Supporting Information
Copyright Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, 2012
A First-Principle Calculation of Sulfur Oxidation on Metallic
Ni(111) and Pt(111), and Bimetallic Ni@Pt(111) and
Pt@Ni(111) Surfaces
Chen-Hao Yeh and Jia-Jen Ho*[a]
cphc_201200215_sm_miscellaneous_information.pdf
S1.1. Computational cell dimensions for the surface layers employed in the
calculations
The unit cell parameters are 3.52Å, and 3.99Å for Ni bulk, and Pt bulk respectively.
The convergence tests for various higher cutoff energies were performed and 400 eV
was verified for this work, and it is indeed suitable to use our current cutoffs and
surface in the system. The lattice parameter of p(2x2) cell for Ni surface layer is a = b
= 4.93Å, c = 22.07Å and for Pt surface layer is a = b = 5.52Å, c = 24.97Å, in
bimetallic system, the parameter for Ni@Pt surface layer is a = b = 5.48Å, c = 25.03Å,
and for Pt@Ni surface layer is a = b = 5.16Å, c = 21.84Å, respectively.
2
S2.1. Possible morphology of sulfur on the Pt(111) surface
The preferential dispersion of sulfur on the metal surface involves multiple sulfur
atoms, constructing various crystalline structures, shown in Figure S1.
The sulfur
crystal near 300 K prefers to form a rhombic, octahedral structure (S8) [1], which
dissociates into four S2 molecules with no reaction barrier and is exothermic by -5.72
eV when the S8 monomer is dispersed on the Pt(111) surface.
The dissociation of
these four S2 molecules into eight sulfur atoms on the neighboring fcc hollow sites
releases a further 1.45 eV.
A similar phenomenon appears on adsorption of S6 (a
cyclic structure resembling cyclohexane) [1] and S4 [2] on Pt(111); both species
decompose, into three and two S2 molecules, and first release -5.21 eV and -3.90 eV,
respectively, and then further dissociate into six and four sulfur atoms exothermically
at 0.89 and 1.69 eV, respectively, as shown in Figure S2. The adsorption energy of a
single S2 molecule on a fcc hollow site of Pt(111) is -3.22 eV with a top-fcc-bridge
(t-f-b) structure [3] (one S atom on top of Pt, the other on a bridge site, but with the
entire S2 molecule centered on the fcc hollow site).
The dissociation of adsorbed S2
into two S atoms onto the nearest two hcp hollow sites has a reaction barrier of height
0.51 eV but is 1.60 eV exothermic.
The calculated average stable energies, E gas ,
per sulfur atom of S2, S4, S6 and S8 are -2.38, -2.88, -3.04 and -3.11 eV, respectively,
which gradually converge to a value about -3.15 eV; the average adsorption energies
3
( E ads ) per sulfur atom of 1 S, 2 S, 4 S, 6 S and 8 S atoms on Pt(111) are -4.88, -4.53,
-4.28, -4.05 and -4.01 eV, respectively, gradually converging to a value about -3.98 eV,
shown in Figure S3. E gas is hence invariably smaller than E ads regardless of the
increasing number of sulfur atoms in the crystalline structure, indicating that the
intermolecular strength between sulfur atoms is less than that between the sulfur atom
and the surface Pt atom.
Reference:
[1] Earnshow, N. Greenwood, Chemistry of the Elements (2nd ed.) 1997,
Butterworth-Heinemann, Oxford UK.
[2] M. W. Wong, R. Steudel, Chem. Phys. Lett. 2003, 379, 162-169.
[3] Z.Y. Yang, R.Q. Wu, J.A. Rodriguez, Phys. Rev. B. 2002, 65, 155409(1-9).
4
(a)
(b)
1.90
(c)
1.93
1.93
1.90
1.90
2.15
(d)
(e)
2.11
(f)
2.14
2.08 2.07
2.11
2.07
2.05
1.97
2.02
2.05
2.07
2.07
2.08
2.14
1.97
2.02
2.25
2.22
(g)
2.07
2.07
2.07 2.07
2.07
2.07
2.07
2.07
Figure S1 The calculated structure and bond lengths of Sx monomers in gas-phase (x
= 2~8).
5
eV
S8(g)
S2(g)
S4(g)
S6(g)
0
~
~
S2(a)
-3
2S2(a)
-3.22
-4
3S2(a)
4S2(a)
-1.60
-3.90
-1.69
-5
2S(a)
4S(a)
-4.82
-5.21
-6
-0.89
-5.72
-1.45
8S(a)
6S(a)
-5.59
-6.10
-7
-7.17
Figure S2 The calculated potential energy surface diagrams of S8, S6, S4 and S2
dissociation on Pt(111) surface.
6
0
average gas-phase stable energy
energy (eV)
-1
average adsorption energy
-2
-3
-4
-5
-6
0
1
2
3
4
5
6
7
8
9
sulfur atoms (number)
Figure S3 Comparison between the average gas-phase stable energy ( E gas ) from S2 to
S8 monomers and the average adsorption energy ( Eads ) of S to 8S atoms on Pt(111).
7
(a)
(b)
S-surface (fcc)
S-surface (hcp)
(d)
(c)
S-surface (Top)
O-surface (Fcc)
(e)
(f)
O-surface (Hcp)
O-surface (Top)
Figure S4 Optimized adsorbed geometries of (a)~(c)：S on fcc, hcp, and top sites,
(d)~(f)：O on fcc, hcp, and top sites, (g)~(i)：O2 on t-f-b, t-h-b and t-b-t sites, (j) and
(k)：SO on fcc and t-f-b sites and (l)~(o) SO2 on top, bri, parallel-hollow and
parallel-bridge sites on pure M(111) surface, respectively. The yellow, red and light
blue spheres represent the S, O and metal surface atoms, respectively.
8
(g)
(h)
O2 -surface (t-f-b)
O 2-surface (t-h-b)
(i)
(j)
O2 - surface (t-b-t)
SO-surface (fcc)
(k)
SO-surface (t-f-b)
(l)
(m)
SO 2-surface (bridge)
SO2-suface (top)
(n)
(o)
SO2-surface (parallel-hollow)
SO 2-surface (parallel-bridge)
Figure S4 continue
9
a)
pure Ni(111) surface
Surface + S(g) +O2(g)
Ni-IM6
Ni-IM7
0
~
~
Electronic Energy (eV)
-4
-4.98
-4.67
-5.12 Ni-IM2
-5
TS1
Ni-IM1 -5.14
Ni-IM6
-6
-4.61
TS4
-5.79
TS2
-6.12
-6.93
Ni-IM3
S(a)
S(a) + O2(a)
Ni-IM2
Ni-IM1
b)
S(a) + O(a) + O(a)
-7.27
-7.24
Ni-IM4
Ni-IM5
SO(a) + O(a)
SO2(a)
Ni-IM4
Ni-IM3
FS
TS3
Ni-IM7
Channel (A)
Channel (B)
-7
-6.19
-6.20
SO2(g)
Ni-IM5
pure Pt(111) surface
Surface + S(g) +O2(g)
0
-3.78
~
~
Pt-IM5
Electronic Energy (eV)
-4
Pt-IM5
-4.54
-4.84
-4.98
TS1
-5.22
Pt-IM1
-5
Pt-IM2
-5.63
TS2
Pt-IM3
-6.19
-6
FS
-7.06
Channel (A)
Channel (B)
-7
S(a)
Pt-IM1
Pt-IM4
S(a) + O2(a)
Pt-IM2
SO(a) + O(a)
Pt-IM3
SO2(a)
SO2(g)
Pt-IM4
Figure S5
Calculated potential-energy diagrams of electronic energy for sulfur oxidation on pure
metal surfaces. The top views of the corresponding intermediates are shown in the
lower and upper parts of the graph. (a) Ni (111) and (b) Pt (111) surfaces.
10
(a) Ni(111)
(b) Ni@Pt(111)
TS1
TS2
TS1
TS2
TS3
TS4
TS3
TS4
(c) Pt(111)
TS1
(d) Pt@Ni(111)
TS2
TS1
TS2
Figure S6
Top views of the transition states in the following sulfur oxidation reactions on (a)
Ni(111), (b) Ni@Pt(111), (c) Pt(111) and (d) Pt@Ni(111) surfaces. The yellow, red,
light blue and dark blue spheres represent the S, O, Ni and Pt atoms, respectively.
11
Figure S7. Projected density of states (PDOS) of the top-layer atoms on (a)
Ni@Pt(111) (blue line) and pure Ni (111) surfaces (red line) ; (b) Pt@Ni(111) (orange
line) and pure Pt(111) (green line) surfaces.
12
a)
pure Ni(111) surface
Surface + S(g) +O2(g)
0
0K
298 K
1073K
-1.22
-1
-1.52
Gibbs Free Energy (eV)
-2
-2.17
-2.64
-2.49
-3
-3.69
-3.50
-4
-3.70
-3.85
-3.99
-4.67
-4.65
-4.76
TS1
-5
-5.12
-4.98
-4.72
-5.18
-5.08
-5.79
-6
-6.12
-5.78
-6.20
TS2
-6.24
TS3
-6.26
-6.19
-7
S(a)
S(a) + O2(a)
S(a) + O(a) + O(a)
13
-7.27
SO(a) + O(a)
-7.24
SO2(a)
SO2(g)
b)
pure Pt(111) surface
Surface + S(g) +O2(g)
0
Gibbs Free Energy (eV)
0K
298 K
1073K
-1.38
-1
-1.88
-1.81
-2
-2.28
-3
-3.62
-3.18
-3.58
-4.24
-4
-4.36
-5
-4.84
-4.05
-4.54
TS1
-4.64
-4.72
-5.22
-4.98
TS2
-5.78
-5.63
-6
-6.03
-6.19
-7
-7.06
S(a)
S(a) + O2(a)
SO(a) + O(a)
SO2(a)
SO2(g)
Figure S8
Calculated possible potential-energy diagram of Gibbs free energy for sulfur
oxidation on pure metal surfaces, (a) Ni(111) and (b) Pt(111) surfaces. The black, red
and blue lines represent the reaction at 0K, 298K and 1073K, respectively.
14
Table S1. Calculated Vibrational Frequencies for O2, SO2 and Surface Species of
Eqn (a) ~ (f)[a] on Ni(111) Surface.
Species, i
vibrational frequencies, ωi,k cm-1
O2(g)
SO2(g)
(a) S(a)
(b) S(a) + O2(a)
1554
1279, 1089, 486
350, 209, 202
662, 400, 399, 351, 320, 221, 220, 188, 175
1249, 360, 320, 244, 230, 170, 119, 80, 46
573, 471, 463, 439, 420, 372, 296, 227, 192
846, 513, 484, 451, 312, 282, 279, 197, 134
1150, 489, 456, 386, 262, 255, 240, 78, 70
876, 720, 410, 324, 258, 246, 161, 114, 87
/
(b) S(a) + O2(a)
(c) S(a) + O(a) + O(a)
(d) SO(a) + O(a)
/
(d) SO(a) + O(a)
(f) SO2(a)
(a).
(b).
(b)/.
(c).
(c)/.
(d).
(e).
S(g) → S(a)
S(a) +O2(g) → S(a) + O2(a)
S(a) +O2(g) → S(a) + O2(a)
S(a) +O2(a) → S(a) + O(a) + O(a)
S(a) +O2(a) → SO(a) + O(a)
S(a) + O(a) + O(a) → SO(a) + O(a)
SO(a) + O(a) → SO2(a)
(f).
SO2(a) → SO2(g)
[a] (a) ~ (f) are the reaction steps in channel A of sulfur oxidation reaction.
(b)/ and (c)/ are the reaction steps in channel B of sulfur oxidation reaction.
15
Table S2. Reaction Energies and Temperature Corrections at 1073K on Ni(111) Surface for Eqn (a) ~ (f). (All energies are in electron volt).
△Eel,j
△Hth,j(gas)
△Hth,j(surf)
△Hj
△Sj( ×103)
-T△Sj
△Gj
reaction
(a)
(b)
/
(b)
(c)
(c)/
(d)
(e)
(f)
-5.12
0.14
-0.02
-0.25
-0.45
-0.45
0.28
0.57
0.58
-5.09
0.26
0.11
-1.48
-1.60
-1.29
1.59
1.71
1.39
-3.50
1.97
1.50
-1.14
-1.79
-1.15
0.03
1.05
0.69
0.01
<0.01
<0.01
<0.01
-0.86
-1.13
-1.79
-1.15
0.03
0.88
-0.15
-0.23
0.05
0.17
1.63
0.16
0.25
-0.06
-0.18
-1.75
-0.97
-1.54
-1.21
-0.15
-0.87
Column 1 lists the reaction equations described in Table S1; column 2 gives reaction electronic energy at 0 K; column 3 gives the T correction
to enthalpy of reaction for gas species only (includes ∆Ezpe,j); column 4 gives the T correction to reaction enthalpy for surface species only
(includes ∆Ezpe,j); column 5 gives reaction enthalpy calculated by adding columns 2, 3, and 4 (include all zero point and thermal corrections);
column 6 gives the entropy of reaction; column 7 represents the value of entropy of reaction multiplied by temperature; column 8 gives the
calculated Gibbs free energy by adding column 5 and column 7
16
Table S3. Calculated Vibrational Frequencies for O2, SO2 and Surface Species of
Eqn (a) ~ (e) on Pt(111) Surface.
Species, i
vibrational frequencies, ωi,k cm-1
O2(g)
SO2(g)
(a) S(a)
1554
1279, 1089, 486
354, 253, 245
1248, 382, 351, 260, 250, 195, 109, 99, 37
1156, 466, 414, 324, 307, 302, 249, 88, 40
1200, 895, 495, 333, 245, 227, 191, 127, 98
/
(b) S(a) + O2(a)
/
(c) SO(a) + O(a)
(e) SO2(a)
17
Table S4. Reaction Energies and Temperature Corrections at 1073K on Pt(111) Surface for Eqn (a) ~ (f). (All energies are in electron volt).
△Eel,j
△Hth,j(gas)
△Hth,j(surf)
△Hj
△Sj( ×103)
-T△Sj
△Gj
reaction
(a)
/
(b)
/
(c)
(e)
(f)
-4.84
-0.14
-0.65
-0.25
-0.45
-
0.28
0.58
<0.01
-4.81
-0.01
-0.65
-1.52
-1.29
-0.17
1.63
1.38
0.18
-3.18
1.37
-0.47
-1.43
0.87
0.69
0.01
-0.87
-1.42
0.69
-0.11
1.71
0.12
-1.84
-1.30
-1.15
Column 1 lists the reaction equations described in Table S1; column 2 gives reaction electronic energy at 0 K; column 3 gives the T correction
to enthalpy of reaction for gas species only (includes ∆Ezpe,j); column 4 gives the T correction to reaction enthalpy for surface species only
(includes ∆Ezpe,j); column 5 gives reaction enthalpy calculated by adding columns 2, 3, and 4 (include all zero point and thermal corrections);
column 6 gives the entropy of reaction; column 7 represents the value of entropy of reaction multiplied by temperature; column 8 gives the
calculated Gibbs free energy by adding column 5 and column 7.
18
Table S5. Calculated Vibrational Frequencies for O2, SO2 and Surface Species of
Eqn (a) ~ (f) on Ni@Pt(111) Surface.
Species, i
vibrational frequencies, ωi,k cm-1
O2(g)
SO2(g)
(a) S(a)
(b) S(a) + O2(a)
1554
1279, 1089, 486
317, 247, 240
655, 471, 466, 384, 333, 322, 259, 240, 208
1253, 353, 319, 264, 256, 211, 111, 67, 94
544, 493, 488, 452, 435, 407, 316, 291, 253
795, 489, 469, 410, 383, 309, 295, 159, 153
1137, 520, 445, 429, 319, 289, 266, 125, 119
851, 620, 411, 355, 305, 286, 192, 148, 119
/
(b) S(a) + O2(a)
(c) S(a) + O(a) + O(a)
(d) SO(a) + O(a)
/
(d) SO(a) + O(a)
(f) SO2(a)
19
Table S6. Reaction Energies and Temperature Corrections at 1073K on Ni@Pt(111) Surface for Eqn (a) ~ (f). (All energies are in electron volt).
△Eel,j
△Hth,j(gas)
△Hth,j(surf)
△Hj
△Sj( ×103)
-T△Sj
△Gj
reaction
(a)
(b)
/
(b)
(c)
/
(c)
(d)
(e)
(f)
-5.87
-1.29
-0.49
-0.25
-0.45
-0.45
0.28
0.57
0.58
-5.84
-1.17
-0.36
-1.50
-1.69
-1.35
1.61
1.82
1.44
-4.23
0.65
1.09
-2.20
-2.55
0.30
0.93
1.94
0.69
<0.01
<0.01
<0.01
<0.01
-0.86
-2.20
-2.55
0.30
0.93
1.77
-0.10
-0.29
0.12
0.09
1.72
0.11
0.31
-0.12
-0.10
-1.84
-2.09
-2.24
0.18
0.83
-0.07
Column 1 lists the reaction equations described in Table S1; column 2 gives reaction electronic energy at 0 K; column 3 gives the T correction
to enthalpy of reaction for gas species only (includes ∆Ezpe,j); column 4 gives the T correction to reaction enthalpy for surface species only
(includes ∆Ezpe,j); column 5 gives reaction enthalpy calculated by adding columns 2, 3, and 4 (include all zero point and thermal corrections);
column 6 gives the entropy of reaction; column 7 represents the value of entropy of reaction multiplied by temperature; column 8 gives the
calculated Gibbs free energy by adding column 5 and column 7.
20
Table S7. Calculated Vibrational Frequencies for O2, SO2 and Surface Species of
Eqn (a) ~ (e) on Pt@Ni(111) Surface.
Species, i
vibrational frequencies, ωi,k cm-1
O2(g)
SO2(g)
(a) S(a)
1554
1279, 1089, 486
324, 180, 165
1227, 347, 312, 194, 171, 115, 108, 96, 48
1106, 599, 245, 195, 180, 158, 88, 28, 161
1232, 1054, 493, 249, 187, 157, 142, 94, 65
/
(b) S(a) + O2(a)
/
(c) SO(a) + O(a)
(e) SO2(a)
21
Table S8. Reaction Energies and Temperature Corrections at 1073K on Pt@Ni(111) Surface for Eqn (a) ~ (f). (All energies are in electron volt).
△Eel,j
△Hth,j(gas)
△Hth,j(surf)
△Hj
△Sj( ×103)
-T△Sj
△Gj
reaction
(a)
/
(b)
/
(c)
(e)
(f)
-3.43
-0.02
-0.34
-0.25
-0.45
-
0.28
0.58
<0.01
-3.40
0.11
-0.34
-1.45
-1.26
-0.03
1.55
1.35
0.03
-1.85
1.46
-0.31
-2.50
0.10
0.69
0.02
-0.87
-2.48
-0.08
-0.20
1.56
0.22
-1.67
-2.26
-1.75
Column 1 lists the reaction equations described in Table S1; column 2 gives reaction electronic energy at 0 K; column 3 gives the T correction
to enthalpy of reaction for gas species only (includes ∆Ezpe,j); column 4 gives the T correction to reaction enthalpy for surface species only
(includes ∆Ezpe,j); column 5 gives reaction enthalpy calculated by adding columns 2, 3, and 4 (include all zero point and thermal corrections);
column 6 gives the entropy of reaction; column 7 represents the value of entropy of reaction multiplied by temperature; column 8 gives the
calculated Gibbs free energy by adding column 5 and column 7.
22
Table S9. Reaction Energies and Temperature Corrections at 298K on Ni(111) Surface for Eqn (a) ~ (f). (All energies are in electron volt).
△Eel,j
△Hth,j(gas)
△Hth,j(surf)
△Hj
△Sj( ×103)
-T△Sj
△Gj
reaction
(a)
(b)
/
(b)
(c)
(c)/
(d)
(e)
(f)
-5.12
0.14
-0.02
-0.07
-0.20
-0.20
0.09
0.20
0.22
-5.10
0.14
<0.01
-1.50
-1.78
-1.46
0.45
0.53
0.44
-4.65
0.67
0.44
-1.14
-1.79
-1.15
0.03
1.05
0.29
0.01
0.01
0.01
<0.01
-0.30
-1.13
-1.78
-1.14
0.03
1.04
-0.13
-0.21
0.06
0.16
1.89
0.04
0.06
-0.02
-0.05
-0.56
-1.09
-1.72
-1.16
-0.02
0.48
Column 1 lists the reaction equations described in Table S1; column 2 gives reaction electronic energy at 0 K; column 3 gives the T correction
to enthalpy of reaction for gas species only (includes ∆Ezpe,j); column 4 gives the T correction to reaction enthalpy for surface species only
(includes ∆Ezpe,j); column 5 gives reaction enthalpy calculated by adding columns 2, 3, and 4 (include all zero point and thermal corrections);
column 6 gives the entropy of reaction; column 7 represents the value of entropy of reaction multiplied by temperature; column 8 gives the
calculated Gibbs free energy by adding column 5 and column 7.
23
Table S10. Reaction Energies and Temperature Corrections at 298K on Pt(111) Surface for Eqn (a) ~ (f). (All energies are in electron volt).
△Eel,j
△Hth,j(gas)
△Hth,j(surf)
△Hj
△Sj( ×103)
-T△Sj
△Gj
reaction
(a)
/
(b)
/
(c)
(e)
(f)
-4.84
-0.14
-0.65
-0.07
-0.20
-
0.09
0.22
0.01
-4.82
-0.12
-0.64
-1.53
-1.46
-0.15
0.46
0.43
0.05
-4.36
0.31
-0.59
-1.43
0.87
0.29
0.02
-0.34
-1.41
0.82
-0.09
1.93
0.03
-0.57
-1.38
0.25
Column 1 lists the reaction equations described in Table S1; column 2 gives reaction electronic energy at 0 K; column 3 gives the T correction
to enthalpy of reaction for gas species only (includes ∆Ezpe,j); column 4 gives the T correction to reaction enthalpy for surface species only
(includes ∆Ezpe,j); column 5 gives reaction enthalpy calculated by adding columns 2, 3, and 4 (include all zero point and thermal corrections);
column 6 gives the entropy of reaction; column 7 represents the value of entropy of reaction multiplied by temperature; column 8 gives the
calculated Gibbs free energy by adding column 5 and column 7.
24
Table S11. Reaction Energies and Temperature Corrections at 298K on Ni@Pt(111) Surface for Eqn (a) ~ (f). (All energies are in electron volt).
△Eel,j
△Hth,j(gas)
△Hth,j(surf)
△Hj
△Sj( ×103)
-T△Sj
△Gj
reaction
(a)
(b)
/
(b)
(c)
(c)/
(d)
(e)
(f)
-5.87
-1.29
-0.49
-0.07
-0.20
-0.20
0.09
0.21
0.22
-5.85
-1.28
-0.47
-1.52
-1.86
-1.51
0.45
0.55
0.45
-5.40
-0.73
-0.02
-2.20
-2.55
0.30
0.93
1.94
0.29
0.01
0.02
<0.01
<0.01
-0.30
-2.19
-2.53
0.30
0.93
1.93
-0.08
-0.26
0.11
0.09
1.97
0.03
0.08
-0.03
-0.03
-0.59
-2.16
-2.45
0.27
0.90
1.34
Column 1 lists the reaction equations described in Table S1; column 2 gives reaction electronic energy at 0 K; column 3 gives the T correction
to enthalpy of reaction for gas species only (includes ∆Ezpe,j); column 4 gives the T correction to reaction enthalpy for surface species only
(includes ∆Ezpe,j); column 5 gives reaction enthalpy calculated by adding columns 2, 3, and 4 (include all zero point and thermal corrections);
column 6 gives the entropy of reaction; column 7 represents the value of entropy of reaction multiplied by temperature; column 8 gives the
calculated Gibbs free energy by adding column 5 and column 7.
25
Table S12. Reaction Energies and Temperature Corrections at 298K on Pt@Ni(111) Surface for Eqn (a) ~ (f). (All energies are in electron volt).
△Eel,j
△Hth,j(gas)
△Hth,j(surf)
△Hj
△Sj( ×103)
-T△Sj
△Gj
reaction
(a)
/
(b)
/
(c)
(e)
(f)
-3.43
-0.02
-0.34
-0.07
-0.20
-
0.09
0.21
<0.01
-3.41
-0.01
-0.34
-1.47
-1.43
-0.02
0.44
0.43
0.01
-2.97
0.42
-0.33
-2.50
0.10
0.29
0.04
-0.34
-2.46
0.05
-0.15
1.78
0.05
-0.53
-2.41
-0.48
Column 1 lists the reaction equations described in Table S1; column 2 gives reaction electronic energy at 0 K; column 3 gives the T correction
to enthalpy of reaction for gas species only (includes ∆Ezpe,j); column 4 gives the T correction to reaction enthalpy for surface species only
(includes ∆Ezpe,j); column 5 gives reaction enthalpy calculated by adding columns 2, 3, and 4 (include all zero point and thermal corrections);
column 6 gives the entropy of reaction; column 7 represents the value of entropy of reaction multiplied by temperature; column 8 gives the
calculated Gibbs free energy by adding column 5 and column 7.
26
Table S13. Calculated Forward and Backward Reaction Rate Constants and Equilibrium Constants of Sulfur Oxidation Reaction at Different
Temperature on Ni(111) and Pt(111) Surface.
Ni(111)
1073K
-1
kf (s )
[a]
S(a) + O2(a) → S(a) + 2O(a)
S(a) + O2(a) → SO(a) + O(a)[b]
S(a) + 2O(a) → SO(a) + O(a)
SO(a) + O(a) → SO2(a)
kr(s )
11
7.82 × 10
6.44 × 1010
5.22 × 1011
2.95 × 108
Pt(111)
K
6
4.29 × 10
3.47 × 102
1.86 × 106
2.99 × 108
kr(s-1)
kf(s )
5
1.83 × 10
1.85 × 108
2.81 × 105
0.98
8
3.80 × 10
6.95 × 104
1.58 × 107
7.29 × 10-6
[b]
kr(s )
11
1.19 × 10
2.53 × 1011
K
-12
2.54 × 10
5.31 × 10-26
5.32 × 10-13
1.79 × 10-5
1.49 × 1019
1.31 × 1030
2.97 × 1019
0.41
298K
-1
kf (s )
[a]
-1
1073K
-1
S(a) + O2(a) → SO(a) + O(a)
SO(a) + O(a) → SO2(a)
298K
-1
-1
K
7
6.88 × 10
6.89 × 105
4
1.73 × 10
3.67 × 106
Channel (A)
Channel (B)
[b]
27
kr(s-1)
kf(s )
5
1.69 × 10
7.82 × 105
K
-6
1.40 × 10
7.26 × 10-19
1.21 × 1011
1.08 × 1024
Table S14: Calculated Forward and Backward Reaction Rate Constants and Equilibrium Constants of Sulfur Oxidation Reaction at Different
Temperature on Ni@Pt(111) and Pt@Ni(111) Surface.
Ni@Pt(111)
1073K
-1
kf (s )
[a]
S(a) + O2(a) → S(a) + 2O(a)
S(a) + O2(a) → SO(a) + O(a)[b]
S(a) + 2O(a) → SO(a) + O(a)
SO(a) + O(a) → SO2(a)
kr(s )
11
7.01 × 10
3.45 × 1011
5.91 × 107
1.21 × 105
Pt@Ni (111)
[a]
37.74
0.57
1.23 × 109
2.45 × 109
-1
K
kr(s-1)
kf(s )
10
1.86 × 10
6.05 × 1011
4.82 × 10-2
4.97 × 10-5
7
2.62 × 10
5.85 × 106
4.47 × 10-9
5.69 × 10-19
1073K
-1
S(a) + O2(a) → SO(a) + O(a)[b]
SO(a) + O(a) → SO2(a)
298K
-1
K
-30
1.91 × 10
6.97 × 10-37
4.45 × 10-4
2.67 × 10-3
1.37 × 1037
8.40 × 1042
1.01 × 10-5
2.13 × 10-16
298K
-1
kf (s )
kr(s )
K
kf(s )
kr(s-1)
K
8.63 × 1012
2.67 × 1012
1.95 × 1011
7.33
44.33
3.64 × 1011
8.95 × 1011
2.27 × 1010
1.49 × 106
1.99 × 10-32
5.99 × 105
1.13 × 1042
Channel (A)
Channel (B)
[b]
28
-1