return to home page

III.G.1.a.

Comparison of levels of theory for H-C


Click on an entry for a histogram of the values.
The subscript refers to how many bonds of that type have been calculated.
average calculated bond lengths (Å)
Methods with predefined basis sets
semi-empirical AM1 1.1551
1072
PM3 1.1250
3723
PM6 1.1766
4232
composite G2 1.1584
3372
G3 1.1639
3994
G3B3 1.1255
4286
G4 1.1066
4072
CBS-Q 1.1859
2606
molecular mechanics DREIDING 1.0925
27

average calculated bond lengths (Å)
Methods with standard basis sets
STO-3G 3-21G 3-21G* 6-31G 6-31G* 6-31G** 6-31+G** 6-311G* 6-311G** 6-31G(2df,p) 6-311+G(3df,2p) 6-311+G(3df,2pd) TZVP cc-pVDZ cc-pVTZ cc-pVQZ aug-cc-pVDZ aug-cc-pVTZ aug-cc-pVQZ cc-pV(D+d)Z cc-pV(T+d)Z aug-cc-pV(T+d)Z cc-pCVDZ cc-pCVTZ Sadlej_pVTZ
hartree fock HF 1.1098
3964
1.0978
4166
1.0978
4052
1.0970
4053
1.1376
10377
1.0991
4053
1.1216
4120
1.0985
4055
1.1001
4015
1.1058
3987
1.0983
2996
1.0810
56
1.1697
4431
1.1059
4050
1.0982
3845
1.0848
658
1.1013
3745
1.0986
3666
1.0875
442
1.0843
7
1.1146
110
1.0756
4
1.0863
33
1.0781
30
1.0897
139
ROHF 1.1017
113
1.0877
332
1.0881
318
1.0889
271
1.0893
351
1.0902
329
1.0893
336
1.0893
336
1.0921
263
1.0927
127
1.0739
5
  1.0841
82
1.0972
329
1.0880
329
1.0910
137
1.0940
221
1.0873
203
1.0923
116
  1.0685
2
       
density functional LSDA 1.1256
3975
1.1218
4058
1.1250
4055
1.1240
4057
1.1209
4042
1.1232
4048
1.1236
4040
1.1222
4040
1.1217
4030
1.1229
3956
1.0945
35
1.0948
30
1.1673
535
1.1303
4014
1.1199
4009
1.1143
114
1.1236
3723
1.1442
427
1.1136
94
1.1085
5
1.0895
4
1.0925
2
1.1035
7
1.0934
7
 
SVWN 1.0991
35
1.1876
3998
1.0982
35
1.0984
35
1.1902
3972
1.1705
529
1.1867
3988
1.1693
529
1.1686
529
1.1710
518
1.0945
35
1.0948
30
1.0960
31
1.1773
529
1.1682
518
1.0955
18
1.1572
362
1.1615
294
1.0956
18
  1.0925
2
1.0925
2
1.1021
4
1.0922
4
 
BLYP 1.1359
3944
1.1204
4056
1.1251
2900
1.1184
4045
1.1245
3958
1.1172
4056
1.1172
4025
1.1220
2900
1.1161
3977
1.1283
3937
1.0919
35
1.0922
30
1.1654
535
1.1269
3939
1.1201
3995
1.0928
18
1.1142
2687
1.0917
35
1.0928
18
1.1066
5
1.0855
4
1.0891
2
1.1023
7
1.0898
7
 
B1B95 1.1237
3954
1.1142
4043
1.1144
4017
1.1136
4026
1.1136
3944
1.1133
4014
1.1142
4089
1.1122
3978
1.1119
3978
1.1132
3854
1.0830
37
1.0836
30
1.1529
558
1.1198
3980
1.1091
3962
1.1024
134
1.1132
3528
1.1233
670
1.1023
118
1.0958
5
1.0809
6
1.0841
4
1.0934
13
1.0832
13
 
B3LYP 1.1258
4033
1.1261
4150
1.1141
4078
1.1139
4074
1.1171
4175
1.1141
4079
1.1150
4152
1.1085
4052
1.1262
1426
1.1180
3906
1.1138
2567
1.0896
56
1.1772
4448
1.1238
4029
1.1162
3970
1.0958
494
1.1395
1894
1.1272
1450
1.0962
431
1.0962
7
1.1227
110
1.0851
4
1.1003
31
1.0880
31
1.1007
139
B3LYPultrafine 1.0985
44
1.0910
57
1.0887
36
1.0897
36
1.1235
3815
1.0894
38
1.1121
665
1.0882
38
1.0881
36
1.0890
36
1.0855
35
1.0890
49
1.1406
60
1.1932
389
1.1649
1626
1.0864
18
1.1603
287
1.1034
3826
1.0865
18
  1.0827
2
1.0827
2
1.0939
4
1.0825
4
 
B3PW91 1.1392
1409
1.1113
4081
1.1116
4056
1.1100
4051
1.1163
3955
1.1124
4043
1.1159
2908
1.1092
3984
1.1277
1390
1.1213
3916
1.0865
35
1.0868
30
1.1592
534
1.1168
4031
1.1088
3970
1.0876
18
1.1076
2694
1.0865
35
1.0876
18
1.0988
5
1.0808
4
1.0841
2
1.0948
7
1.0849
7
 
mPW1PW91 1.1356
1507
1.1092
4045
1.1239
1773
1.1101
4015
1.1123
4002
1.1082
4019
1.1091
4040
1.1082
4042
1.1082
3996
1.1195
3936
1.0852
35
1.0854
30
1.1581
532
1.1158
3994
1.1221
2226
1.0862
18
1.1156
3021
1.1440
338
1.0863
18
1.0971
5
1.0795
4
1.0828
2
1.0931
7
1.0836
7
 
M06-2X 1.1609
618
1.1590
616
1.1590
616
1.1523
618
1.1747
4061
1.1538
607
1.1530
618
1.1513
618
1.1510
618
1.1530
607
1.0846
35
1.0844
30
1.1571
536
1.1590
618
1.1487
620
1.0851
18
1.1410
409
1.1450
329
1.0850
18
1.0965
5
1.0790
4
1.0828
2
1.0928
7
1.0831
7
 
PBEPBE 1.1464
1422
1.1244
4009
1.1381
1505
1.1355
1486
1.1218
3947
1.1205
3984
1.1206
4007
1.1193
4019
1.1175
3994
1.1373
3873
1.1218
2648
1.1512
56
1.1683
525
1.1247
3854
1.1243
3952
1.1133
131
1.1452
525
1.1458
998
1.1131
115
1.1042
7
1.0923
9
1.0917
2
1.1026
7
1.0925
7
1.1077
139
PBEPBEultrafine 1.1042
35
1.1007
56
1.0977
35
1.0977
35
1.1370
4463
1.0969
37
1.1023
70
1.0961
37
1.0959
35
1.0967
35
1.0940
35
1.0980
49
1.1495
60
1.1991
396
1.1887
396
1.0951
18
1.1682
287
1.1651
272
1.0952
18
  1.0917
2
1.0917
2
1.1012
4
1.0914
4
 
PBE1PBE 1.1756
498
1.1727
506
1.1727
506
1.1661
498
1.1803
4066
1.1667
498
1.1661
498
1.1651
498
1.1649
498
1.1657
498
1.0866
35
1.0870
30
1.1656
488
1.1726
498
1.1631
498
1.0878
18
1.1510
345
1.1566
281
1.0878
18
  1.0844
2
1.0843
2
1.0932
4
1.0841
4
 
HSEh1PBE 1.1635
618
1.1593
626
1.1593
626
1.1539
618
1.1763
4024
1.1539
618
1.1540
618
1.1529
618
1.1528
618
1.1536
618
1.0863
35
1.0866
30
1.1589
536
1.1606
618
1.1505
620
1.0874
18
1.1418
417
1.1469
329
1.0874
18
1.0984
5
1.0806
4
1.0839
2
1.0943
7
1.0848
7
 
TPSSh   1.1334
78
1.1334
78
1.1323
78
1.1788
4313
1.1328
78
1.1786
4288
1.1319
78
        1.1683
41
1.1400
78
1.1753
4306
  1.1538
56
1.1389
65
    1.0847
2
1.0847
2
1.0936
4
1.0841
4
 
Moller Plesset perturbation MP2 1.1425
1410
1.1110
4133
1.1106
3990
1.1134
3975
1.1422
4812
1.1045
4007
1.1314
9038
1.1086
3886
1.1090
3971
1.1201
2541
1.0828
38
1.3189
54
1.1752
4449
1.1189
4016
1.1400
3722
1.0915
175
1.1239
1809
1.1421
575
1.0903
154
1.0969
7
1.1222
107
1.0844
4
1.0972
49
1.0829
49
1.1024
139
MP2=FULL 1.1425
1369
1.1232
2265
1.1245
1810
1.1262
1799
1.1317
4703
1.1115
2791
1.1119
2839
1.1084
3922
1.1293
1325
1.1228
1326
1.0820
35
1.0827
30
1.1542
548
1.1296
2232
1.1462
2595
1.0894
170
1.1355
633
1.1314
412
1.0886
165
1.0959
7
1.1170
110
1.0798
4
1.0964
49
1.0817
49
 
ROMP2 1.1252
152
1.1082
147
1.1082
147
1.1116
147
1.1087
146
1.1042
147
1.1037
147
1.1079
147
1.1088
144
1.1069
147
1.0815
5
  1.0894
65
1.1199
140
1.1048
133
1.1286
28
1.1085
131
1.0829
34
1.1228
31
           
MP3 1.1039
35
1.0893
35
1.0893
35
1.0930
35
1.1100
3826
1.0829
35
1.1737
4309
1.0879
35
1.0879
35
1.0847
35
1.0835
35
1.0835
30
1.1375
60
1.1520
60
1.1362
60
1.0832
18
1.0962
35
1.0833
35
1.0822
8
1.1003
2
1.0803
2
1.0805
2
1.0945
4
1.0800
4
 
MP3=FULL         1.1815
4308
  1.1727
3974
          1.1726
37
1.1865
37
1.1667
37
          1.0754
2
1.0757
2
     
MP4 1.1067
69
1.1453
1004
1.0953
77
1.1063
130
1.1783
1264
1.0860
38
1.0866
38
1.0927
89
1.1357
642
1.0864
50
1.0868
35
1.0868
30
1.2494
207
1.2428
238
1.1561
338
1.0865
18
1.1803
189
1.1152
130
1.0868
18
1.1030
5
1.0801
4
1.0849
2
1.0986
7
1.0843
7
 
MP4=FULL 1.1065
35
1.2195
273
1.0924
35
1.0961
35
1.2212
260
1.0846
35
1.0852
35
1.0913
35
1.2416
223
1.0856
35
1.0852
35
1.0859
30
1.0867
31
1.2287
263
1.1997
186
1.0840
18
1.1763
196
1.1099
140
1.0846
18
  1.0794
2
1.0797
2
1.0964
4
1.0820
4
 
B2PLYP 1.2654
91
1.2510
91
1.2511
91
1.2524
91
1.1812
3606
1.2490
91
1.2492
91
1.2492
91
1.2492
91
1.2298
103
    1.2469
91
1.2581
91
1.1570
3677
  1.2763
81
1.2729
78
    1.0815
2
1.0816
2
     
B2PLYP=FULL 1.2654
91
1.2510
91
1.2511
91
1.2523
91
1.2505
91
1.2486
91
1.2489
91
1.2491
91
1.2490
91
1.2482
91
    1.2466
91
1.2578
91
1.2443
91
  1.2759
81
1.2719
78
    1.0801
2
1.0802
2
     
B2PLYP=FULLultrafine         1.1642
2753
                                       
Configuration interaction CID 1.1019
45
1.1236
1521
1.1266
1401
1.1267
1399
1.1383
2692
1.0928
98
1.0993
60
1.1206
1406
1.0858
80
1.0802
50
1.0800
35
1.0801
30
1.0815
31
1.0947
53
1.0799
44
1.0806
18
1.0924
35
1.0797
35
1.0802
8
  1.0778
2
1.0779
2
1.0917
4
1.0772
4
 
CISD 1.1019
45
1.1237
1537
1.1266
1411
1.1267
1405
1.1482
2679
1.0956
95
1.0826
57
1.1218
1378
1.0860
80
1.0811
49
1.0803
35
1.0804
30
1.0819
31
1.1131
58
1.2768
50
1.0808
18
1.0926
35
1.0800
35
1.0805
8
  1.0780
2
1.0781
2
1.0919
4
1.0774
4
 
Quadratic configuration interaction QCISD 1.1192
246
1.1459
3276
1.1337
1532
1.1339
1554
1.1386
2298
1.1198
1573
1.1190
1530
1.1276
1945
1.1322
1641
1.1371
889
1.0854
35
1.0854
30
1.1654
482
1.1341
1449
1.1403
675
1.0851
18
1.1530
359
1.0904
242
1.0842
8
1.0988
7
1.0823
9
1.0826
2
1.0992
11
1.0846
11
 
QCISD(T) 1.1083
35
1.0954
59
1.0940
41
1.0982
41
1.1573
977
1.0872
60
1.0880
75
1.1018
111
1.0924
100
1.0884
38
1.0869
35
1.0869
30
1.1463
270
1.1407
491
1.1060
351
1.0865
18
1.1172
307
1.1102
225
1.0868
18
  1.0842
2
1.0844
2
1.0990
7
1.0859
11
 
QCISD(T)=FULL         1.0831
2
  1.0777
2
            1.0948
2
1.0731
2
1.0744
2
1.0934
2
1.0741
2
1.0750
2
           
QCISD(TQ) 1.1084
35
1.0933
35
1.0919
29
1.0956
29
1.0918
37
1.0860
35
1.0861
37
1.0907
29
1.0912
35
1.0870
29
1.0861
29
1.0904
16
1.0902
24
1.1008
37
1.0863
20
1.0835
10
1.0992
37
1.0850
10
1.0777
2
           
QCISD(TQ)=FULL         1.0832
2
  1.0779
2
            1.0950
2
1.0732
2
1.0745
2
1.0937
2
1.0742
2
1.0751
2
           
Coupled Cluster CCD 1.1192
240
1.1314
1611
1.1344
1492
1.1334
1546
1.1499
2811
1.1226
1488
1.1214
1394
1.1270
1536
1.1379
928
1.1339
864
1.0848
35
1.0848
30
1.1640
486
1.1393
1426
1.1420
643
1.0852
20
1.1465
424
1.0916
303
1.0853
10
1.0983
7
1.0805
6
1.0840
4
1.1018
35
1.0864
35
 
CCSD 1.1078
35
1.0942
56
1.0927
38
1.0964
38
1.1559
1105
1.0856
57
1.0876
70
1.0915
98
1.0897
78
1.0865
35
1.0852
35
1.0852
30
1.1506
283
1.1404
506
1.0989
396
1.0871
56
1.1173
190
1.1123
130
1.0882
29
  1.0821
2
1.0823
2
1.0962
4
1.0815
4
 
CCSD=FULL 1.1077
35
1.0921
35
1.0921
35
1.0958
35
1.2088
314
1.0839
35
1.0843
35
1.0901
35
1.0894
35
1.0845
35
1.0836
35
1.0854
24
1.2213
267
1.2195
302
1.0974
210
1.0842
50
1.1165
193
1.1136
109
1.0862
27
  1.0771
2
1.0773
2
1.0954
4
1.0803
4
 
CCSD(T) 1.1083
35
1.0956
71
1.0939
41
1.0982
41
1.1427
1092
1.1138
207
1.0931
96
1.0933
107
1.0922
95
1.0884
38
1.0884
40
1.0876
34
1.1480
263
1.1398
542
1.1072
422
1.0966
88
1.1181
398
1.1119
277
1.0947
70
1.1001
7
1.0859
7
1.0862
4
1.1010
52
1.0862
48
 
CCSD(T)=FULL 1.1082
35
1.0934
35
1.0934
35
1.0971
35
1.1714
504
1.0851
35
1.0856
35
1.0921
30
1.0909
35
1.0858
35
1.0852
35
1.0859
30
1.2037
291
1.1634
380
1.1614
286
1.0939
90
1.1142
287
1.1075
172
1.0908
56
1.0992
7
1.0778
6
1.0810
4
1.1002
52
1.0849
52
 

average calculated bond lengths (Å)
Methods with effective core potentials (select basis sets)
CEP-31G CEP-31G* CEP-121G CEP-121G* LANL2DZ SDD
hartree fock HF 1.1066
4073
1.1089
3955
1.1034
4079
1.1051
3970
1.1008
4073
1.1010
4079
ROHF 1.0900
12
1.0823
5
1.0871
12
1.0781
5
1.0839
12
1.0837
12
density functional LSDA 1.1111
35
1.1117
35
1.1060
35
1.1065
35
1.0996
35
1.0995
35
SVWN 1.1111
35
1.1117
35
1.1060
35
1.1065
35
1.0996
35
1.0995
35
BLYP 1.1058
35
1.1061
35
1.0990
35
1.0991
35
1.0992
35
1.0993
35
B1B95 1.1223
3028
1.1226
2985
1.1078
119
1.1098
111
1.1061
119
1.1060
119
B3LYP 1.1224
4061
1.1231
3928
1.1157
4047
1.1174
3905
1.1149
4039
1.1160
4022
B3LYPultrafine 1.0996
47
1.1005
47
1.0937
47
1.0943
47
1.0932
49
1.0928
47
B3PW91 1.0974
35
1.0985
35
1.0922
35
1.0929
35
1.0908
35
1.0908
35
mPW1PW91 1.0954
35
1.0966
35
1.0904
35
1.0912
35
1.0889
35
1.0889
35
M06-2X 1.0955
35
1.0963
35
1.0887
35
1.0897
35
1.0887
35
1.0886
35
PBEPBE 1.1057
35
1.1063
35
1.0998
35
1.1003
35
1.0993
35
1.0993
35
PBEPBEultrafine 1.1057
35
1.1063
35
1.0998
35
1.1003
35
1.0993
35
1.0993
35
PBE1PBE 1.0968
35
1.0980
35
1.0917
35
1.0926
35
1.0903
35
1.0903
35
HSEh1PBE 1.0970
35
1.0982
35
1.0918
35
1.0927
35
1.0902
35
1.0902
35
Moller Plesset perturbation MP2 1.1288
4057
1.1234
3920
1.1207
4027
1.1147
3907
1.1194
4057
1.1193
4048
MP2=FULL 1.1040
35
1.0986
35
1.0959
35
1.0894
35
1.0970
35
1.0969
35
ROMP2 1.1101
12
1.0956
5
1.1030
12
1.0872
5
1.1030
12
1.1033
12
MP3 1.1061
35
1.1003
35
1.0976
35
1.0903
35
1.0983
35
1.0981
35
MP4 1.1090
35
1.1033
35
1.1009
35
1.0936
35
1.1011
35
1.1010
35
MP4=FULL 1.1090
35
1.1033
35
1.1009
35
1.0936
35
1.1010
35
1.1009
35
Configuration interaction CID 1.1035
35
1.0973
35
1.0951
35
1.0878
35
1.0955
35
1.0954
35
CISD 1.1034
35
1.0973
35
1.0952
35
1.0881
35
1.0955
35
1.0954
35
Quadratic configuration interaction QCISD 1.1093
35
1.1028
35
1.1010
35
1.0930
35
1.1012
35
1.1010
35
QCISD(T) 1.1104
35
1.1041
35
1.1022
35
1.0943
35
1.1023
35
1.1022
35
QCISD(TQ) 1.1105
35
1.1041
35
1.1021
35
1.0942
35
1.1023
35
1.1022
35
Coupled Cluster CCD 1.1092
35
1.1026
35
1.1007
35
1.0925
35
1.1010
35
1.1009
35
CCSD 1.1093
35
1.1027
35
1.1009
35
1.0928
35
1.1011
35
1.1010
35
CCSD=FULL 1.1093
35
1.1027
35
1.1009
35
1.0928
35
1.1010
35
1.1008
35
CCSD(T) 1.1104
35
1.1041
35
1.1021
35
1.0942
35
1.1023
35
1.1022
35
CCSD(T)=FULL 1.1104
35
1.1041
35
1.1021
35
1.0942
35
1.1022
35
1.1020
35
For descriptions of the methods (AM1, HF, MP2, ...) and basis sets (3-21G, 3-21G*, 6-31G, ...) see the glossary in section I.C. Predefined means the basis set used is determined by the method.