	2.31	2.36	1.42	1.46
5Ni	−2.12	−2.99	2.34	2.38	1.60	1.62
6Ni	−2.30	−3.07	2.35	2.38	1.66	1.68
7Ni	−2.46	−3.12	2.38	2.40	1.84	1.88
9Ni	−2.72	−3.24	2.37	2.41	2.01	2.08
10Ni	−2.72	−3.59	2.38	2.43	2.13	2.19

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Fig. 6 The linear regression of and binding energy (E_B).

The result indicates that the binding energy displays a linear trend with increasing . According to the equation: , the value of intercept at the hypothetical limit of indicates the maximum binding energy of Ni clusters deposited on the surface of MGr, E_B,0 = −4.63 eV, the slope k = 5.43 eV Å⁻¹, and Pearson's r² = 93.3%. Additionally, the thermodynamically unfavorable condition E_B ≥ 0 eV, in which Ni cluster cannot be adsorbed, can be estimated by the maximal normalized radius of gyration .

Electronic property. Analysis of the total density of states (DOS) of Ni and C element in Ni_x/MGr systems is displayed in Fig. 7, the DOS of C orbitals has little transformation with the size of the cluster in Ni_x/MGr system. However, the area and height of PDOS for Ni orbitals increased with the number of Ni atom, revealing that the electrical density increased with the number of Ni atoms. The asymmetry behavior of Ni orbitals near the Fermi level represents a magnetic and a metallic character of Ni_x/MGr system.³⁰ It also shows that the occupation of Ni 3d-orbital increased by forming a bundle o states in between the valence band of MGr and the unoccupied C states with the number of Ni atoms, which basically illustrates the squeezed and deformed electron cloud. These states can be assigned to d-type orbitals of Ni, possibly leading to a decrease in the band gap. Additionally, the intersection region between C orbital and Ni orbital suggests that part of C atoms in MGr or part of Ni atoms in cluster is activated, resulting in forming C–Ni bonds. Fig. S2 in ESI† indicated that the content of Ni atoms had an obvious influence on the PDOS of Ni atom.

Fig. 7 DOS of Ni atom and C atom in (a) three, (b) five, (c) seven and (d) nine Ni atoms adsorbed on MGr. The DOS is projected on the orbitals of C (blue) and Ni (red) atoms.

C. CO₂ adsorption on Ni/MGr systems

CO₂ adsorption on Ni_x cluster. The adsorption of CO₂ molecules on isolated Ni_x (x = 2, 3, 4, 5, 6, 7, 10) clusters have been optimized in Fig. S3.† The four-atomic Ni cluster is exhibited in Fig. 8(a). It can be seen that the linear CO₂ became a bent structure with an intersection angle of O–C–O 136.26°. The binding energy of CO₂ onto the Ni₄ cluster is −1.80 eV, where one C–O bond is 1.263 Å and the other C–O bond is 1.262 Å, listed in Table 3. Compared with Ni (100) (−1.13 eV),¹³ the binding energy of CO₂ on Ni cluster is lower, indicating the adsorption of CO₂ molecule to be thermodynamically favorable on the surface of Ni clusters.

Fig. 8 Most stable configurations of CO₂ adsorbed on (a) a four-atomic Ni cluster, (b) the clean monovacancy graphene surface and (c) on monovacancy graphene supported Ni. (d)–(f) Correspond profile projections of (a)–(c), respectively. The EP (g–i) of CO₂ shows similar binding mechanisms on the three surfaces. Red lobes indicate electron loss, blue lobes electron excess. The isosurfaces are constructed at 0.0675 e⁻¹ Å⁻³.

Table 3 Binding energy E_B, C–O bond length d_C–O and O–C–O angle α_O–C–C of CO₂ adsorbed on an isolated four-atomic Ni cluster, on MGr and on a graphene deposited Ni₄ cluster

Substrate	EB,CO2 (eV)	dC–O(1) (Å)	dC–O(2) (Å)	αO–C–O (°)
Ni4 cluster	−1.80 eV	1.263	1.262	136.26
MGr	−1.35 eV	1.376	1.377	107.86
Ni4/MGr	−2.72 eV	1.250	1.243	140.31

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CO₂ adsorption on MGr. According to the results of Liu,⁵² the interaction with defective graphene (MGr) surface would yield stronger CO₂-surface interactions compared to perfect graphene or the 5–7–7–5 and 5–5–8 vacancy sites, therefore in the present work the MGr model was implemented in all calculations. Due to the interactions between the adsorbent and adsorbate, the surface carbon atoms of grapheme moved toward the CO₂ molecule, and the C atom of CO₂ roughly located on the top of losing carbon with two O atoms toward to the two C adjacent to the missing C atom [Fig. 8(b and e)]. The binding energy of CO₂ onto the MGr is −1.35 eV, where one C–O bond is 1.376 Å, the other C–O bond is 1.377 Å, and the O–C–O angle is found to be 107.86°. Fig. 8(h) testifies that the electron moved toward the region between the reactive carbon atom of MGr and the central carbon atom of CO₂, as well as the region between the missing C atom of MGr and O atom of CO₂. These regions accumulated electrons indicate the formation of a new C–C bond and two C–O bonds. Besides, the bent structure can transfer electrons well from the vacancy site onto the surface of Gr to CO₂ molecule.

CO₂ adsorption on Ni_x/MGr. For the purpose of further exploring the influence of CO₂ adsorption on MGr surface by deposition of Ni clusters for carbon capture and sequestration applications, CO₂ adsorption on Ni_x/MGr has been investigated in Fig. S4.† It shows that the lineal CO₂ structure turned into a bent form, similar to the adsorption behavior of CO₂ on Ni_x. From Table S1,† it can be seen that when the activation capacity of CO₂ was accessible, the E_B for CO₂ on Ni_x/MGr are lower than Ni_x, indicating that Ni cluster, as a medium, could transfer electrons form CO₂ to MGr, and the adsorption energy of CO₂ was enhanced significantly. On the other hand, CO₂ molecule could change the electron distribution of Ni_x/MGr, and led to the system to be more stable.

CO₂ adsorption on Ni₄/MGr surface is showed in Fig. 8(c and f). Compared with Ni₄ and MGr, the strongest interaction was that of Ni₄/MGr with a binding energy of −2.72 eV (Tables 2 and S1†), where the one C–O bond was elongated to 1.250 Å, the other was elongated to 1.243 Å, and the O–C–O angle was found to be 140.31°. Compared with isolated Ni cluster and original MGr, CO₂ on Ni_x/MGr had the highest absorption energy, indicating the supported Ni clusters could significantly improve the adsorption energy of CO₂ by changing its structure.

D. Electronic structure

Mulliken charge, electrostatic potential and PDOS (Fig. 9 and S5†) of Ni₄ and CO₂ were calculated when CO₂ adsorbed in the stable configurations on the surface of models discussed above. Electron transfer between adsorbate and adsorbent materials by Mulliken charge analysis is listed in Table 4, and electrostatic potential generated by Mulliken charge analysis is showed in Fig. 8(g–i), the isosurfaces were constructed at 0.0675 e⁻¹ Å⁻³. Negative value lobes of electrostatic potential indicate the region of gain electrons, whereas positive value lobes represent lost electrons. As shown in the Fig. 8, the negative charge enriched in the region of O atoms, positive charge enriched in the region of Ni atoms, indicating the C, O and neighboring Ni atoms activated obviously. This leads to forming a higher electron density surrounding CO₂ compared to that of CO₂ in the gas phase, which further indicates that accumulated electrons in these regions can easily help form a new bond of C–Ni or two Ni–O bonds.

Fig. 9 PDOS of CO₂ and Ni₄ on different systems, (a) pure CO₂, (b–d) CO₂ on the Ni₄, MGr, and Ni₄/MGr surface, and (e) isolated Ni cluster, (f–h) Ni₄ on the CO₂–Ni₄, Ni₄/MGr, and CO₂–Ni₄/MGr surface.

Table 4 Mulliken charges of CO₂, Ni₄ and MGr on Ni₄ cluster, MGr and Ni₄/MGr

Atom	Ni4	CO2–Ni4	CO2–MGr	Ni4–MGr	CO2–Ni4/MGr
a Represents the sum of Mulliken atomic charges of CO2 on different models.b Represents the sum of Mulliken atomic charges of Ni4 on different models.c Represents the sum of Mulliken atomic charges of MGr on different models.
Ni1	−0.001	0.171	—	0.219	0.172
Ni2	0.005	0.047	—	0.246	0.281
Ni3	−0.003	0.167	—	0.205	0.321
Ni4	−0.001	0.048	—	0.004	0.120
O1	—	−0.432	−0.423	—	−0.408
C1	—	0.431	0.394	—	0.443
O2	—	−0.433	−0.450	—	−0.386
Sum^a	0	−0.434	−0.479	—	−0.351
Sum^b	0	0.434	—	0.674	0.885
Sum^c	0	—	0.479	−0.674	−0.534

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For Mulliken charge, positive value denotes the gain of electrons compared to that of the original structure, while negative value represents a loss. The sum of Mulliken atomic charges of CO₂ on different models in Table 4 shows that the CO₂ molecule gained electrons, Ni₄ cluster losed electrons, and MGr surface gained electrons as CO₂. Electron transfer from Ni cluster to CO₂ and the surface of MGr, indicating Ni cluster acting as a Lewis base donating its electron to the MGr and CO₂, while MGr and CO₂ molecule acting as Lewis acids withdrawing electron density from the surface of Ni cluster. The adsorption of small molecules onto the surface of MGr changes the charge distribution. Compared with CO₂ adsorbed on isolated Ni₄ and MGr, Ni₄ cluster in the system of CO₂–Ni₄/MGr has the maximum amount of donated electrons of 0.885, indicating the strongest activation level of Ni₄. This phenomenon is consistent with the results manifested by binding energy and the electrostatic potential. The mutual transfer of multi-electron indicates a strong activation capacity and a significant change on its structure, which will greatly enhance the adsorption capacity of CO₂.

The projected density of states (PDOS) of CO₂ and Ni₄ cluster on different systems are displayed in Fig. 9 and S5.† Compared with the PDOS of pure CO₂ [Fig. 9(a)], the peaks of s and p orbitals for CO₂ become wider and lower when CO₂ adsorb on Ni cluster, MGr and Ni₄/MGr systems, especially the p orbits near the Fermi level, which indicates that CO₂ was activated and chemical adsorption occurred between CO₂ and those adsorbents. The phenomenon of p orbitals in chart (b) and (c) moved towards to right indicates total energy in the two systems becoming lower compared with original structure, in agreement with the theory reaction occurred toward a lower entropy direction, namely, the system is more stable after adsorption of CO₂.

Fig. 9(f–h) depicts the PDOS of Ni₄ cluster in the system of CO₂–Ni₄, Ni₄–MGr and CO₂–Ni₄/MGr, respectively. Compared with isolated Ni cluster [Fig. 9(e)], the occupied 3d and p orbitals have a significantly change in Fig. 9(f–h), with peaks generally becoming lower and wider, which reveals the electron cloud around the Ni cluster was out of shape and electrons were bound by MGr and CO₂ when adsorption occurred. Besides, Fermi level moved towards to the direction of low energy in Fig. 9(g and h), indicating the system becomes stable owing to the adsorption occurred between Ni cluster, CO₂ molecule and MGr. This adsorption lead to a change in the PDOS and it suggests that s and p orbitals of CO₂ and Ni atoms turned relatively larger, but there was little influence on d orbital.

IV Conclusions

DFT calculations were carried out to investigate the adsorption microcosmic mechanism and fundamental properties of CO₂ adsorption on supported Ni clusters on monovacancy graphene surface for catalytic applications. The results show that, Ni cluster tended to be a metal crystal structure with the increasing of atomic numbers, the average bond length of Ni–Ni tended to be a stable value with the size up to seven atoms, and the formation energy verged to a steady state with nine Ni atoms.

Binding energy and structural properties of Ni clusters on MGr were investigated by using DFT. It was found that binding energy became stable with increasing Ni atom numbers, and stabilized with increasing cluster size up to ten atoms adsorbed on MGr. The average bond length of Ni–Ni in isolated state and in MGr-supported Ni clusters with the increasing number of Ni atoms elongated to 2.38 Å and 2.43 Å, respectively. The value of maximal normalized radius of gyration indicates small Ni particles were stable on the MGr surface when radius of gyration exceeded 0.854 Å. The radius of gyration showed a linear correlation with binding energy of Ni cluster.

CO₂ adsorbed on different systems (isolated Ni_x cluster, MGr, and Ni_x/MGr) yielded a significantly lower binding energy (−2.72 eV) of CO₂ on MGr supported Ni₄ cluster than on isolated Ni₄ cluster (−1.80 eV). The catalytic activities of CO₂ were enhanced on the surface of MGr by supporting Ni₄ cluster. Additionally, Mulliken charge, electrostatic potential (EP) and partial density of states (PDOS) were also analyzed based on a change of the electronic structure of the Ni cluster deposited on MGr surface. More electrons transferred from Ni₄ cluster to the region of MGr supported metal system when CO₂ was adsorbed. The mechanism was proposed on CO₂ adsorption onto MGr deposited with Ni clusters at the molecular level. Our work affords important significance for CO₂ storage, capture and catalytic reaction of hydrocarbon production from CO₂.

Abbreviation

MGr	Monovacancy graphene
Nix/MGr	Nickel cluster deposited on the surface of MGr
EP	Electrostatic potential
PDOS	Partial density of states

Acknowledgements

This work was supported by National Basic Research Program of China (973 Program) (2011CB201202) & the National Natural Science Foundation of China (No. 21376154).

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Footnote

† Electronic supplementary information (ESI) available: The optimized structures of perfect-graphene sheet and one Ni atom deposited on graphene were listed, PDOS of Ni atom and C atom were analyzed in different adsorption system, stable configurations of CO₂ adsorbed on Ni_x cluster and CO₂ adsorbed on MGr surface deposition of Ni_x cluster were calculated, sum of density of states projected on the atoms of the CO₂ molecule adsorbed on isolated Ni₄, on MGr surface and on the Ni₄/MGr system. See DOI: 10.1039/c6ra14009b

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