Supporting information for
Pathways and kinetics of methane and ethane C-H bond cleavage on PdO(101)
Abbin Antony(a), Aravind Asthagiri(b) and Jason F. Weaver(a)*
(a)
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
(b)
William G. Lowrie Department of Chemical & Biomolecular Engineering, The Ohio State University,
Columbus, OH 43210, USA
Table 1 summarizes the DFT-D3 binding energies of methane and ethane states on PdO(101) surface
and the corresponding zero point corrected energies and activation barriers assuming 3N and 3N-2 harmonic
modes. Zero point energies are evaluated employing the vibrational mode frequencies in Equation (i) where the
number of modes for chemisorbed alkane is 3N if all are treated harmonic, 3N-2 if two modes are treated free
and 3N-6 for isolated alkane (gas). Based on the definition of binding energy in the section titled
“Computational Details, (Equation (2))” section, zero point corrected binding energy is evaluated as shown in
Equation (ii).
(i)
(ii)
State
Methane 2
Ethane  (+)
2
Ethane  (-)
2
Ethane 
1
IS
TS
FS
IS
TS
FS
IS
TS
FS
IS
TS
FS
E
(kJ/mol)
40.5
-24.1
82.8
55.2
-22.4
99.0
190.6
179.4
194.9
190.1
179.1
194.9
Er
(kJ/mol)
64.6
77.6
67.6
63.0
3N Harmonic modes
3N-2 Harmonic modes
E (ZPC)
(kJ/mol)
39.1
-16.1
75.1
55.3
-12.6
94.7
56.4
-0.1
95.8
53.5
1.5
95.5
55.2
E (ZPC)
(kJ/mol)
40.2
-14.9
77.6
56.1
-11.8
67.8
67.6
57.1
0.6
56.5
63.0
54.0
2.1
51.9
Er (ZPC)
(kJ/mol)
Er (ZPC)
(kJ/mol)
55.1
Table 1: Binding energies, zero point corrected binding energies evaluated by treating 3N and 3N-2 modes
harmonics and corresponding activation barriers.
Tables 2 and 3 lists the normal mode vibrational frequencies computed for isolated methane and
methane 2 complex on PdO(101) using DFT and DFT-D3. Table 4 and 5 lists the vibrational frequencies for
isolated ethane and the three ethane σ-complexes on PdO(101) determined using DFT-D3. The tag ‘i’ stands for
an imaginary mode and the highlighted modes corresponds to motions that reflects the change in geometry
going from reactants to products. Note that the non-highlighted imaginary modes are observed due to the
relatively flat potential energy surface about the cus-Pd atom. This feature of the potential energy surface results
in configurations relaxing onto another saddle point when performing imaginary mode calculations (imc) where
the configuration is pushed along the imaginary mode. Binding energies, geometries and vibrational modes of
the newly relaxed configurations are very similar to the configurations prior imc. Vibrational modes identified
as free motions for micro kinetic analysis have been tagged as ‘(fm)’
Isolated CH4
Mode No.
νj (cm-1)
DFT
DFT-D3
3102
3097
1
3101
3096
2
3095
3095
3
2982
2981
4
1512
1512
5
1503
1502
6
1285
1285
7
1284
1285
8
1274
1274
9
Table 2: Vibrational mode frequencies of isolated methane molecule predicted by DFT and DFT-D3.
CH4 2(+)
νj (cm-1)
DFT
DFT-D3
IS
TS
FS
IS
TS
FS
3134
3109 3595
3137
3103 3591
1
3057
3044 3077
3054
3037 3058
2
2888
2954 3038
2853
2951 3041
3
2816
1604 2948
2778
1609 2945
4
1490
1376 1392
1493
1374 1391
5
1466
1354 1389
1459
1352 1380
6
1294
1147 1143
1297
1150 1144
7
825
1276
1089
829
1277
1089
8
740
1168
698
738
1157
701
9
714
10
220
544
718
242
543
694
158
478
698
197
482
11
499
157
209
494
179
210
12
185
87
107
176
(fm)148 (fm) 108
13
116
52
92i
111
52 (fm) 87i
14
95
15
31 1244i
41i
(fm) 38
1245i
Table 3: Vibrational mode frequencies of the initial, transition and final states of methane 2 complex
predicted by DFT and DFT-D3.
Mode No.
Mode No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
3055
3054
3029
3028
2976
2974
1456
1455
1446
1446
1368
1353
1173
1172
996
798
796
285
Ethane
2(-)
Ethane
2(+)
Isolated
C2H6
IS
TS
FS
3072
3059
3038
2990
2798
2672
1469
1455
1434
1410
1358
1283
1171
1126
1003
828
782
305
214
140
(fm) 98
57
(fm) 27
57i
3070
3047
3046
2989
2978
1635
1440
1436
1377
1349
1206
1142
1097
952
942
872
541
436
230
195
107
(fm) 67
(fm) 72i
1324i
3600
3027
3002
2981
2947
2932
1431
1426
1406
1343
1186
1125
1009
918
881
816
691
680
481
247
222
144
64
24
IS
TS
3059
3032
3058
3010
3041
3001
2984
2951
2775
2931
2700
1615
1466
1438
1447
1433
1435
1355
1407
1336
1365
1199
1279
1161
1178
1058
1122
987
1003
892
836
877
776
584
286
442
214
227
134
204
(fm) 89
147
75 (fm) 68
(fm) 31 (fm) 37i
95i
1290i
FS
3591
3017
2997
2988
2937
2934
1428
1425
1407
1337
1186
1133
1012
917
883
817
690
685
479
241
222
139
70
41
Table 4: Vibrational mode frequencies of isolated ethane molecule and ethane 2(+) and 2(-) complexes on
PdO(101) predicted by DFT-D3.
Ethane
1
Mode No.
IS
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
3086
3061
3016
3003
2782
2656
1442
1423
1403
1387
1335
1304
1158
1101
997
795
750
410
266
118
104
97
(fm) 47
(fm) 35i
TS
3050
3013
2997
2947
2901
1620
1430
1425
1351
1341
1196
1156
1057
988
887
869
589
445
224
207
144
(fm) 72
(fm) 25
1280i
FS
3600
3027
3002
2981
2947
2932
1431
1426
1406
1343
1186
1125
1009
918
881
816
691
680
481
247
222
144
64
24
Table 5: Vibrational mode frequencies of ethane 1 complexe on PdO(101) predicted by DFT-D3.