Computational and Theoretical Chemistry 1106 (2017) 7–14

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Computational and Theoretical Chemistry

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Dissociation of methane on Ni4 cluster-A DFT study

Ghanashyam Roy a,⇑, Asoke Prasun Chattopadhyay b
a
Department of Chemistry, Krishnagar Govt. College, West Bengal 741101, India
b
Department of Chemistry, University of Kalyani, West Bengal 741235, India

a r t i c l e i n f o a b s t r a c t

Article history: The sequential four step dissociation of methane on Ni4 cluster has been investigated using density func-
Received 27 December 2016 tional theory. The adsorption of CH4, CHx, C and H are exothermic and Gibbs free energy changes are neg-
Received in revised form 23 February 2017 ative on bare cluster. The dissociation of methane on Ni4 cluster is endothermic and thermodynamically
Accepted 28 February 2017
not favorable at standard condition (T = 298 K, P = 1 atm). The dissociation of CHx (x = 1–3) species on
Available online 1 March 2017
bare cluster show higher activation energy barrier than on the hydrogen preadsorbed cluster. The ele-
mentary step, CH ? C, shows the highest activation energy barrier. Hence CH is the most stable interme-
Keywords:
diate. The Gibbs free energy changes are negative above 450 K for CH4 ? CH3, CH3 ? CH2 and CH2 ? CH,
Methane
Dissociation
whereas for CH ? C above 550 K at 1 atm. Coke formation is possible above 550 K.
Adsorption Ó 2017 Elsevier B.V. All rights reserved.
Density functional theory (DFT)

1. Introduction CH3, CH2, and CH intermediates on a Ni(1 1 1) methanation catalyst

using static secondary ion mass spectrometry.
The catalytic decomposition of methane on metallic surfaces Wang and Whitten [5] calculated the chemisorption energies of
has tremendous industrial importance. Methane can be used as CH and CH2 on Ni(1 1 1) surface, 3.12 eV and 2.90 eV, respectively.
an alternative source of hydrogen. Hydrogen can be produced Recently, Watwe et al. [6] studied the stability and reactivity of CHx
through steam methane reforming (Eq. (1)) coupled with water- species on Ni(1 1 1) by using periodic infinite plane wave slab cal-
gas shift reaction (Eq. (2)) of methane in the following scheme: culations, and found that all CHx species prefer threefold sites and
CH as the most abundant hydrocarbon species on Ni(1 1 1). Sieg-
CH4 ðgÞ þ H2 OðgÞ ! COðgÞ þ 3H2 ðgÞ ð1Þ
bahn et al. also demonstrated that CH is the most stable hydrocar-
bon species on Ni(1 0 0) by using size-limited cluster models [7].
COðgÞ þ H2 OðgÞ ! CO2 ðgÞ þ H2 ðgÞ ð2Þ
Because of their cost, noble metal catalysts cannot be used in
Hydrogen can be also produced through partial oxidation of industrial scale, so Ni is the preferred SMR catalyst [2]. Unfortu-
methane to syngas (Eq. (3)) nately, the efficiency of Ni catalyst is severely hindered by carbon
formation, which leads to encapsulation or even destruction of Ni
CH4 ðgÞ þ 1=2O2 ðgÞ ! COðgÞ þ 2H2 ðgÞ ð3Þ
catalyst particles [8,9]. Researchers have demonstrated that alloy-
By the process of steam methane reforming (SMR), 95% of the ing Ni with another metal can result in a catalyst that exhibits
hydrogen are produced in the United States [1]. CO2 is produced resistant to carbon formation [10–12]. Moreover, less coke forma-
as a byproduct. Now-a-days, experimental researchers are actively tion has been observed on Ni(1 1 1) than the Ni(1 0 0) surface due to
developing industrial membrane reactors capable of the in situ higher potential energy barrier to the elementary step CH ? C [13].
separation of the CO2(g) and H2(g) products. The carbon dioxide Clusters are better catalyst than bulk surfaces due to its higher
can be pumped underground for sequestration, and hydrogen can surface to volume ratio. Yang et al. [14] found that the catalytic
be used in automobiles, fuel cell systems, or industrial processes. activity on Cu29 clusters for the synthesis of CH3OH via CO2 hydro-
The evidence of methane decomposition mechanism may be genation is higher than that of bulk Cu(1 1 1) surface, indicating
supported by some surface science experiments; Ceyer et al. [2,3] that Cu clusters could be a potential catalyst for CO2 hydrogenation
have identified CH3 on Ni(1 1 1) surface with high-resolution elec- to methanol. Nano-and sub-nanoscale clusters are of scientific
tron energy loss spectroscopy. Kaminsky et al. [4] have detected interest due to distinct optical, magnetic, and catalytic properties
which differ from bulk materials [15].
⇑ Corresponding author. Au et al. [16] calculated adsorption energies of CH4, CH3, CH2,
E-mail address: ghanashyamroy96@gmail.co (G. Roy). CH and C intermediates on Ni, Pd, Pt and Cu clusters of size

http://dx.doi.org/10.1016/j.comptc.2017.02.030
2210-271X/Ó 2017 Elsevier B.V. All rights reserved.
8 G. Roy, A.P. Chattopadhyay / Computational and Theoretical Chemistry 1106 (2017) 7–14

between 7 and 13 atoms. Liu et al. [17] comparatively studied Applying Gaussian thermodynamics, the enthalpy of adsorption
methane dissociation on the surfaces of Ni13 cluster and Ni(1 1 1). (DH) and Gibbs free energy change (DG) are calculated from the
Recently, Zhang et al. [18] studied the dissociation of methane on enthalpy and Gibbs free energy differences between adsorption
tetrahedral Ni4 cluster, supported on a-Al2O3 (0001). The struc- system and sum of bare cluster and free adsorbate, respectively.
tural, magnetic and adsorption properties of CH3 and CH4 on Nin
(n = 2–16, 21, 55) clusters have been investigated based on density DH ¼ Hcluster=adsorbate  ðHcluster þ Hadsorbate Þ ð4Þ
functional theory (DFT) with the spin polarized generalized gradi-
ent approximation, using the Perdew–Burke–Ernzerhof functional DG ¼ Gcluster=adsorbate  ðGcluster þ Gadsorbate Þ ð5Þ
[19]. Petkov et al. [20] reported the stability, electronic and mag-
All the structures are visualized with Gauss View 5 package
netic properties of tetrahedral Ni4 cluster containing impurity H,
[29].
O, and C atoms. However, the mechanism of adsorption and disso-
ciation of methane on Ni4 cluster is still not clear.
Here, we introduced the dissociative adsorption of methane on 3. Results and discussion
tetrahedral Ni4 cluster. The adsorption or binding of CH4, CH3, CH2,
CH, C and H species at top (c1), bridging (b2) and three fold (c3) 3.1. Tetrahedral Ni4 cluster
sites are calculated. The partial density of states are plotted to
understand the electronic properties of adsorption. The sequential Table 1 represents the calculated binding energy, geometry,
four step dissociation of methane, CH4 ? CH3 ? CH2 ? CH ? C, dipole moment and Mulliken charges of tetrahedral Ni4 cluster at
has been discussed. The dissociation of CHx on bare cluster is also singlet state. Goel et al. [30] studied the geometries and binding
introduced. The dissociation energy, activation energy barrier, zero energies of the tetrahedral, distorted tetrahedral, square planar,
point energy corrected dissociation energy, enthalpy and Gibbs and rhombic Ni4 cluster at different spin states. They calculated
free energies are calculated. The variation of DG with respect to binding energy, 4.48 eV/atom, and NiANi bond distances,
temperature is plotted. 2.448 Å, 2.690 Å, 2.430 Å, 2.662 Å, 2.420 Å and 2.463 Å for tetrahe-
dral geometry at singlet state. Reddy et al. [31] calculated the elec-
2. Computational methods tronic structure of tetrahedral Ni4, corresponding NiANi bond
distances, 2.24 Å (DMOL) and 2.20 (MD), and binding energies,
All the geometry optimizations and subsequent frequency cal- 4.04 eV/atom (DMOL) and 2.77 eV/atom (MD).
culations have been carried out at the generalized gradient approx-
imation (GGA) [21] using Perdew-Burke-Ernzerhof (PBE) exchange 3.2. Adsorption of CH4, CHx (x=1–3), C, and H on Ni4 cluster
correlation functional [22] with the aid of Gaussian 09W package
[23]. For nickel atoms, the Los Alamos National Laboratory [24] The calculated adsorption or binding energies, binding energies
basis set of double-f quality [LANL2DZ] is used and the corre- after zero-point energy correction, reaction enthalpies, change in
sponding scalar relativistic effective core potential that replaces Gibbs free energies and real frequencies of CH4, CH3, CH2,CH,C
the inner-shell electrons. The 6-31G⁄⁄ basis set is applied for car- and H are listed in Table 2. The stable geometries are shown in
bon and hydrogen atoms [25] and Wood-Boring quasi-relativistic Fig. 1.
effective core pseudo potential, MWB2 is used for the neutral car- Methane molecule is adsorbed on top site (Fig. 1a) of Ni4 cluster
bon atom. All the atoms are relaxed during optimization. For opti- at a distance of 2.240 Å and calculated Eb, DG and DH are 0.42 eV,
mized stable geometry, the number of imaginary frequency values 0.31 eV and 0.40 eV respectively, indicating a thermodynami-
turns out to be zero, confirming the existence of minima on the cally favorable and exothermic process. Liu et al. [17] also observed
potential energy surface. the adsorption of methane on top site of both Ni4 and Ni13 clusters.
For locating transition state (TS), Synchronous Transit-Guided However, the adsorption of methane molecule on transition metal
Quasi-Newton (STQN) [26] method has been introduced. The surfaces is generally classified as a process of physisorption where
opt = QST2 and QST3 keywords are used. The IRC calculation is fol- the attraction arises due to the van der Waals forces of interaction.
lowed to make sure that each transition state connects the Previously, the calculated adsorption energy on transition metal
expected reactant and product [27,28]. The binding or adsorption surfaces are 0.01 eV, both experimentally [32,33] and theoreti-
energy (Eb) is calculated as: cally [34]. Moreover, the interaction between Ni(1 1 1) surface
and CH4 is repulsive nature [35], whereas the repulsion is
Eb ¼ Ecluster=adsorbate  ðEcluster þ Eadsorbate Þ ð1Þ decreased in clusters. Here, we observed elongation of the two
CAH (1.122, 1.125 Å) bonds, present towards the Ni atom of Ni4
where Ecluster/adsorbate, Ecluster, and Eadsorbate are the total electronic cluster. However, no physisorption of CH4 has been found at bridg-
energies of the optimized structures of the adsorption configura- ing and three fold sides of Ni4 cluster, in agreement with Liu et al.
tion, the bare cluster, and the isolated radical or adsorbate, respec-
tively. The dissociation energy (Ediss) for CH4 is defined as the
difference between the energies of dissociated state on the cluster Table 1
Binding energy/atom (eV),Geometry, Dipole moment (Debye) and Mulliken charges
(EDS) and the sum of bare cluster (Ecluster) and free adsorbate.
(e) for tetrahedral Ni4 cluster.

Ediss ¼ EDS  ðEcluster þ ECH4 Þ ð2Þ Binding Geometry Dipole Mulliken

energy moment charges

The zero point energy corrected energies (ZPE) are calculated Bond distance
4.50 1–2, 2–3, 3–4 = 2.350 0.0068 1 = 3 = 0.003
after zero point energy correction. The electronic energy barrier
1–3 = 2.271, 1–4 = 2.351 2 = 4 = 0.003
(EAct) for each elementary step is calculated as the difference 2–4 = 2.334
between the electronic energies of transition state (TS) and initial Bond angle
state (IS). 1–2–3 = 57.77, 1–3–2 = 61.107
2–1–3 = 61.113, 1–4–2 = 60.224
1–4–3 = 57.779, 2–3–4 = 60.231
EAct ¼ ETS  EIS ð3Þ
 G. Roy, A.P. Chattopadhyay / Computational and Theoretical Chemistry 1106 (2017) 7–14 9

Table 2
Binding energies (Eb, eV), Binding energies after Zero-point energy correction (Eb (ZPE), eV), Enthalpies (DH, eV, at 298 K, 1 atm), Gibbs free energies (DG, eV, at 298 K, 1 atm),
Mulliken charges (q, e) and Real vibrational frequencies (cm1) for CH4, CH3, CH2, CH, C and H on Ni4 cluster.

Adsorbates Binding site EAds EAds (ZPE) DH DG q Real frequencies

CH4 Top 0.42 0.41 0.40 0.13 C = 0.37 12.44,42.41,77.84,143.93,145.68,
H1 = 0.15 167.72,202.38,211.81,222.52,
H2 = 0.15 246.06,334.04,401.52,1180.63,
H3 = 0.10 1302.01,1305.40, 1441.92,1510.93,
H4 = 0.13 2761.15. 2860.32,3096.09,3163.51
CH3 Bridge 2.46 2.37 2.39 1.99 C = 0.42 26.85,86.89,95.58,164.12,184.07,
H1 = 0.13 198.19, 198.97,254.49,322.53,
H2 = 0.12 417.68,490.46, 573.62,1159.63,
H3 = 0.12 1322.67,1376.33,1778.39,2995.43
CH2 Top 4.43 4.28 4.31 3.89 C = 0.19 40.72,86.88,139.57,159.99,
H1 = 0.08 192.44,201.56,219.41,244.26,
H2 = 0.09 321.09,518.59,631.38,705.21,
1296.19,3029.90,3036.30
Bridge 5.37 5.15 5.19 4.73 C = 0.30 65.53,106.30,130.40,180.81,
H = 0.11 95.50,224.23, 307.11,449.94,
H = 0.12 502.42,517.49,556.41,602.23,
1235.97,3003.42,3110.04
Three fold 4.99 4.85 4.90 4.44 C = 0.34 39.05,140.77,175.25,190.19,
H1 = 0.14 216.24,230.22,292.21,317.11,
H2 = 0.14 409.73,441.11,575.51,688.34,
1286.83,2634.04,2921.39
CH Top 4.83 4.88 4.72 4.35 C = 0.06 40.72,46.11,160.48,162.50,
H = 0.07 207.54,223.42,223.99,326,03,
534.99,536.25,682.22,3055.14
Four fold 6.89 6.71 6.77 6.30 C = 0.25 116.57,147.59,160.55,216.43,
H = 0.14 220.04,216.43,220.04,270.20,
374.87,536.40,627.69,661.07,
687.26,3015
C Top 6.46 6.40 6.42 6.13 C = 0.03 36.37,41.90,156.83,158.83,
203.12,221.59,222.01,323.32,
782.21
Three fold 9.04 8.94 8.98 8.60 C = 0.09 101.73,105.19,156.94,202.07,
202.92,288.96,595.23,595.94,
687.63
Four fold 9.09 8.94 9.03 8.72 C = 0.13 38.76,53.35,80.81,146.09,181.30,
305.53,628.42,665.48,792.91
H Top 2.61 2.47 2.46 2.22 H = 0.05 115.23,130.98,203.86,215.04,
220.55,261.75,310.90,338.24,
1692.99
Bridge 2.59 2.41 2.46 2.16 H = 0.04 110.12,122.05,173.46,174.61,
285.05,329.64,330.46,1247.41,
1429.65

[17] study. Thus, Ni4 cluster binds and activates CH4 strongly than and 3.85 eV for top, three fold (hcp) and three fold (fcc) sites,
on surface. respectively. Therefore, CH2 binds strongly on Ni4 cluster than Ni
The stable adsorption geometry for CH3 species is observed at (1 1 1) surface.
bridging site (Fig. 1b) of bare Ni4 cluster. The CAH bond points For CH intermediate, two stable structure are obtained, at top
toward the nearest metal atom, elongated to 1.128 Å. The calcu- site (Fig. 1f) and tetra coordinated or four fold site (Fig. 1g). The cal-
lated binding energy is 2.46 eV, whereas no stable binding is culated binding energies are 4.83 eV and 6.89 eV for top and
observed on top and three fold sites of Ni4 cluster. However, the four fold sites, respectively. CH shows the highest binding energy
calculated binding energies on top, bridging and three fold sites among all CHx intermediates at four fold site. However, no elonga-
are 2.60 eV, 2.55 eV and 2.51 eV, respectively on Ni13 cluster tion of the CAH bond has been observed. Moreover, CH prefers to
[17]. Further, the calculated Eb on top and three fold sites of bind three fold sites of both hcp (Eb, 6.35 eV) and fcc (Eb,
hexagonal-close-packed (hcp) and face-centered cubic (fcc) on Ni 6.27 eV) on Ni(1 1 1) surface [13].
(1 1 1) surface [13] are 1.55 eV, 1.78 eV and 1.81 eV, respec- For C atom, three stable structures are observed on bare Ni4
tively. These results indicate that the CH3 prefers to bind cluster cluster. The binding energies are 6.46 eV, 9.04 eV and
strongly than the surface. 9.09 eV for top (Fig. 1h), three fold (Fig. 1i) and four fold (Fig. 1j)
For CH2 intermediate, three stable structures are found on bare sites, respectively. On Ni(1 1 1) [13] surface, C atom binds on three
Ni4 cluster. The calculated binding energies are 4.43 eV, 5.37 eV fold sites of hcp and fcc, and corresponding binding energies are
and 4.99 eV for top (Fig. 1c), bridging (Fig. 1d) and three fold 6.61 eV and 6.52 eV, respectively. C also shows stronger binding
(Fig. 1e) sites, respectively. The CAH bond of CH2 adsorbed at three energy on Ni4 cluster than the surface.
fold site points toward the nearest metal atom is elongated to The hydogen atom prefers to bind at top (Fig. 1k) and bridging
1.142 Å on Ni4 cluster. The NiAC bond distance is shortest at top sites (Fig. 1l) on Ni4 cluster. The calculated binding energies are
site (1.787 Å) than bridging (1.866 Å, 1.878 Å) and three fold sites 2.61 eV and 2.59 eV on top and bridging sites, respectively.
(1.936 Å, 1.884 Å, 1.905 Å), indicating strongest binding at top site. However, Liu et al. [17] calculated binding energies for H on top,
However, on the Ni(1 1 1) surface [13] Eb are 2.78 eV, 3.83 eV bridging and three fold sites of Ni13 cluster are 2.77 eV,
10 G. Roy, A.P. Chattopadhyay / Computational and Theoretical Chemistry 1106 (2017) 7–14

Bond Distances C1-H2=1.122Å,C1-H3=1.125Å Ni-C=2.240Å,C1-H4=1.097Å,C1-H5=1.099Å

Bond Angles H2-C1-H4=109.77⁰,H3-C1-H4=109.71⁰, H4-C1-H5=110.68⁰,H2-C1-H5=105.98⁰
(a)

Bond Distances C1-H2=1.107Å,C1-H3=1.107Å,C1-H4=1.128Å,Ni1-C=2.027Å, Ni2-C=2.073Å

Bond Angles H2-C1-H3=109.92⁰,H3-C1-H4=104.74⁰,H2-C1-H4=105.14⁰
(b)

Bond Distances C1-H2=1.106Å C1-H2=1.106Å C1-H2=1.142Å

C1-H3=1.101Å C1-H3=1.105Å C1-H3=1.116Å
Ni-C=1.787Å Ni1-C=1.866Å Ni1-C=1.936Å
Ni2-C=1.878Å Ni2-C=1.884Å
Ni3-C=1.905Å
Bond Angles H2-C1-H3=112.09⁰ H2-C1-H3=115.70⁰ H-C-H=106.68⁰
(c) (d) (e)

Bond Distances C-H=1.106Å,Ni-C=1.704Å C-H=1.109Å, Ni1-C=1.872Å

Ni2-C=1.901Å,Ni3-C=1.900Å, Ni4-C=1.872Å
(f) (g)

Bond Distances Ni-C=1.653Å Ni1-C=1.764Å,Ni2-C=1.764Å, Ni1-C=1.779Å,Ni2-C=1.764Å

Ni3-C=1.764Å Ni3-C=1.765Å,Ni4-C=1.783Å
(h) (i) (j)

Ni-H=1.512Å Ni1-H=1.721Å,Ni2-H=1.720Å
(k) (l)
Fig. 1. Stable geometries of adsorption (a) CH4 on top, (b) CH3 on bridge, (c) CH2 on top, (d) CH2 on bridge, (e) CH2 on three fold, (f) CH on top, (g) CH on four fold, (h) C at top,
(i) C at three fold, (j) C at four fold, (k) H at top, and (l) H at bridge. Small off-white ball represents hydrogen, Larger off-white ball represents carbon, Blue ball represents
Nickel.

3.12 eV and 3.11 eV, respectively. We observed no stable bind- all the adsorbates have different charges, indicating that electron
ing on three fold site of Ni4 cluster. Wang et al. [13] calculated bind- transfer from both cluster to adsorbate and vice versa are possible,
ing energies for H atom are 2.2 eV, 2.76 eV and 2.77 eV for top, in agreement with the PDOS analysis.
three fold (hcp) and three fold (fcc) sites, respectively on Ni(1 1 1) For CH4, the S and P bands are slightly shifted to more negative
surface. direction, from energy 16.5 eV to 17.75 eV and from energy
9.26 eV to 10.32 eV, respectively, indicating charge transfer
3.3. Electronic properties of adsorption from methane to the cluster. No orbital overlap has been observed.
However, due to charge transfer from methane to cluster, weak
In order to understand the electronic structure of adsorption for binding interaction takes place, which causes more stronger bind-
CH4, CH3, CH2, CH, C and H on Ni4 cluster, the partial density of ing on the cluster than the bulk surfaces. In addition, broadening of
states (PDOS) are calculated at free as well as adsorbed state and the anti-bonding level is observed due charge transfer from cluster
compared them, are shown in Figs. 2 and 3. As given in Table 2, to adsorbent, which is responsible for weakening of the CAH bond.
 G. Roy, A.P. Chattopadhyay / Computational and Theoretical Chemistry 1106 (2017) 7–14 11

Fig. 2. Partial density of states of free and adsorbed CH4, CH3, CH2 and CH on Ni4 cluster.

For CH3 adsorbed at bridging site, the highest occupied molec- 10.61 eV causes stronger binding. The LUMO, px orbital at
ular orbital (HOMO) is pz (non-bonded) shifted from 5.15 eV to 4.35 eV is shifted to less negative direction at 3.31 eV. The
8.06 eV. In addition, p-type orbital overlap has been observed broadening of the anti-bonding orbital is observed, which is shifted
between C(pz) and Ni(d) at 8.06 eV which causes slightly stronger from 2.58 eV to 4.56 eV.
binding with the cluster. For CH, adsorbed at top site, the S band, at 15.33 eV (at free
For CH2, adsorbed at three fold site, the HOMO (pz, non-bonded) state) is shifted to more positive direction at 13.61 eV, indicating
at 5.22 eV (at free state) shifted to more negative direction to charge transfer from metal cluster to the bonding orbital CH(r),
7.01 eV, where p-type of overlap with Ni(d) is observed. Further, which causes CAH bond shorter and stronger. The CAH bond
r-type of orbital overlap between C(sp) and Ni(s) orbital at distances at free and adsorbed states are 1.140 Å and 1.106 Å,
12 G. Roy, A.P. Chattopadhyay / Computational and Theoretical Chemistry 1106 (2017) 7–14

Fig. 3. Partial density of states of free and adsorbed C and H on Ni4 cluster.

respectively. In addition, a r-type overlap between CH(sp)-Ni(d)

orbitals at 9.22 eV, and two p-type of overlaps, C(px)-Ni(d) and
C(pz)-Ni(d) orbitals at 6.74 eV are observed.
For C, the S band is shifted to the more negative direction from
12.39 eV to 14.3 eV, forming a strong r-type overlap between C
(s) and Ni(sp) orbitals. At 7.13 eV, two p-type of overlaps, C(px)-
Ni(d) and C(pz)-Ni(d) are observed. For H, the S band at 7.35 eV
moves to more negative direction at 8.15 eV, a r-type of overlap
between H(s) and Ni(sp) orbitals is observed at top site.
The binding energy increases as the number of non-bonded p
orbital (filled/half-filled) increases on the C atom which causes
the formation of p-bond with the cluster. Further, greater the shift-
ing of orbital (s/p) energy labels towards the more negative direc-
tion, greater will be the binding energy. Moreover, the shifting of S
bands towards the less negative direction causes the CAH bond
stronger, whereas broadening of the anti-bonding orbital (r⁄)
towards more positive direction, makes CAH bond weaker. There-
fore, the order of binding energy increases as:CH4 < CH3  H
< CH2 < CH < C.

3.4. CH4 sequential decomposition Fig. 4. Energy profile diagram of the sequential decomposition of methane on Ni4
cluster. IS = Initial state, TS = Transition State and DS = Dissociated State.

The energy profile diagram of methane dissociation is shown on

Fig. 4. The dissociation energies, zero point energy correction dis-
sociation energies, reaction enthalpies, change in Gibbs free ener- by 1.47 eV for Ni7 cluster and 0.31 eV for Ni13 cluster. Liu et al. [37]
gies, activation energy barriers, and respective imaginary calculated the Eact and Ediss are 1.18 eV and 0.39 eV, respectively on
frequencies for the transition states are illustrated in Table 3. Ni(1 1 1) surface.
In elementary step 1, CH4 ? CH3 + H, the physisorped methane In elementary step 2, CH3 + H ? CH2 + 2H, the dissociated state
considered as the Initial state 1, undergoes dissociation on top site. 1 is considered as the initial state 2. We let H remain present on b2
The dissociated state 1 is the coadsorption of CH3 and H, as shown site of the cluster. CH3 is adsorbed on the top site and CAH bond
in Fig. 4, which is endothermic by 0.45 eV. The calculated activa- distances are 1.100 Å, 1.105 Å and 1.104 Å, undergoes dissociation
tion energy barrier is 1.28 eV and the process is thermodynami- on adjacent b2 site. The breaking CAH bond distances are 1.788 Å
cally not favorable at standard condition (T = 298 K, P = 1 atm). and 2.642 Å for TS2 and DS2, respectively. The calculated Ediss
The breaking CAH bond distances are 1.632 Å and 2.821 Å for tran- and Eact are 0.49 eV and 0.42 eV, respectively. Liu et al. [37] calcu-
sition state 1 and dissociated state 1, respectively. Burghgraef et al. lated the Ediss and EAct are 0.21 eV and 0.78 eV, respectively on Ni
[36] observed the dissociation of CH4 to CH3 and H is endothermic (1 1 1) surface.
 G. Roy, A.P. Chattopadhyay / Computational and Theoretical Chemistry 1106 (2017) 7–14 13

Table 3
Dissociation energies (Ediss, eV), Zero point energy correction dissociation energies (Ediss (ZPE), eV), Enthalpies (DH, eV, at 298 K, 1 atm), Gibbs free energies (DG, eV, at 298 K,
1 atm), Activation energy barriers (Eact, eV) and Imaginary vibrational frequencies (cm1) for the transition states.

Elemetary steps Ediss Ediss (ZPE) DH DG Eact Imaginary vibrational

frequency
1 CH4 ? CH3 + H 0.45 0.34 0.32 0.68 1.28 873.35
2 CH3 + H ? CH2 + 2 H 0.49 0.22 0.15 0.61 0.42 612.49
3 CH2 + H ? CH + 3 H 0.56 0.11 0.08 0.53 0.29 74.26
4 CH + 3 H ? C + 4 H 1.13 0.64 0.61 1.05 0.87 788.58
Dissociation on the bare Ni4 cluster
CH3 ? CH2 + H 1.80 1.83 1.87 1.41 0.84 561.65
(Bridging) CH2 ? CH + H 4.93 4.87 4.92 4.44 0.78 742.79
(Three fold) CH2 ? CH + H 4.89 4.82 4.87 4.40 0.33 729.28
CH ? C + H 6.46 6.34 6.40 5.96 1.37 701.73

In elementary step 3, CH2 + 2H ? CH + 3H, the dissociated state

2 is considered as the initial state 3, where CH2 (1.104 Å, 1.110 Å) is
adsorbed at b2 site, undergoes dissociation on three fold site. Here,
two predissociated hydrogen remain present on the cluster. The
calculated Ediss and EAct are 0.56 eV and 0.29 eV, respectively. On
Ni(1 1 1) surface [38], the Ediss and Eact are 0.34 eV and 0.37 eV,
respectively.
In elementary step 4, CH + 3H ? C + 4H, here the DS3 is the IS4,
where three preadsorbed hydrogens are present in the cluster.
Here, CH (1.108 Å) species is adsorbed on three fold site, dissoci-
ates to form surface H adsorbed on adjacent top site and C remain
present on c3 site. The breaking CAH bond distances at transition
state 4 and dissociated state 4 are 1.735 Å and 2.266 Å, respec-
tively. The calculated Ediss and Eact for this step are 1.13 eV and
0.87 eV, respectively. This step is the highest endothermic step
by 1.05 eV. On Ni(1 1 1) surface [38], Ediss and Eact are 0.61 eV and
1.36 eV, respectively. It has been found that the endothermic nat-
ure increases as the number of predissociated hydrogen increases
Fig. 5. Energy profile diagram of decomposition of CH3, CH2 and CH on H free bare
on the cluster, which is attributed due to repulsion of the surface Ni4 Cluster; IS = Initial state, TS = Transition State, DS = Dissociated state.
hydrogens and CHx.

The dissociation of CHx on bare cluster are exothermic and DG

3.5. Dissociation of CH3, CH2 and CH on bare Ni4 cluster
values are negative, indicating thermodynamically favorable pro-
cess at standard condition. The activation energy barriers for the
To understand the effect of the presence of pre-dissociated sur-
dissociation of CHx on bare cluster are higher than the hydrogen
face hydrogen on the cluster, the dissociation of CH3, CH2 and CH
preadsorbed cluster. The endothermic nature of the dissociation
studied on bare cluster separately. For CH3 ? CH2 + H, the stable
in hydrogen preadsorbed cluster, shifts the initial states to higher
geometry of CH3 on b2 site, as shown on Fig. 3b, is the initial state.
energy level. Hence, the difference between transition state and
The CAH bond which is pointed towards Ni atom, elongated to
initial state is decreased; consequently Eact becomes lower in
1.128 Å, considered for dissociation and after dissociation the dis-
hydrogen preadsorbed cluster.
sociated H adsorbed on adjacent b2 site. The breaking CAH bond
distances at TS and dissociated state are 1.804 Å and 3.538 Å,
respectively. The calculated Ediss and Eact are 1.80 eV and
0.84 eV, respectively are listed in Table 3. The potential energy sur-
face is displayed in Fig. 5.
For CH2 ? CH + H, the initial state is CH2 (1.105, 1.106 Å)
adsorbed at bridging site (Fig. 3d). The calculated Ediss and EAct
are 4.93 eV and 0.78 eV, respectively. The breaking CAH bond
distances at TS and dissociated states are 1.557 Å and 2.375 Å,
respectively. While CH2 (1.142, 1.116 Å) adsorbed at three fold site
is the initial state, the calculated Ediss and Eact are 4.89 eV and
0.33 eV, respectively. The breaking CAH bond distances at TS and
dissociated states are 1.641 Å and 2.503 Å, respectively. The activa-
tion energy barrier at c3 site is less than the b2 site, indicating as
the number of binding metal atom increases, the activation energy
barrier decreases.
For CH ? C + H, the four fold adsorbed stable CH (1.109 Å)
geometry (Fig. 3g) is considered as the initial state. At the TS and
dissociated state, the breaking CAH bond distances are 1.511 Å
and 2.502 Å, respectively. The calculated Ediss and Eact are
6.46 eV and 1.37 eV, respectively. Fig. 6. IRC plot for all the transition states.
14 G. Roy, A.P. Chattopadhyay / Computational and Theoretical Chemistry 1106 (2017) 7–14

cluster decreases the dissociation energy barrier for CHx. As the

number of binding metal atoms increases, lower is the energy bar-
rier. CH intermediate is the most stable intermediate among all
CHx due to its highest potential energy barrier of dissociation.
The carbon coking can be controlled by keeping the dissociation
temperature below 525 K at 1 atm pressure.

Acknowledgement

The corresponding author acknowledges the Department of

Chemistry, Kalyani University for financial and computational
support.

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